{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Multivariate Kalman Filters\n",
"\n",
"Filtering Multiple Random Variables"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from __future__ import division, print_function\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#format the book\n",
"import book_format\n",
"book_format.set_style()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now ready to study and implement the full, multivariate form of the Kalman filter. In the last chapter we learned how multivariate Gaussians express the correlation between multiple random variables, such as the position and velocity of an aircraft. We also learned how correlation between variables drastically improves the posterior. If we only roughly know position and velocity, but they are correlated, then our new estimate can be very accurate.\n",
"\n",
"I prefer that you develop an intuition for how these filters work through several worked examples. I'm going to gloss over many issues. Some things I show you will only work for special cases, others will be 'magical' - it will not be clear how I derived a certain result. If I started with rigorous, generalized equations you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. \n",
"\n",
"To make this possible we will restrict ourselves to a subset of problems which we can describe with Newton's equations of motion. These filters are called *discretized continuous-time kinematic filters*. In the **Kalman Filter Math** chapter we will develop the math for non-Newtonian systems. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Newton's Equations of Motion\n",
"\n",
"Newton's equations of motion tells us that given a constant velocity $v$ of a system we can compute its position $x$ after time $t$ with:\n",
"\n",
"$$x = vt + x_0$$\n",
"\n",
"For example, if we start at position 13, our velocity is 10 m/s, and we travel for 12 seconds our final position is 133 ($10\\times 12 + 13$).\n",
"\n",
"We can incorporate constant acceleration with this equation\n",
"\n",
"$$x = \\frac{1}{2}at^2 + v_0t + x_0$$\n",
"\n",
"And if we assume constant jerk we get\n",
"\n",
"$$x = \\frac{1}{6}jt^3 + \\frac{1}{2}a_0 t^2 + v_0 t + x_0$$\n",
"\n",
"These equations were generated by integrating a differential equation. Given a constant velocity v we can compute the distance traveled over time with the equation\n",
"\n",
"$$x = vt + x_0$$\n",
"\n",
"which we can derive with\n",
"\n",
"$$\\begin{aligned} v &= \\frac{dx}{dt}\\\\\n",
"dx &= v\\, dt \\\\\n",
"\\int_{x_0}^x\\, dx &= \\int_0^t v\\, dt\\\\\n",
"x - x_0 &= vt - 0\\\\\n",
"x &= vt + x_0\\end{aligned}$$\n",
"\n",
"\n",
"When you design a Kalman filter you start with a system of differential equations that describe the dynamics of the system. Most systems of differential equations do not easily integrate in this way. We start with Newton's equation because we can integrate and get a closed form solution, which makes the Kalman filter easier to design. An added benefit is that Newton's equations are the right equations to use to track moving objects, one of the main uses of Kalman filters."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Kalman Filter Algorithm\n",
"\n",
"The algorithm is the same Bayesian filter algorithm that we have used in every chapter. The update step is slightly more complicated, but I will explain why when we get to it.\n",
"\n",
"**Initialization**\n",
"\n",
" 1. Initialize the state of the filter\n",
" 2. Initialize our belief in the state\n",
" \n",
"**Predict**\n",
"\n",
" 1. Use process model to predict state at the next time step\n",
" 2. Adjust belief to account for the uncertainty in prediction \n",
"**Update**\n",
"\n",
" 1. Get a measurement and associated belief about its accuracy\n",
" 2. Compute residual between estimated state and measurement\n",
" 3. Compute scaling factor based on whether the measurement\n",
" or prediction is more accurate\n",
" 4. set state between the prediction and measurement based \n",
" on scaling factor\n",
" 5. update belief in the state based on how certain we are \n",
" in the measurement\n",
" \n",
"As a reminder, here is a graphical depiction of the algorithm:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import kf_book.book_plots as book_plots\n",
"book_plots.show_residual_chart()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The univariate Kalman filter represented the state with a univariate Gaussian. Naturally the multivariate Kalman filter will use a multivariate Gaussian for the state. We learned in the last chapter that multivariate Gaussians use a vector for the mean and a matrix for the covariances. That means that the Kalman filter needs to use linear algebra to perform the estimations.\n",
"\n",
"I don't want you to memorize these equations, but I have listed the univariate and multivariate equations below. They are quite similar.\n",
"\n",
"**Predict**\n",
"\n",
"$\\begin{array}{|l|l|l|}\n",
"\\hline\n",
"\\text{Univariate} & \\text{Univariate} & \\text{Multivariate}\\\\\n",
"& \\text{(Kalman form)} & \\\\\n",
"\\hline\n",
"\\bar \\mu = \\mu + \\mu_{f_x} & \\bar x = x + dx & \\bar{\\mathbf x} = \\mathbf{Fx} + \\mathbf{Bu}\\\\\n",
"\\bar\\sigma^2 = \\sigma_x^2 + \\sigma_{f_x}^2 & \\bar P = P + Q & \\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q \\\\\n",
"\\hline\n",
"\\end{array}$\n",
"\n",
"Without worrying about the specifics of the linear algebra, we can see that:\n",
"\n",
"$\\mathbf x,\\, \\mathbf P$ are the state mean and covariance. They correspond to $x$ and $\\sigma^2$.\n",
"\n",
"$\\mathbf F$ is the *state transition function*. When multiplied by $\\bf x$ it computes the prior. \n",
"\n",
"$\\mathbf Q$ is the process covariance. It corresponds to $\\sigma^2_{f_x}$.\n",
"\n",
"$\\mathbf B$ and $\\mathbf u$ are new to us. They let us model control inputs to the system.\n",
"\n",
"**Update**\n",
"\n",
"$\\begin{array}{|l|l|l|}\n",
"\\hline\n",
"\\text{Univariate} & \\text{Univariate} & \\text{Multivariate}\\\\\n",
"& \\text{(Kalman form)} & \\\\\n",
"\\hline\n",
"& y = z - \\bar x & \\mathbf y = \\mathbf z - \\mathbf{H\\bar x} \\\\\n",
"& K = \\frac{\\bar P}{\\bar P+R}&\n",
"\\mathbf K = \\mathbf{\\bar{P}H}^\\mathsf T (\\mathbf{H\\bar{P}H}^\\mathsf T + \\mathbf R)^{-1} \\\\\n",
"\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2} & x = \\bar x + Ky & \\mathbf x = \\bar{\\mathbf x} + \\mathbf{Ky} \\\\\n",
"\\sigma^2 = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} & P = (1-K)\\bar P &\n",
"\\mathbf P = (\\mathbf I - \\mathbf{KH})\\mathbf{\\bar{P}} \\\\\n",
"\\hline\n",
"\\end{array}$\n",
"\n",
"$\\mathbf H$ is the measurement function. We haven't seen this yet in this book and I'll explain it later. If you mentally remove $\\mathbf H$ from the equations, you should be able to see these equations are similar as well.\n",
"\n",
"$\\mathbf z,\\, \\mathbf R$ are the measurement mean and noise covariance. They correspond to $z$ and $\\sigma_z^2$ in the univariate filter (I've substituted $\\mu$ with $x$ for the univariate equations to make the notation as similar as possible).\n",
"\n",
"$\\mathbf y$ and $\\mathbf K$ are the residual and Kalman gain. \n",
"\n",
"The details will be different than the univariate filter because these are vectors and matrices, but the concepts are exactly the same: \n",
"\n",
"- Use a Gaussian to represent our estimate of the state and error\n",
"- Use a Gaussian to represent the measurement and its error\n",
"- Use a Gaussian to represent the process model\n",
"- Use the process model to predict the next state (the prior)\n",
"- Form an estimate part way between the measurement and the prior\n",
"\n",
"Your job as a designer will be to design the state $\\left(\\mathbf x, \\mathbf P\\right)$, the process $\\left(\\mathbf F, \\mathbf Q\\right)$, the measurement $\\left(\\mathbf z, \\mathbf R\\right)$, and the measurement function $\\mathbf H$. If the system has control inputs, such as a robot, you will also design $\\mathbf B$ and $\\mathbf u$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have programmed the equations of the Kalman filter into the `predict` and `update` functions in FilterPy. You will import them with:\n",
"\n",
"```python\n",
"from filterpy.kalman import predict, update\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tracking a Dog\n",
"\n",
"Let's go back to our tried and true problem of tracking a dog. This time we will include the fundamental insight of the previous chapter and use *hidden variables* to improve our estimates. I could start with the math, but instead let's implement a filter, learning as we go. On the surface the math is different and perhaps more complicated than the previous chapters, but the ideas are all the same - we are just multiplying and adding Gaussians.\n",
"\n",
"We start by writing a simulation for the dog. The simulation will run for `count` steps, moving the dog forward approximately 1 meter for each step. At each step the velocity will vary according to the process variance `process_var`. After updating the position we compute a measurement with an assumed sensor variance of `z_var`. The function returns an NumPy array of the positions and another of the measurements."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"import numpy as np\n",
"from numpy.random import randn\n",
"\n",
"def compute_dog_data(z_var, process_var, count=1, dt=1.):\n",
" \"returns track, measurements 1D ndarrays\"\n",
" x, vel = 0., 1.\n",
" z_std = math.sqrt(z_var) \n",
" p_std = math.sqrt(process_var)\n",
" xs, zs = [], []\n",
" for _ in range(count):\n",
" v = vel + (randn() * p_std)\n",
" x += v*dt \n",
" xs.append(x)\n",
" zs.append(x + randn() * z_std) \n",
" return np.array(xs), np.array(zs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Predict Step\n",
"\n",
"For the prediction we need to design the state and covariance, the process model and the process noise, and optionally the control input. We'll take them in order."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Design State Variable\n",
"\n",
"We previously tracked a dog in one dimension by using a Gaussian. The mean $(\\mu)$ represented the most likely position, and the variance ($\\sigma^2$) represented the probability distribution of the position. The position is the *state* of the system, and we call $\\mu$ the *state variable*. \n",
"\n",
"In this problem we will be tracking both the position and velocity of the dog. This requires us to use a multivariate Gaussian represented with the state vector $\\mathbf x$ and its corresponding covariance matrix $\\mathbf P$. \n",
"\n",
"State variables can either be *observed variables* - directly measured by a sensor, or *hidden variables* - inferred from the observed variables. For our dog tracking problem the sensor only reads position, so position is observed and velocity is hidden. We will learn how to track hidden variables soon.\n",
"\n",
"It is important to understand that tracking position and velocity is a design choice with implications and assumptions that we are not yet prepared to explore. For example, we could also track acceleration, or even jerk. For now, recall that in the last chapter we showed that including velocity in the covariance matrix resulted in much smaller variances in position. We will learn how the Kalman filter computes estimates for hidden variables later in this chapter. \n",
"\n",
"In the univariate chapter we represented the dog's position with a scalar value (e.g. $\\mu=3.27$). In the last chapter we learned to use a multivariate Gaussian for multiple variables. For example, if we wanted to specify a position of 10.0 m and a velocity of 4.5 m/s, we would write:\n",
"\n",
"$$\\mu = \\begin{bmatrix}10.0\\\\4.5\\end{bmatrix}$$\n",
"\n",
"The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix (called a *vector*) to store $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot x$, for velocity. I use Newton's dot notation for derivatives; $\\dot x$ represents the first derivative of x with respect to t: $\\dot x = \\frac{dx}{dt}$. Kalman filter equations use $\\mathbf x$ for the state, so we define $\\mathbf x$ as:\n",
"\n",
"$$\\mathbf x =\\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}$$\n",
"\n",
"We use $\\mathbf x$ instead of $\\mu$, but recognize this is the mean of the multivariate Gaussian.\n",
"\n",
"Another way to write this is $\\mathbf x =\\begin{bmatrix}x & \\dot x\\end{bmatrix}^\\mathsf T$ because the transpose of a row vector is a column vector. This notation is easier to use in text because it takes less vertical space.\n",
"\n",
"$\\mathbf x$ and the position $x$ coincidentally have the same name. If we were tracking the dog in the y-axis we would write $\\mathbf x =\\begin{bmatrix}y & \\dot y\\end{bmatrix}^\\mathsf T$, not $\\mathbf y =\\begin{bmatrix}y & \\dot y\\end{bmatrix}^\\mathsf T$. $\\mathbf x$ is the standard name for the state variable used in the Kalman filter literature and we will not vary it to give it a more meaningful name. This consistency in naming allows us to communicate with our peers.\n",
"\n",
"Let's code this. Initialization of `x` is as simple as"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[10. ],\n",
" [ 4.5]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.array([[10.0],\n",
" [4.5]])\n",
"x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I often use the transpose in my code to turn a row matrix into a column vector, as I find it easier to type and read:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[10. ],\n",
" [ 4.5]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.array([[10., 4.5]]).T\n",
"x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, NumPy recognizes 1D arrays as vectors, so I can simplify this line to use a 1D array."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([10. , 4.5])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.array([10.0, 4.5])\n",
"x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All of the array elements have the same type, typically either `float` or `int`. If the list contains all `int`s then the created array will also have a data type of `int`, otherwise it will be `float`. I will often take advantage of this by only specifying one number as a floating point:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1., 0., 0., 0., 0., 0.])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([1., 0, 0, 0, 0, 0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are some examples."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[19.]\n",
" [48.]]\n",
"\n"
]
}
],
"source": [
"A = np.array([[1, 2], [3, 4]])\n",
"x = np.array([[10.0], [4.5]])\n",
"\n",
"# matrix multiply\n",
"print(np.dot(A, x))\n",
"print()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In Python 3.5+ we have the matrix multiplier @, where `np.dot(A, B) == A @ B`. It is somewhat less useful then you might realize because it requires both `A` and `B` to be arrays. It is entirely valid in the math in this book for some of these variables to be scalars, therefore the utility of `@` is often lost. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": true,
"tags": [
"raises-exception"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[19.]\n",
" [48.]]\n",
"\n",
"[[19.]\n",
" [48.]]\n",
"\n",
"[19. 48.]\n"
]
}
],
"source": [
"# alternative matrix multiply)\n",
"print(A @ x)\n",
"print()\n",
"\n",
"x = np.array([[10.0, 4.5]]).T\n",
"print(A @ x)\n",
"print()\n",
"\n",
"x = np.array([10.0, 4.5])\n",
"print(A @ x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The last returns a 1D array, but I have written the Kalman filter class to be able to handle this. In retrospect that might lead to confusion, but it does work. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Design State Covariance\n",
"\n",
"The other half of the state Gaussian is the covariance matrix $\\mathbf P$. In the univariate Kalman filter we specified an initial value for $\\sigma^2$, and then the filter took care of updating its value as measurements were added to the filter. The same thing happens in the multidimensional Kalman filter. We specify an initial value for $\\mathbf P$ and the filter updates it during each epoch.\n",
"\n",
"We need to set the variances to reasonable values. For example, we may choose $\\sigma_\\mathtt{pos}^2=500 m^2$ if we are quite uncertain about the initial position. Top speed for a dog is around 21 m/s, so in the absence of any other information about the velocity we can set $3\\sigma_\\mathtt{vel}=21$, or $\\sigma_\\mathtt{vel}^2=7^2=49$. \n",
"\n",
"In the last chapter we showed that the position and velocities are correlated. But how correlated are they for a dog? I have no idea. As we will see the filter computes this for us, so I initialize the covariances to zero. Of course, if you know the covariances you should use them.\n",
"\n",
"Recall that the diagonals of the covariance matrix contains the variance of each variable, and the off-diagonal elements contains the covariances. Thus we have:\n",
"\n",
"$$\n",
"\\mathbf P = \\begin{bmatrix}500 & 0 \\\\ 0&49\\end{bmatrix}\n",
"$$\n",
"\n",
"We can use `numpy.diag`, which creates a diagonal matrix from the values for the diagonal. Recall from linear algebra that a diagonal matrix is one with zeros in the off-diagonal elements."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[500., 0.],\n",
" [ 0., 49.]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P = np.diag([500., 49.])\n",
"P"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I could have written:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[500., 0.],\n",
" [ 0., 49.]])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P = np.array([[500., 0.],\n",
" [0., 49.]])\n",
"P"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are done. We've expressed the state of the filter as a multivariate Gaussian and implemented it in code."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Design the Process Model\n",
"\n",
"The next step is designing the *process model*. It is a mathematical model which describes the behavior of the system. The filter uses it to predict the state after a discrete time step. We do this with a set of equations that describe the dynamics of the system.\n",
"\n",
"In the univariate chapter we modeled the dog's motion with\n",
"\n",
"$$ x = v \\Delta t + x_0$$\n",
"\n",
"We implemented this as follows:\n",
"\n",
"```python\n",
"def predict(pos, movement):\n",
" return gaussian(pos.mean + movement.mean, \n",
" pos.var + movement.var)\n",
"```\n",
"\n",
"We will do the same thing in this chapter, using multivariate Gaussians instead of univariate Gaussians. You might imagine this sort of implementation:\n",
"\n",
"$$ \\mathbf x = \\begin{bmatrix}5.4\\\\4.2\\end{bmatrix}, \\, \\, \n",
"\\dot{\\mathbf x} = \\begin{bmatrix}1.1\\\\0.\\end{bmatrix} \\\\\n",
"\\mathbf x = \\dot{\\mathbf x}t + \\mathbf x$$\n",
"\n",
"But we need to generalize this. The Kalman filter equations work with any linear system, not just Newtonian ones. Maybe the system you are filtering is the plumbing system in a chemical plant, and the flow in a given pipe is determined by a linear combination of the settings of different valves. \n",
"\n",
"$$\\mathtt{pipe_1} = 0.134(\\mathtt{valve}_1) + 0.41(\\mathtt{valve}_2 - \\mathtt{valve}_3) + 1.34$$\n",
"$$\\mathtt{pipe_2} = 0.210(\\mathtt{valve}_2) - 0.62(\\mathtt{valve}_1 - \\mathtt{valve}_5) + 1.86$$\n",
"\n",
"Linear algebra has a powerful way to express systems of equations. Take this system\n",
"\n",
"$$\\begin{cases}\n",
"2x+3y=8\\\\4x-y=2\n",
"\\end{cases}$$\n",
"\n",
"We can put this in matrix form by writing:\n",
"\n",
"$$\\begin{bmatrix}2& 3 \\\\ 4&-1\\end{bmatrix} \\begin{bmatrix}x\\\\y\\end{bmatrix} = \\begin{bmatrix}8\\\\2\\end{bmatrix}$$\n",
"\n",
"If you perform the [matrix multiplication](https://en.wikipedia.org/wiki/Matrix_multiplication#General_definition_of_the_matrix_product) in this equation the result will be the two equations above. In linear algebra we would write this as $\\mathbf{Ax}=\\mathbf B$, where\n",
"\n",
"$$\\mathbf{A} = \\begin{bmatrix}2& 3 \\\\ 4&-1\\end{bmatrix},\\, \\mathbf x = \\begin{bmatrix}x\\\\y\\end{bmatrix}, \\mathbf B=\\begin{bmatrix}8\\\\2\\end{bmatrix}$$\n",
"\n",
"And then we can use the SciPy's `linalg` package to solve for $\\mathbf x$:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.],\n",
" [2.]])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.linalg import solve\n",
"A = np.array([[2, 3],[4, -1]])\n",
"b = np.array([[8], [2]])\n",
"x = solve(A, b)\n",
"x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use the process model to perform the *innovation*, because the equations tell us what the next state will be given the current state. Kalman filters implement this using this linear equation, where $\\mathbf{\\bar x}$ is the *prior*, or predicted state:\n",
"\n",
"$$\\mathbf{\\bar x} = \\mathbf{Fx}$$\n",
"\n",
"which we can make explicit as\n",
"\n",
"$$\\begin{bmatrix} \\bar x \\\\ \\dot{\\bar x}\\end{bmatrix} = \\begin{bmatrix}? & ? \\\\? & ?\\end{bmatrix}\\begin{bmatrix}x\\\\\\dot x\\end{bmatrix}$$\n",
"\n",
"Our job as Kalman filters designers is to specify $\\mathbf F$ such that $\\bar{\\mathbf x} = \\mathbf{Fx}$ performs the innovation (prediction) for our system. To do this we need one equation for each state variable. In our problem $\\mathbf x = \\begin{bmatrix}x & \\dot x\\end{bmatrix}^\\mathtt{T}$, so we need one equation to compute the position $x$ and another to compute the velocity $\\dot x$ . We already know the equation for the position innovation:\n",
"\n",
"$$\\bar x = x + \\dot x \\Delta t$$\n",
"\n",
"What is our equation for velocity? We have no predictive model for how our dog's velocity will change over time. In this case we assume that it remains constant between innovations. Of course this is not exactly true, but so long as the velocity doesn't change too much over each innovation you will see that the filter performs very well. So we say\n",
"\n",
"$$\\bar{\\dot x} = \\dot x$$\n",
"\n",
"This gives us the process model for our system \n",
"\n",
"$$\\begin{cases}\n",
"\\begin{aligned}\n",
"\\bar x &= x + \\dot x \\Delta t \\\\\n",
"\\bar{\\dot x} &= \\dot x\n",
"\\end{aligned}\n",
"\\end{cases}$$\n",
"\n",
"This correctly has one equation for each variable in the state, isolated on the left hand side. We need to express this set of equations in the form $\\bar{\\mathbf x} = \\mathbf{Fx}$. Rearranging terms makes it easier to see what to do.\n",
"\n",
"$$\\begin{cases}\n",
"\\begin{aligned}\n",
"\\bar x &= 1x + &\\Delta t\\, \\dot x \\\\\n",
"\\bar{\\dot x} &=0x + &1\\, \\dot x\n",
"\\end{aligned}\n",
"\\end{cases}$$\n",
"\n",
"We can rewrite this in matrix form as\n",
"\n",
"$$\\begin{aligned}\n",
"\\begin{bmatrix}\\bar x \\\\ \\bar{\\dot x}\\end{bmatrix} &= \\begin{bmatrix}1&\\Delta t \\\\ 0&1\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}\\\\\n",
"\\mathbf{\\bar x} &= \\mathbf{Fx}\n",
"\\end{aligned}$$\n",
"\n",
"$\\mathbf F$ is called the *state transition function* or the *state transition matrix*. In later chapters it will be a true function, not a matrix, so calling it a function is a bit more general."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1. , 0.1],\n",
" [0. , 1. ]])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dt = 0.1\n",
"F = np.array([[1, dt],\n",
" [0, 1]])\n",
"F"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test this! FilterPy has a `predict` method that performs the prediction by computing $\\mathbf{\\bar x} = \\mathbf{Fx}$. Let's call it and see what happens. We've set the position to 10.0 and the velocity to 4.5 meter/sec. We've defined `dt = 0.1`, which means the time step is 0.1 seconds, so we expect the new position to be 10.45 meters after the innovation. The velocity should be unchanged."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [10.45 4.5 ]\n"
]
}
],
"source": [
"from filterpy.kalman import predict\n",
"\n",
"x = np.array([10.0, 4.5])\n",
"P = np.diag([500, 49])\n",
"F = np.array([[1, dt], [0, 1]])\n",
"\n",
"# Q is the process noise\n",
"x, P = predict(x=x, P=P, F=F, Q=0)\n",
"print('x =', x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This worked. If we call `predict()` several times in a row the value will be updated each time. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [10.9 4.5]\n",
"x = [11.35 4.5 ]\n",
"x = [11.8 4.5]\n",
"x = [12.25 4.5 ]\n"
]
}
],
"source": [
"for _ in range(4):\n",
" x, P = predict(x=x, P=P, F=F, Q=0)\n",
" print('x =', x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`predict()` computes both the mean and covariance of the innovation. This is the value of $\\mathbf P$ after five innovations (predictions), which we denote $\\mathbf{\\bar P}$ in the Kalman filter equations."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[512.25 24.5 ]\n",
" [ 24.5 49. ]]\n"
]
}
],
"source": [
"print(P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Inspecting the diagonals shows us that the position variance got larger. We've performed five prediction steps with no measurements, and our uncertainty grew. The off-diagonal elements became non-zero - the Kalman filter detected a correlation between position and velocity! The variance of the velocity did not change.\n",
"\n",
"Here I plot the covariance before and after the prediction. The initial value is in solid red, and the prior (prediction) is in dashed black. I've altered the covariance and time step to better illustrate the change."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from filterpy.stats import plot_covariance_ellipse\n",
"\n",
"dt = 0.3\n",
"F = np.array([[1, dt], [0, 1]])\n",
"x = np.array([10.0, 4.5])\n",
"P = np.diag([500, 500])\n",
"plot_covariance_ellipse(x, P, edgecolor='r')\n",
"x, P = predict(x, P, F, Q=0)\n",
"plot_covariance_ellipse(x, P, edgecolor='k', ls='dashed')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see that the center of the ellipse shifted by a small amount (from 10 to 11.35) because the position changed. The ellipse also elongated, showing the correlation between position and velocity. How does the filter compute new values for $\\mathbf{\\bar P}$, and what is it based on? Note that I set the process noise `Q` to zero each time, so it is not due to me adding noise. It's a little to early to discuss this, but recall that in every filter so far the predict step entailed a loss of information. The same is true here. I will give you the details once we have covered a bit more ground."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Design Process Noise\n",
"\n",
"A quick review on *process noise*. A car is driving along the road with the cruise control on; it should travel at a constant speed. We model this with $\\bar x_k=\\dot x_k\\Delta t + x_{k-1}$. However, it is affected by a number of unknown factors. The cruise control cannot perfectly maintain a constant velocity. Winds affect the car, as do hills and potholes. Passengers roll down windows, changing the drag profile of the car. \n",
"\n",
"We can model this system with the differential equation\n",
"\n",
"$$\\dot{\\mathbf x} = f(\\mathbf x) + w$$\n",
"\n",
"where $f(\\mathbf x)$ models the state transition and $w$ is *white process noise*.\n",
"\n",
"We will learn how to go from a set of differential equations to the Kalman filter matrices in the **Kalman Filter Math** chapter. In this chapter we take advantage of the fact that Newton already derived the equations of motion for us. For now you just need to know that we account for the noise in the system by adding a process noise covariance matrix $\\mathbf Q$ to the covariance $\\mathbf P$. We do not add anything to $\\mathbf x$ because the noise is *white* - which means that the mean of the noise will be 0. If the mean is 0, $\\mathbf x$ will not change.\n",
"\n",
"The univariate Kalman filter used `variance = variance + process_noise` to compute the variance for the variance of the prediction step. The multivariate Kalman filter does the same, essentially `P = P + Q`. I say 'essentially' because there are other terms unrelated to noise in the covariance equation that we will see later.\n",
"\n",
"Deriving the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. For now know that $\\mathbf Q$ equals the expected value of the white noise $w$, computed as $\\mathbf Q = \\mathbb E[\\mathbf{ww}^\\mathsf T]$. In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter.\n",
"\n",
"FilterPy provides functions which compute $\\mathbf Q$ for the kinematic problems of this chapter. `Q_discrete_white_noise` takes 3 parameters. `dim`, which specifies the dimension of the matrix, `dt`, which is the time step in seconds, and `var`, the variance in the noise. Briefly, it discretizes the noise over the given time period under assumptions that we will discuss later. This code computes $\\mathbf Q$ for white noise with a variance of 2.35 and a time step of 1 seconds:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[0.588 1.175]\n",
" [1.175 2.35 ]]\n"
]
}
],
"source": [
"from filterpy.common import Q_discrete_white_noise\n",
"Q = Q_discrete_white_noise(dim=2, dt=1., var=2.35)\n",
"print(Q)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Design the Control Function\n",
"\n",
"The Kalman filter does not just filter data, it allows us to incorporate the control inputs of systems like robots and airplanes. Suppose we are controlling a robot. At each time step we would send steering and velocity signals to the robot based on its current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity and control inputs to the drive motors. Remember, we *never* throw information away.\n",
"\n",
"For a linear system the effect of control inputs can be described as a set of linear equations, which we can express with linear algebra as\n",
"\n",
"$$\\Delta\\mathbf x = \\mathbf{Bu}$$\n",
"\n",
"Here $\\mathbf u$ is the *control input*, and $\\mathbf B$ is the *control input model* or *control function*. For example, $\\mathbf u$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf B$ yields $\\Delta[\\begin{smallmatrix}x\\\\\\dot x\\end{smallmatrix}]$. In other words, it must compute how much $\\mathbf x$ changes due to the control input.\n",
"\n",
"Therefore the complete Kalman filter equation for the prior mean is\n",
"\n",
"$$\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu}$$\n",
"\n",
"and this is the equation that is computed when you call `KalmanFilter.predict()`.\n",
"\n",
"Your dog may be trained to respond to voice commands. All available evidence suggests that my dog has no control inputs whatsoever, so I set $\\mathbf B$ to zero. In Python we write:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [12.7 4.5]\n",
"P = [[680.587 301.175]\n",
" [301.175 502.35 ]]\n"
]
}
],
"source": [
"B = 0. # my dog doesn't listen to me!\n",
"u = 0\n",
"x, P = predict(x, P, F, Q, B, u)\n",
"print('x =', x)\n",
"print('P =', P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Setting $\\mathbf B$ and $\\mathbf u$ to zero is not necessary since `predict` uses 0 for their default value:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ True, True])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"predict(x, P, F, Q)[0] == predict(x, P, F, Q, B, u)[0]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ True, True],\n",
" [ True, True]])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"predict(x, P, F, Q)[1] == predict(x, P, F, Q, B, u)[1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"#### Prediction: Summary\n",
"\n",
"Your job as a designer is to specify the matrices for\n",
"\n",
"* $\\mathbf x$, $\\mathbf P$: the state and covariance\n",
"* $\\mathbf F$, $\\mathbf Q$: the process model and noise covariance\n",
"* $\\mathbf{B,u}$: Optionally, the control input and function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Update Step\n",
"\n",
"Now we can implement the update step of the filter. You only have to supply two more matrices, and they are easy to understand. \n",
"\n",
"### Design the Measurement Function\n",
"\n",
"The Kalman filter computes the update step in what we call *measurement space*. We mostly ignored this issue in the univariate chapter because of the complication it adds. We tracked our dog's position using a sensor that reported his position. Computing the *residual* was easy - subtract the filter's predicted position from the measurement:\n",
"\n",
"$$ \\mathtt{residual} = \\mathtt{measured\\, \\, position} - \\mathtt{predicted\\, \\, position}$$\n",
"\n",
"We need to compute the residual because we scale it by the Kalman gain to get the new estimate.\n",
"\n",
"What would happen if we were trying to track temperature using a thermometer that outputs a voltage corresponding to the temperature reading? The equation for the residual computation would be meaningless; you can't subtract a temperature from a voltage.\n",
"\n",
"$$ \\mathtt{residual} = \\mathtt{voltage} - \\mathtt{temperature}\\;\\;\\;(NONSENSE!)$$\n",
"\n",
"\n",
"We need to convert the temperature into a voltage so we can perform the subtraction. For the thermometer we might write:\n",
"\n",
"```python\n",
"CELSIUS_TO_VOLTS = 0.21475\n",
"residual = voltage - (CELSIUS_TO_VOLTS * predicted_temperature)\n",
"```\n",
" \n",
"The Kalman filter generalizes this problem by having you supply a *measurement function* that converts a state into a measurement. \n",
"\n",
"Why are we working in measurement space? Why not work in state space by converting the voltage into a temperature, allowing the residual to be a difference in temperature?\n",
"\n",
"We cannot do that because most measurements are not *invertible*. The state for the tracking problem contains the hidden variable $\\dot x$. There is no way to convert a measurement of position into a state containing velocity. On the other hand, it is trivial to convert a state containing position and velocity into a equivalent \"measurement\" containing only position. We have to work in measurement space to make the computation of the residual possible.\n",
"\n",
"Both the measurement $\\mathbf z$ and state $\\mathbf x$ are vectors so we need to use a matrix to perform the conversion. The Kalman filter equation that performs this step is:\n",
"\n",
"$$\\mathbf y = \\mathbf z - \\mathbf{H \\bar x}$$\n",
"\n",
"where $\\mathbf y$ is the residual, $\\mathbf{\\bar x}$ is the prior, $\\mathbf z$ is the measurement, and $\\mathbf H$ is the measurement function. So we take the prior, convert it to a measurement by multiplying it with $\\mathbf H$, and subtract that from the measurement. This gives us the difference between our prediction and measurement in measurement space!\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need to design $\\mathbf H$ so that $\\mathbf{H\\bar x}$ yields a measurement. For this problem we have a sensor that measures position, so $\\mathbf z$ will be a one variable vector:\n",
"\n",
"$$\\mathbf z = \\begin{bmatrix}z\\end{bmatrix}$$\n",
"\n",
"The residual equation will have the form\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\textbf{y} &= \\mathbf z - \\mathbf{H\\bar x} \\\\\n",
"\\begin{bmatrix}y \\end{bmatrix} &= \\begin{bmatrix}z\\end{bmatrix} - \\begin{bmatrix}?&?\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"$\\mathbf H$ has to be a 1x2 matrix for $\\mathbf{Hx}$ to be 1x1. Recall that multiplying matrices $m\\times n$ by $n\\times p$ yields a $m\\times p$ matrix.\n",
"\n",
"We will want to multiply the position $x$ by 1 to get the corresponding measurement of the position. We do not need to use velocity to find the corresponding measurement so we multiply $\\dot x$ by 0.\n",
"\n",
"$$\\begin{aligned}\n",
"\\textbf{y} &= \\mathbf z - \\begin{bmatrix}1&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix} \\\\\n",
"&= [z] - [x]\n",
"\\end{aligned}$$\n",
"\n",
"And so, for our Kalman filter we set\n",
"\n",
"$$\\mathbf H=\\begin{bmatrix}1&0\\end{bmatrix}$$"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"H = np.array([[1., 0.]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have designed the majority of our Kalman filter. All that is left is to model the noise in the sensors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Design the Measurement\n",
"\n",
"The measurement is implemented with $\\mathbf z$, the measurement mean, and $\\mathbf R$, the measurement covariance. \n",
"\n",
"$\\mathbf z$ is easy. it contains the measurement(s) as a vector. We have only one measurement, so we have:\n",
"\n",
"$$\\mathbf z = \\begin{bmatrix}z\\end{bmatrix}$$\n",
"\n",
"If we have two sensors or measurements we'd have:\n",
"\n",
"$$\\mathbf z = \\begin{bmatrix}z_1 \\\\ z_2\\end{bmatrix}$$\n",
"\n",
"\n",
"The *measurement noise matrix* models the noise in our sensors as a covariance matrix. In practice this can be difficult. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. We will learn to deal with these problems later.\n",
"\n",
"The Kalman filter equations uses a covariance matrix $\\mathbf R$ for the measurement noise. The matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is a covariance matrix to account for correlations between the sensors. We have only 1 sensor so R is:\n",
"\n",
"$$R = \\begin{bmatrix}\\sigma^2_z\\end{bmatrix}$$\n",
"\n",
"If $\\sigma^2_z$ is 5 meters squared we'd have $R = \\begin{bmatrix}5\\end{bmatrix}$. \n",
"\n",
"If we had two position sensors, the first with a variance of 5 m$^2$, the second with a variance of 3 m$^2$, we would write\n",
"\n",
"$$R = \\begin{bmatrix}5&0\\\\0&3\\end{bmatrix}$$\n",
"\n",
"We put the variances on the diagonal because this is a *covariance* matrix, where the variances lie on the diagonal, and the covariances, if any, lie in the off-diagonal elements. Here we assume there is no correlation in the noise between the two sensors, so the covariances are 0.\n",
"\n",
"For our problem we only have one sensor, so we can implement this as"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"R = np.array([[5.]])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We perform the update by calling `update`. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [ 1.085 -0.64 ]\n"
]
}
],
"source": [
"from filterpy.kalman import update\n",
"z = 1.\n",
"x, P = update(x, P, z, R, H)\n",
"print('x =', x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Keeping track of all of these variables is burdensome, so FilterPy also implements the filter with the class `KalmanFilter`. I will use the class in the rest of this book, but I wanted you to see the procedural form of these functions since I know some of you are not fans of object oriented programming."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implementing the Kalman Filter\n",
"\n",
"I've given you all of the code for the filter, but now let's collect it in one place. First we construct a `KalmanFilter` object. We have to specify the number of variables in the state with the `dim_x` parameter, and the number of measurements with `dim_z`. We have two random variables in the state and one measurement, so we write:\n",
"\n",
"```python\n",
"from filterpy.kalman import KalmanFilter\n",
"dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n",
"```\n",
"\n",
"This creates an object with default values for all the Kalman filter matrices:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [[0. 0.]]\n",
"R = [[1.]]\n",
"Q = \n",
" [[1. 0.]\n",
" [0. 1.]]\n"
]
}
],
"source": [
"from filterpy.kalman import KalmanFilter\n",
"dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n",
"print('x = ', dog_filter.x.T)\n",
"print('R = ', dog_filter.R)\n",
"print('Q = \\n', dog_filter.Q)\n",
"# etc..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we initialize the filter's matrices and vectors with values valid for our problem. I've put this in a function to allow you to specify different initial values for `R`, `P`, and `Q` and put it in a helper function. We will be creating and running many of these filters, and this saves us a lot of headaches."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"from filterpy.kalman import KalmanFilter\n",
"from filterpy.common import Q_discrete_white_noise\n",
"\n",
"def pos_vel_filter(x, P, R, Q=0., dt=1.0):\n",
" \"\"\" Returns a KalmanFilter which implements a\n",
" constant velocity model for a state [x dx].T\n",
" \"\"\"\n",
" \n",
" kf = KalmanFilter(dim_x=2, dim_z=1)\n",
" kf.x = np.array([x[0], x[1]]) # location and velocity\n",
" kf.F = np.array([[1., dt],\n",
" [0., 1.]]) # state transition matrix\n",
" kf.H = np.array([[1., 0]]) # Measurement function\n",
" kf.R *= R # measurement uncertainty\n",
" if np.isscalar(P):\n",
" kf.P *= P # covariance matrix \n",
" else:\n",
" kf.P[:] = P # [:] makes deep copy\n",
" if np.isscalar(Q):\n",
" kf.Q = Q_discrete_white_noise(dim=2, dt=dt, var=Q)\n",
" else:\n",
" kf.Q[:] = Q\n",
" return kf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`KalmanFilter` initializes `R`, `P`, and `Q` to the identity matrix, so `kf.P *= P` is one way to quickly assign all of the diagonal elements to the same scalar value. Now we create the filter:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"dt = .1\n",
"x = np.array([0., 0.]) \n",
"kf = pos_vel_filter(x, P=500, R=5, Q=0.1, dt=dt)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can inspect the current values of all attributes of the filter by entering the variable on the command line."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"KalmanFilter object\n",
"dim_x = 2\n",
"dim_z = 1\n",
"dim_u = 0\n",
"x = [0. 0.]\n",
"P = [[500. 0.]\n",
" [ 0. 500.]]\n",
"x_prior = [[0. 0.]].T\n",
"P_prior = [[1. 0.]\n",
" [0. 1.]]\n",
"x_post = [[0. 0.]].T\n",
"P_post = [[1. 0.]\n",
" [0. 1.]]\n",
"F = [[1. 0.1]\n",
" [0. 1. ]]\n",
"Q = [[0. 0. ]\n",
" [0. 0.001]]\n",
"R = [[5.]]\n",
"H = [[1. 0.]]\n",
"K = [[0. 0.]].T\n",
"y = [[0.]]\n",
"S = [[0.]]\n",
"SI = [[0.]]\n",
"M = [[0.]]\n",
"B = None\n",
"z = [[None]]\n",
"log-likelihood = -708.3964185322641\n",
"likelihood = 2.2250738585072014e-308\n",
"mahalanobis = 0.0\n",
"alpha = 1.0\n",
"inv = "
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All that is left is to write the code to run the Kalman filter. "
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"from kf_book.mkf_internal import plot_track\n",
"\n",
"def run(x0=(0.,0.), P=500, R=0, Q=0, dt=1.0, \n",
" track=None, zs=None,\n",
" count=0, do_plot=True, **kwargs):\n",
" \"\"\"\n",
" track is the actual position of the dog, zs are the \n",
" corresponding measurements. \n",
" \"\"\"\n",
"\n",
" # Simulate dog if no data provided. \n",
" if zs is None:\n",
" track, zs = compute_dog_data(R, Q, count)\n",
"\n",
" # create the Kalman filter\n",
" kf = pos_vel_filter(x0, R=R, P=P, Q=Q, dt=dt) \n",
"\n",
" # run the kalman filter and store the results\n",
" xs, cov = [], []\n",
" for z in zs:\n",
" kf.predict()\n",
" kf.update(z)\n",
" xs.append(kf.x)\n",
" cov.append(kf.P)\n",
"\n",
" xs, cov = np.array(xs), np.array(cov)\n",
" if do_plot:\n",
" plot_track(xs[:, 0], track, zs, cov, **kwargs)\n",
" return xs, cov"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is the complete code for the filter, and most of it is boilerplate. I've made it flexible enough to support several uses in this chapter, so it is a bit verbose. Let's work through it line by line. \n",
"\n",
"The first lines checks to see if you provided it with measurement data in `data`. If not, it creates the data using the `compute_dog_data` function we wrote earlier.\n",
"\n",
"The next lines uses our helper function to create a Kalman filter.\n",
"\n",
"```python\n",
"# create the Kalman filter\n",
" kf = pos_vel_filter(x0, R=R, P=P, Q=Q, dt=dt)\n",
"```\n",
"\n",
"All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The `KalmanFilter` class provides the two methods `update()` and `predict()` for this purpose. `update()` performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n",
"\n",
"Absent the work of storing the results, the loop reads:\n",
"\n",
"```python\n",
" for z in zs:\n",
" kf.predict()\n",
" kf.update(z)\n",
"```\n",
"\n",
"Each call to `predict` and `update` modifies the state variables `x` and `P`. Therefore, after the call to `predict`, `kf.x` contains the prior. After the call to update, `kf.x` contains the posterior. `data` contains the actual position and measurement of the dog, so we use `[:, 1]` to get an array of measurements.\n",
"\n",
"It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the `KalmanFilter` matrices; executing the filter is trivial.\n",
"\n",
"The rest of the code optionally plots the results and then returns the saved states and covariances.\n",
"\n",
"Let's run it. We have 50 measurements with a noise variance of 10 and a process variance of 0.01."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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jTjzxRLFy5UrVe5966ilhsViE2WwWF1xwgbjlllvEDTfcIC688EKRnp4uysrK/Mq//PLLhclkUk09SkQkxPTbLZfLJZYtWyauvvpqIYQQP//5z0VWVpbYt2/ftLY7Ubvlva2ptAnTPS/OZJa06dQn2G3HeMtD0UZp3T4JwTYqErHjQ4o//elP4tRTTxXx8fEiLi5OVFVViZ/+9KcBn8sTrAZkdHRU5OTkiBUrVvgt8z7R7d27V3zta18TqampIi4uTpx22mnitddeC1jms88+K04//XSRmJgorFarWLRokbj33nvFyMiI33t/+9vfiosuukiUlJSIuLg4kZaWJpYuXSo2bdoUcArtifzoRz9SpvTeunXruO977733xKpVq0RqaqpITEwUp59+unj55ZfF9u3bg9bxCfZ2xuv4CCHE+++/L9asWSOysrKExWIReXl54itf+Yp44YUX/N67a9cusXbtWlFUVCRiYmJEWlqaqKioENdcc4148803Ve/t6+sTsbGx4z4/gYhoOu2WEEK8/vrrwmw2i/vvv18kJiaKjz/+eNrbnKjd8jbVNmE658WZdnymU59gth0TLQ9FG6VV+yQE26hIxY4PzVgwGhAhhLjvvvsEAPHZZ5+pXj+eEzxFvoceekgAEO+++264q0JEUeTUU08VJpNJ/N///d+Myxiv3SL9YBsVmQxCHOfDWEjXTjvtNHz88cd45ZVXpjRffiA2mw1lZWVYsmQJXnnlFeX1pqYmlJSUYO3atXjiiSeCVGOKBCMjI5g/fz5OO+00bN26NdzVIaIo8dZbb2H16tWw2Wz45JNPpvTIgkDGa7dIH9hGRS5ObkAz9tZbb2Hnzp0QQoz7rJ2piI2NxVNPPYWTTz4Zw8PDQawhRaqmpiZcc8012Lx5c7irQkRRYufOnVizZg1+9atf4aKLLsKdd94547LYbukb26jIxSs+NCM7d+7E2WefjV/+8pf4y1/+gqGhoSlNGzkdvOJDRETBcPDgQZx22mlYt24dNm7ciOrqaixZsgRvvfUWVq5cGe7qEVGIsOND08YGhIiIIkVPTw9OP/10nHXWWXjkkUeU1y+77DI0Nzfjgw8+CGPtiCiU2PGhaWEDQkRERESRaFZ0fFwul9+Tlw0Gg/JkZiIiCg0hZ/tUvWY0GmE08pZQtlVERLPDTNsqs5aVmiqXy8WbA4mIZqmEhAR2fMC2iohoNptKW8WWjIiIiIiIoh47PkREREREFPXY8SEiIiIioqg37Xt8BgcH8ZOf/AQ7duzA559/jq6uLvzoRz/Cj3/8Y7/3fvbZZ/j+97+PDz/8EGazGeeccw42b96MefPmqd4X6MZQjiknIgq9QPex8OZ9iW0VEdHsMNO2atodn+7ubjz66KOoqqrCRRddhMceeyzg+2pra7Fy5UosXboUzz//PGw2GzZu3IgzzzwTO3bsQFZW1oQV5SxCRESzAzs+EtsqIqLZS5OOz9y5c9Hb2wuDwYCurq5xOz4bN26E1WrFq6++iuTkZADAsmXLUFpais2bN2PTpk3T3TQREREREdGMTLvjM5XelMPhwKuvvoorrrhC6fQAstO0atUqvPzyy5p0fPbt2weHwwGz2YyFCxcGvfxIwRwk5iAxB4k5SMwh/LgPJOYgMQeJOXgwC0mLHDR5jk99fT1GRkawZMkSv2VLlizBG2+8AZvNhtjY2KBud2RkBHa7HRaLJajlRhrmIDEHiTlIzEFiDuHHfSAxB4k5SMzBg1lIWuSgScenu7sbAJCenu63LD09HUII9Pb2Ii8vb9wyampqMHfuXNUVo9HRUdTW1gIA0tLSUFRUpFrH4XAAAOx2u195XV1dOHz4MACgqKgIaWlpyjKn04nq6moAQFJSkt/kC42NjRgYGAAAVFRUwGz2xNbX14eDBw8CAPLz81X3LgHArl27IIRAXFycX2/10KFD6OnpAQCUlZWpOoJDQ0Oor68HAGRnZ/tltWfPHuVgWLRokWqZ+8nidrsdQ0NDSExMVJbZbDbU1dUBkPuisLBQte6+ffswMjICg8Hg13Ht7OxEa2srAHn1LjU1VVnmcDhQU1MDAEhOTkZJSYlq3YaGBgwODgIAKisrYTKZlGW9vb1obm4GAMyZMweZmZmqdXfu3AkAiI+PR2lpqWpZc3Mzent7AQDl5eWwWq3KMvcTfe12O9rb25Gbm6tat6amBg6HA1arFeXl5aplra2t6OzsBAAsWLAACQkJyrKjR49i//79AICMjAwUFBSo1q2rq4PNZoPJZEJlZaVqWUdHB9ra2gAAxcXFSElJUZaNjY1h7969AICUlBQUFxer1q2vr8fQ0BAAYPHixar7Crq7u9HS0gIAKCgoQEZGBnzZ7XbU19dj/vz5qtebmprQ398PADjhhBMQExOjLOvv70dTUxMAIC8vD9nZ2ap1q6ur4XQ6ERsbi7KyMtWylpYW5VxQWlqK+Ph4Zdnw8DAOHDgAAMjKykJ+fr5q3draWoyOjsJsNqOiokK1rL29HUeOHAEAlJSUTPkc4b5abbfbsXPnTlRVVanK1cs5wjeH+fPnq84Ro6OjIG0ZDAblf3rGHCTmIDEHD2YhaZGDJh0ft4kqOtmHcDgcyhdXNyGE0qlxd3K8xcfHj/tUbZfLpazr7hh4m6hch8OhLPetk3e5TqczYLlCiIC9VafTeVzlBurgAfKLZHt7u1KON+8MA5Xr/qyB9o93fScqd7IMfWm1b0pKSpQOyngZOhyOgDcmT7RvJsvQvW8CLZuoXPe6k5UbyEQZLl68GJ999pmq/PHq5Guyzzo2NgaXy6XqyAYqd6YZBspoquX6Hi9LlizB3r17MTw8HPDz6uUcsWTJErS0tKC9vR12uz3g3zJpK9BoCD1iDhJzkJiDB7OQtMhBk46P+9dm96+93np6emAwGFRXCwJWzGz2+/JtMBiULwfev6h6rzPe5TCj0agsC/RFd6rl+tbJu9xAX/4sFguEEAHLNZlMx1Wu97/jlev7Wb0zDFSu+7MG6vhMtdzZsm8m+6zuzzlZhjMp1+l0Blw2UbnudScq93gznOyz+prss8bExMDpdGqSocvlmvbfzWw8DiPxHEFERBSNDOI4ft7r6upCVlaW33N8HA4HkpOTsXbtWvz2t79VrXPeeeehoaEB+/btU15zuVzKMCi3pKQkThFKRBRiPB+Pj9kQEc0OMz0fa3K2NpvNWL16NV566SVVpZqbm7F9+3asWbNGi80SEREREREFNKOhbn/9618xPDysdGr27NmDrVu3AgDOP/98xMfH4+6778by5ctxwQUX4I477lAeYJqZmYlbb701eJ/AS2dnpzLEyPcGYj1hDhJzkJiDxBwk5hB+3AcSc5CYg8QcPJiFpEUOM+r4XHfddcosRQDwwgsv4IUXXgAgZzcqLi5GeXk53n77bdx+++249NJLYTabcc4552Dz5s2a7cTW1lZlFiM9HyjMQWIOEnOQmIPEHMKP+0BiDhJzkJiDB7OQtMhhRh0f9/S2k1m2bBm2bds2k03MyKjDhcMDDqQncLw1ERHNTgOjTvQddSAt3n9SCiIi0o6m01mH2m932LB9fw/u+NI8nB3uyoTR3Llz4XK5dH/DLXOQmIPEHCTmEH5/rLXjr3u6ces5xTgj3JUJIx6LEnOQmIMHs5C0yCGqOj4l2SnYvr8H3TZ9P4disqnC9YI5SMxBYg4Scwi/pHj5IFqjxTrJO6Mbj0WJOUjMwYNZSFrkEFVdycL0OADAoZ6RMNeEiIgosFiLHOI26vB/UC4REWknujo+afEAgJa+o2GuCRERUWBWs2x6R+3OMNeEiEhfomqoW35KDADgUI++Oz4OhwNCCBgMhoBPg9cL5iAxB4k5SMwh/CxGAwBgZMwR5pqEF49FiTlIzMGDWUha5BBVaQ60NQEA+kccGLDZkRxrCWt9wqWmpkaZ/q+qqirc1Qkb5iAxB4k5SMwh/Pp7ugAA7Z3dYa5JePFYlJiDxBw8mIWkRQ5RNdQtzmJEcoz8JU3vV32IiGh2sphkOzXm1PdEPEREoRZVV3ySk5ORl9yJga5RHOoZQUV+SrirFBbJyclwOBy6vjwKMAc35iAxB4k5hF9yQhyAfgijvvcBj0WJOUjMwYNZSFrkEFWJlpSUYEF+L+q62tDSq98rPiUlJeGuwqzAHCTmIDEHiTmE35zcLADtsFhjw12VsOKxKDEHiTl4MAtJixyiaqgb4DWzWy+ntCYiotnHapbTWdvsnM6aiCiUoq/jozzLR79XfIiIaPZSprN2cDprIqJQirqOT8GxKz6HdDzUjYiIZi+rxd3x4RUfIqJQiqp7fBoaGuDslx2eQz0jytzfetPQ0KDcDDZv3rxwVydsmIPEHCTmIDGH8Ovp7AAADA7bwlyT8OKxKDEHiTl4MAtJixyiquMzODiIONcYDABG7E50D48hM9Ea7mqF3ODgoDLvuZ4xB4k5SMxBYg7h5xiV96Da7Poe6sZjUWIOEnPwYBaSFjlE3VA3i8mA9Dh54ygnOCAiotkmxv0cHxef40NEFEoGIUTYz7wulwuDg4Oq15KSkmA0Tq9f5nTKX88ue/QjfHqwF7/6+olYXZUftHpGCncOAGAymcJYk/BiDhJzkJiDNFkOwTofR6NgZVPb1o/z/usfSIu34PONXw5mFSMK/yYl5iAxBw9mIU2Uw0zPx1E11M0dSlF6PD492KvbCQ70/EfijTlIzEFiDhJzCL/4GDlsQ++TG/BYlJiDxBw8mIWkRQ5R+RNeQZp7SmsOdSMiotmFs7oREYVHdHZ80t0PMdXnFR8iIpq93M/xcboEHE52foiIQiWqhrr19vbC5XIhzSLHBOp1cgN3DkajEWlpaeGuTtgwB4k5SMxBYg7hNzI0oPz3qMMFsykqf4OcFI9FiTlIzMGDWUha5BBVHZ/m5mbY7XZgTM6Yc7h3BC6XgNGor2f5uHOwWCy6/oNhDhJzkJiDxBzCr721RfnvUYcLCfp76gIAHotuzEFiDh7MQtIih6j8mSkjzgSz0YAxpwtHBvX9gDgiIppdjAYDjo120/2zfIiIQimqrvjMmTNHuSSWl9qDQz0jONQzgryUuHBXLaS8c9Az5iAxB4k5SMwh/ObMmQOruQ2OMaeuJzjgsSgxB4k5eDALSYscoqrjk5mZqfx3YVr8sY7PUawoSQ9jrULPOwc9Yw4Sc5CYg8Qcwi8zMxNxMSYMjzkx6tDvFR8eixJzkJiDB7OQtMgharuShWnumd30OcEBERHNXlazfD7FqF2/V3yIiEItejs+6cee5cMprYmIaJbhs3yIiEJP047Pxx9/jK985StISkpCYmIiVq1ahffee0/LTSoKjz3L51APOz5ERHr32GOPwWAwIDEx0W/ZZ599hnPPPReJiYlITU3FmjVr0NDQoGl9lCs+Oh7qRkQUaprd4/PJJ5/grLPOwooVK/DUU09BCIEHHngAX/ziF7F9+3aceuqpQd/mzp07lWnvCtIKAehzqJt3DlVVVeGuTtgwB4k5SMxB0mMOhw8fxoYNG5Cfn4/+/n7VstraWqxcuRJLly7F888/D5vNho0bN+LMM8/Ejh07kJWVFfT67Ny5E45R2TbZdDzUTY/HYiDMQWIOHsxC0iIHzTo+P/zhD5GamorXXnsN8fHy6su5556LefPmYcOGDZpf+XHf49PWPwK70wWLTh8QR0Skd9deey3OOusspKenY+vWraplGzduhNVqxauvvork5GQAwLJly1BaWorNmzdj06ZNmtTp2Eg3XvEhIgohzXoD7733HlauXKl0egAgKSkJZ511Ft5//320tbUFfZvx8fFISEhAfHw8spKssJqNcAmgtU9fV328c9Az5iAxB4k5SHrL4emnn8Y777yDhx9+2G+Zw+HAq6++iksuuUTp9ADA3LlzsWrVKrz88sua1Ck+Ph5xMfJ3Rz1PbqC3Y3E8zEFiDh7MQtIiB82u+IyNjcFq9X8ctfu13bt3Iy8vL6jbLC0tVf3/grQ41HcOo6V3BHMzEoK6rdnMNwe9Yg4Sc5CYg6SnHDo6OnDTTTfhZz/7GQoKCvyW19fXY2RkBEuWLPFbtmTJErzxxhuw2WyIjY0ddxs1NTWYO3euquM0OjqK2tpaAEBaWl+k46gAACAASURBVBqKior81jMbhHyvz+QGXV1dOHz4MACgqKhI9bRyp9OJ6upqAPKHxHnz5qnWbWxsxMDAAACgoqICZrOnie/r68PBgwcBAPn5+X5D+Hbt2gUhBOLi4rBw4ULVskOHDqGnpwcAUFZWpspjaGgI9fX1AIDs7Gy/dn3Pnj3KUJVFixapliUmJqKjowNjY2MYGhpS3X9ls9lQV1cHAEhPT0dhYaFq3X379mFkZAQGg8Fv/3V2dqK1tRWA7MSmpqYqyxwOB2pqagAAycnJKCkpUa3b0NCAwcFBAEBlZSVMJpOyrLe3F83NzQDk80V8p9rduXMnAPllzffvrLm5Gb29vQCA8vJy1fejnJwcNDY2YmxsDO3t7cjNzVWtW1NTA4fDAavVivLyctWy1tZWdHZ2AgAWLFiAhATPd52jR49i//79AICMjAy/v4G6ujrYbDaYTCZUVlaqlnV0dCg/UBcXFyMlJUVZNjY2hr179wIAUlJSUFxcrFq3vr4eQ0NDAIDFixernsHS3d2NlpYWAEBBQQEyMjKUZfPnz8fu3bsxNjaG+vp6zJ8/X1VuU1OTMlT1hBNOQExMjLKsv78fTU1NAIC8vDxkZ2er1q2urobT6URsbCzKyspUy1paWtDd3Q1Anh+9v2QPDw/jwIEDAICsrCzk5+er1q2trcXo6CjMZjMqKipUy9rb23HkyBEAQElJybTPEWNjYxgbG/N7necIaXR01C+bqdCs47No0SJ8+OGHqgcPORwOfPTRRwCgHGTjmUljsn//fhw9KiczqKqqQmF6POo7h3Go56iuDpS2tjZ0dHQAkCcSvTYmAwMDaGxsBCAbFr02Ji6XC7t37wYgTyJ6bkx8zxHeeI6QZtqYzEbr169HWVkZrrvuuoDL3cdnerr/s97S09MhhEBvb++EP9I5HA4IIVSvCSFgt9uV5YHWMRvdHR/1UDeXy6Ws63L5Xw2arFz3ct86eZfrdPoPr7Pb7RBCwGKx+C1zOp3HVa57+UTl+n5W7wwDlev+rAaDYcblTpahL632zWSf1W63w+FwBHyI40T7Zirl2u32gMsmKte97mTlBjLVDAOt710nX5N91rGxMbhcLtV3j0DlzjTDQBlNtdzZchxG4jliJjTr+Nxwww246qqrcP311+P//b//B5fLhbvvvlv5AjDZU1hn2ph4h+e+z+dQ71G4XLE8UMDGxLdcNiZsTNzYmCDgdiLViy++iFdeeQWff/55wPOZt4mWT7au2Wz2e4/BYFD2p3cn2Hsd96xuvpMbGI1GZd1A56bJynUv962Td7mB/l4tFguEEAHLNZlMx1Wu97/jlev7Wb0zDFSu+7MG2j9TLXeyDH1ptW8m+6zuzzlZhjMp1+l0Blw2UbnudScq93gznOyz+prss8bExMDpdGqSocvlmvbfzWw8DiPxHDETmnV8rrzySnR2duLee+/Fb3/7WwDAqaeeig0bNmDTpk2YM2fOxBWbYWPiHVxB2rFn+fSM8EA5ho2Julw2JmxM3HiOQMDtRKKhoSF897vfxQ033ID8/Hz09fUBgDJspK+vDxaLRbkyGmgEQk9PDwwGg+rKdiAVFRV+GVqt1glnICotLUVetQ1obPa74pOZmTnu08pNJtOE5fpeafeWmpo64WcJNNzPrbCw0G90gFtiYuKEdfK92ugtLy9v3KtpsbGxE5bre3XUW1ZW1riz8ZnN5gnL9b2a6y0tLU11JdjXROUWFRUFHM4EyFESE63re9XbW35+vt8Vc7f4+PgJy/W9Su8tOzvb7wq/W0xMzITl+o4q8JaRkaEakeDNaDROWK7vKAhvKSkpE67rO/rCW0FBQcChsACQkJAwYbm+o0W85ebm+o00cZvKOWI8PEdIVqs14FDAyRiExj/vjY6OYv/+/UhKSsLcuXOxbt06PPPMM+js7ERcnOyYuFwuZRiUW1JS0qRXhXw1NzfLIQRmM4qKivB/u9uw/pnPcGJRKl5ef3rQPtNs55uDXjEHiTlIzEGaLIdgnY/DqampacIGHgAuvPBCbN26FcnJyVi7dq3yA53beeedh4aGBuzbt095LZht1X+9exgvVvfgupXzcft54395imb8m5SYg8QcPJiFNFEOMz0fa3bFx81qtSo97ebmZjz33HP4zne+o3R6gqm3t1cZ015UVKQMddPbs3x8c9Ar5iAxB4k5SHrIITc3F9u3b/d7/Wc/+xneeecd/PWvf0VmZibMZjNWr16Nl156CQ888ACSkpIAyLZq+/btuPnmmzWpX29vL1x2GwB9z+qmh2NxKpiDxBw8mIWkRQ6adXyqq6vx4osv4uSTT4bVasXOnTvxs5/9DKWlpfjJT36i1WZVCtNl56pzcBQ2uxOxFv/hIEREFF1iY2OxcuVKv9efeOIJmEwm1bK7774by5cvxwUXXIA77rhDeYBpZmYmbr31Vs3qaDHJIYV8jg8RUeho1vGJiYnBW2+9hYceeghDQ0MoKirCtddeizvuuEM1Q1YwlZeXQwihjFFPibMgyWrG4KgDLb1HsSA7SZPtzja+OegVc5CYg8QcJOagVl5ejrfffhu33347Lr30UpjNZpxzzjnYvHnzuPeJBGObRZ1NwJ4DftNZ6wmPRYk5SMzBg1lIWuSgWcdn4cKFeOedd7QqPiDf5wYZDAbMSYtDbfsgDvWM6KbjE+j5SXrEHCTmIDEHSc85PPHEE3jiiSf8Xl+2bBm2bdsWsnpYrVYkxMlp4212/V7x0fOx6I05SMzBg1lIWuQQOXerzlBhumdKayIiotnAPZ21nq/4EBGFWvR3fHQ6wQEREc1eVrNsftnxISIKHc1ndQulgYEBZSyg+2nu7gkODvXo54pPoBz0iDlIzEFiDhJzCL+BgQE4lVnd9DvUjceixBwk5uDBLCQtcoiqjk9jY6My7Z37YUnuKz56GuoWKAc9Yg4Sc5CYg8Qcwq+xsRHdHfL5E3q+4sNjUWIOEnPwYBaSFjlE/VC3AuWKD4e6ERHR7BCjTGet344PEVGoRdUVn5ycHDidTphMnuf1uK/49I/YMWCzIznWEq7qhUygHPSIOUjMQWIOEnMIv5ycHOSOxgLo0/VQNx6LEnOQmIMHs5C0yCGqOj65ubl+ryVYzUhPiEHP8BgO9RxFRX5KGGoWWoFy0CPmIDEHiTlIzCH8cnNzUWCPBaDv5/jwWJSYg8QcPJiFpEUOUT/UDQAK0+RwN87sRkREs4HV4p7VTb9XfIiIQk0XHZ8C97N8dDSzGxERzV7Kc3zs+r3iQ0QUarro+PBZPkRENJvwOT5ERKEXVff41NTUKNPeVVRUKK8XpOnrWT7j5aA3zEFiDhJzkJhD+NXU1KB7SD7HZ8zpgsslYDQawlyr0OOxKDEHiTl4MAtJixyiquPjcDjgcDhgMKgbkMJ0fT3LZ7wc9IY5SMxBYg4Scwg/h8MBg/Dc2zPqcCEuRn+zN/FYlJiDxBw8mIWkRQ5R1fGxWq0wGo2wWNRTVhdnyI5PU/dRjDqcytjqaDVeDnrDHCTmIDEHiTmEn9VqRRI8Dfmow6nLjg+PRYk5SMzBg1lIWuRgEEKIoJU2Qy6XC4ODg6rXkpKSYDQG5xYkIQSW/3QbuobG8Py6U7GiJD0o5RIRRRutz8eRLNjZzL/r/+B0CXx01xeRkxwbjCoSEenCTM/HumjJDAYDvjAvAwDwYUN3mGtDRETkNcEBZ3YjIgoJXXR8AOCUYx2fjxrZ8SEiovDzzOzGZ/kQEYWCfjo+x4a3/fNgLxsZIiIKu1jLsWf5cEprIqKQiKrJDVpbW+F0OmEymZCfn69atiA7ERkJMegeHsOuln4sL47e+3wmykFPmIPEHCTmIDGH8FP2AeQttja7Pn+M47EoMQeJOXgwC0mLHKKq49PZ2anM9+0bkMFgwCnzMvCX3W34sL47qjs+E+WgJ8xBYg4Sc5CYQ/i594EJssOj1ys+PBYl5iAxBw9mIWmRg26GugHAKfNkZ+ejxp4w14SIiPTOYpJTWnP4NRFRaETVFZ8FCxZACDHug47cM7t9erAHYw4XYszR2e+bLAe9YA4Sc5CYg8Qcws+9D5I/2gH09Ot2VjceixJzkJiDB7OQtMghqjo+CQkJEy4vzU5EekIMeobHsKulDydH6XC3yXLQC+YgMQeJOUjMIfzc+yDeKh/Kp9ehbjwWJeYgMQcPZiFpkUN0XvIYh7zPR3Z2+DwfIiIKp1gLp7MmIgolXXV8AO/n+fA+HyIiCh+rWU5nbdPpUDciolCLqqFuR48eVcYCxsfHB3zPF0qO3efT1Bu19/lMJQc9YA4Sc5CYg8Qcws+9D0wG2eHR6xUfHosSc5CYgwezkLTIIao6Pvv371emvauqqgr4Hu/7fHYf7sOyudF3n89UctAD5iAxB4k5SMwh/Nz7wDY8BAC6ndyAx6LEHCTm4MEsJC1y0PRyx+eff46LLroI+fn5iI+PR3l5Oe655x4cPXpUy81OyGg04Asl7vt8ONyNiIjCwzOdtT47PkREoabZFZ89e/bgtNNOQ1lZGR588EFkZmbi3XffxT333IN//vOf+N///d+gbzMjI0N5wutEvlCSjr9Wt+PDhm58d9WCoNcj3KaaQ7RjDhJzkJiDxBzCz70PUhJcAIZ0O9SNx6LEHCTm4MEsJC1y0Kzj88c//hE2mw0vvvgi5s+fDwA455xz0NbWhkcffRS9vb1IS0sL6jYLCgqm9L5T5nvu87E7XbCYous+n6nmEO2Yg8QcJOYgMYfwc++DzH2jADp1O7kBj0WJOUjMwYNZSFrkoNk3fotFPp8gJSVF9XpqaiqMRiNiYmK02vSkFmYnIS3eghG7E7ta+sNWDyIi0i+rmdNZExGFkmZXfNauXYsHH3wQ1113HTZt2oSsrCy88847eOSRR/Dd73530ocS1dTUYO7cuUhOTlZeGx0dRW1tLQAgLS0NRUVFqnX279+v3D/kexNUV1cXDh8+DAAoKirCF0oy8FqNHO62tCAZ1dXVAICkpCTMmzdPtW5jYyMGBgYAABUVFTCbPbH19fXh4MGDAID8/HxkZWWp1t21axeEEIiLi8PChQtVyw4dOoSeHnmfUVlZGWJjY5VlQ0NDqK+vBwBkZ2cjLy9Pte6ePXuUG74WLVqkWtbW1oaOjg4AwPz585GYmKgss9lsqKurAwCkp6ejsLBQte6+ffswMjICg8GAJUuWqJZ1dnaitbUVADB37lykpqYqyxwOB2pqagAAycnJKCkpUa3b0NCAwcFBAEBlZaXqsmVvby+am5sBAHPmzEFmZqZq3Z07dwIA4uPjUVpaqlrW3NyM3t5eAEB5eTmsVquybGBgAI2NjQCAnJwc5ObmqtatqamBw+GA1WpFeXm5allrays6OzsByCcHex+vR48exf79+wHIy7C+v0jU1dXBZrPBZDKhsrJStayjowNtbW0AgOLiYtUPA2NjY9i7dy8A+YNBcXGxat36+noMDcmboRcvXgyj0fO7RXd3N1paWgDIX0gyMjKUZS6XC7t37wYAJCYmKldg3ZqamtDfL38AOOGEE1Q/SvT396OpqQkAkJeXh+zsbNW61dXVcDqdiI2NRVlZmWpZS0sLurvl87JKS0tVM7IMDw/jwIEDAICsrCzk5+er1q2trcXo6CjMZjMqKipUy9rb23HkyBEAQElJiWbnCO8r0k6nUzfniNHRUVBoeDo++rziQ0QUapp1fIqLi/HBBx/g4osvVn3R+t73vocHH3xw0vUdDgeEEKrXhBCw2+3K8kDruJf7crlcyjKXy4UvzEtXOj7XnlUy5XJ96+RdrtPp/6ud3W6HEEK5AubN6XQeV7njfVbvcl0udYPqnWGgct2f1WAwzLjc4903vma6byb7rHa7HQ6HQ9WBcJto30ylXLvdHnDZROW6152s3ECmmmGg9b3r5Guyzzo2NgaXyxVw/G0wMgyU0VTLnS3HYSSeIyg0rBb5d6PXWd2IiEJNs45PU1MTVq9ejZycHGzduhVZWVn46KOPcO+992JoaAiPP/74xBUzm/2+fBsMBuXLgfcvqm42m015ny+j0aisazQalQeZ/vPgsft8JijXbDYry33L9i430Jc/i8UCIUTAck0m03GV6/2vN/cvxAaDwe9LvXeGgcp1f9ZAGXrXd6JyJ8vQl+++8TXTfeO+AmIwGMbN0Lve3ibaN5NlaLFYxr0Zb6Jy3etOVO5MMty3b59fvcerk6/JPmtMTAycTqcmGbpcrmn/3Ux0HNbV1SlXMwOVq9VxONvOEb45BPpbJm3V1dXBbrejt2sEgH6HurlzsFgsfleM9YQ5SMzBg1lIWuRgEBr9vHf55Zdj+/btaGhoUA0T+sMf/oArr7wSb7/9Ns4++2wA8hdH9zAot6SkpIBfPiayc+fOKc/37XIJnHTvG+g7asdL60/DSUXBnWghnKaTQzRjDhJzkJiDNFkOwTofR6Ngt1UfHLbjFx/04LT5Gfjjd04JZlUjAv8mJeYgMQcPZiFNlMNMz8eatWQ7duzAokWL/O7lWb58OQAo4+WDyWQywWg0TmnaO/XzfLqDXpdwmk4O0Yw5SMxBYg4Scwg/9z6IjZH7wGbX5xUfHosSc5CYgwezkLTIQbOhbvn5+aiursbQ0JDqxtkPPvgAgDZT1PneSD6ZL5Rk4PWaI/iwoQfrVwa9OmEz3RyiFXOQmIPEHCTmEH7ufTBQ1wG806nbyQ14LErMQWIOHsxC0iIHzTo+N910Ey666CJ86Utfws0334zMzEx8+OGHuP/++7Fo0SJ89atf1WrTU6bc59PUE5XP8yEiotnLaj42uYFOOz5ERKGm2Tf9r33ta3jzzTeRnJyMG2+8ERdccAG2bNmCdevW4d133w3rc3zcynOTkBJnwfCYE9WH+TwfIiIKHauFz/EhIgolza74AMCqVauwatUqLTdxXNz3+fxtjxzudmIUTXBARESzm/IcH05nTUQUEpp2fEKto6NDmUbY90GL41lalIq/7TmCvW0DGtcudGaSQzRiDhJzkJiDxBzCz70PhgfGAOh3qBuPRYk5SMzBg1lIWuQQVR2ftrY2Zdq7qQa0MDsJALC/Y0jLqoXUTHKIRsxBYg4Sc5CYQ/i590H/mHxmkl5ndeOxKDEHiTl4MAtJixx0fzd/aY6cca6+cwhOF59YTkREoRFjlB2fUYcLGj1Sj4iIvETVFZ/i4mIIIab15PGCtHjEWoyw2V1o7jmKksyEyVea5WaSQzRiDhJzkJiDxBzCz70PhkadANoAAGNOlzLLm17wWJSYg8QcPJiFpEUOUdXxSUlJmfY6JqMB87MSUdM6gH1HBqOi4zOTHKIRc5CYg8QcJOYQfu59EOc1m9uoQ38dHx6LEnOQmIMHs5C0yEH3Q90AYGGOvM/nQBTd50NERLNbjNez4zizGxGR9tjxAbAgW97ns+/IYJhrQkREemEwGDxTWvNZPkREmouqoW5jY2PKf0/nAanuKz77j0THFZ+Z5hBtmIPEHCTmIDGH8PPeB7EWE0YdLth0eMWHx6LEHCTm4MEsJC1yiKqOz969e5Vp76qqqqa8Xmm2emY3kzGybyabaQ7RhjlIzEFiDhJzCD/vfaDnKz48FiXmIDEHD2YhaZEDh7oBKEyPh9VsxKjDhUM9R8NdHSIi0gmrxd3x0d8VHyKiUIuqKz4pKSnKE16nw2Q0YEG2Z2a34gif2W2mOUQb5iAxB4k5SMwh/Lz3gdXcB0CfkxvwWJSYg8QcPJiFpEUOUdXxKS4unvG6pcc6Pvs7hvDliuDVKRyOJ4dowhwk5iAxB4k5hJ/3PrCaDwHQ51A3HosSc5CYgwezkLTIgUPdjilVJjjgzG5ERBQannt89HfFh4go1NjxOaZUmdI6OmZ2IyKi2S/WIodw2Oz6u+JDRBRq7Pgc457S2j2zGxERRaYdO3bgX/7lX1BUVIS4uDikp6fj1FNPxdNPP+333s8++wznnnsuEhMTkZqaijVr1qChoSFkdeUVHyKi0Imqe3zq6+uVae/mz58/rXV9Z3aL5AkOjieHaMIcJOYgMQdJDzn09fWhsLAQX//61zFnzhwMDw/jmWeewbe+9S00NTXhBz/4AQCgtrYWK1euxNKlS/H888/DZrNh48aNOPPMM7Fjxw5kZWVpUj/vfWA1yys+euz46OFYnArmIDEHD2YhaZFDVHV8hoaGlICmy2Q0YH5WIva0yQkOIrnjczw5RBPmIDEHiTlIeshh5cqVWLlypeq1Cy64AI2NjXj00UeVjs/GjRthtVrx6quvIjk5GQCwbNkylJaWYvPmzdi0aZMm9fPeB8p01joc6qaHY3EqmIPEHDyYhaRFDhzq5qU0x32fDyc4ICKKNpmZmTCb5e99DocDr776Ki655BKl0wMAc+fOxapVq/Dyyy+HpE4c6kZEFDpRdcVn8eLFx7W++z6fAx2RPcHB8eYQLZiDxBwk5iDpKQeXywWXy4Xe3l688MILeP311/HrX/8agBxCMTIygiVLlvitt2TJErzxxhuw2WyIjY2dcBs1NTWYO3euqvM0OjqK2tpaAEBaWhqKiopU68THx+PoUfmwbN+hbl1dXTh8+DAAoKioCGlpacp6TqcT1dXVAICkpCTMmzdPVW5jYyMGBgYAABUVFUonD5DD/w4ePAgAyM/P9xvGt2vXLgghEBcXh4ULF6qWHTp0CD09PQCAsrIyVSZDQ0Oor68HAGRnZyMvL0+17p49e5RfbBctWqRalpWVhc7OTqWcxMREZZnNZkNdXR0AID09HYWFhap19+3bh5GRERgMBr992NnZidbWVgCyI5uamqosczgcqKmpAQAkJyejpKREtW5DQwMGB+WPn5WVlarnh/T29qK5uRkAMGfOHGRmZqrW3blzJwC5f0tLS1XLmpub0dvbCwAoLy+H1WpVlhUXF6OpqQkA0N7ejtzcXNW6NTU1cDgcsFqtKC8vVy1rbW1VMlywYAESEjyjVY4ePYr9+/cDADIyMlBQUKBat66uDjabDSaTCZWVlaplHR0daGtrU+qXkpKiLBsbG8PevXsByOes+E45XF9fj6Eh+T1q8eLFMBo9v7F3d3ejpaUFAFBQUICMjAxlWUVFhbJv6uvr/YY2NTU1ob+/HwBwwgknICYmRlnW39+vZJiXl4fs7GzVutXV1XA6nYiNjUVZWZlqWUtLC7q7uwEApaWliI+PV5YNDw/jwIEDAOTxmp+fr1q3trYWo6OjMJvNqKhQPwulvb0dR44cAQCUlJTM+Bzhi+cIaXR0NGA+k4mqjo/3H9dMLMiOjis+x5tDtGAOEnOQmIOkpxzWr1+PRx55BAAQExODhx56COvWrQMA5YtOenq633rp6ekQQqC3t9evkfblcDgghHpCHCEE7Ha7sjzQOu7lsceGcLiHurlcLmWZy+V/FWiq5frWybtcp9N/WJ3dbocQIuCQEqfTeVzlupf7muizemcYqFz3ZzUYDBPWd6JyJ8twOvUFZr5vvNcdL0OHwxHwb3eifTNZhu59E2jZROVOpb4zydBoNCrLAq3vXSdfk33WsbExuFyugA/CDEaGgTKaarmz5TiMxHPETERVx+d4eV/xcboETEb/EyoREUWGu+66C1dffTU6Ojrwyiuv4Prrr8fw8DA2bNigvCfQF+epLHMzm81+7zMYDMqXA+9fVL3XcS/3veJjNBqVZYG+6E61XN86eZcb6MufxWKBECJguSaT6bjK9f53vHJ9P6t3hoHKdX/WQPtoquVOlqEvrfbNZJ/V/Tkny3Am5TqdzoDLJirXve5E5R5vhpN9Vl+TfdaYmBg4nU5NMnS5XNP+u5mNx2EkniNmwiBm2mUKIpfLpVxadktKSgr5L5NOl8AJG1/DmMOFd25bibkZkTvBARHRTMyW87EWrrvuOjz22GNobW1FT08PysvL8Zvf/Abr169Xve+2227DL37xCxw9elQ1ZEOLbH715n784o19+PqKQty/xn/YHRER+Zvp+Tiqrvh0d3fD5XLBaDSqxo1OlXtmt71tA9h/ZChiOz7Hm0O0YA4Sc5CYg6TnHFasWIH//u//RkNDA5YtW4a4uDjs3r3b7327d+/GggULJr2/Z6a894FnVjf9TW6g52PRG3OQmIMHs5C0yCGqOj4tLS3KDVIzDWhhjuz47OsYxLmLcoJcw9AIRg7RgDlIzEFiDpKec9i+fTuMRiPmzZsHs9mM1atX46WXXsIDDzyApCQ51Lm5uRnbt2/HzTffrFk9vPeB1SxvGtfjrG56Pha9MQeJOXgwC0mLHKKq4xMMpccmODhwJLJndiMi0qtrrrkGycnJWLFiBXJyctDV1YUXXngBzz33HG677TZltqK7774by5cvxwUXXIA77rhDeYBpZmYmbr311pDU1T2dtU2Hz/EhIgq1qOr4FBQUKJfEZqr02AQH+zoid2a3YOQQDZiDxBwk5iDpIYdTTz0Vf/jDH7Blyxb09fUhMTERVVVVeOqpp/DNb35TeV95eTnefvtt3H777bj00kthNptxzjnnYPPmzX5TuQaT9z5obLYB0OcVHz0ci1PBHCTm4MEsJC1y0Gxyg29/+9vYsmXLuMs/+OADnHLKKQBm1820DZ1DOOcX7yDWYsSeu8+DkTO7EZGOzKbz8WyjRTZ/3d2G6575DMuL0/DCtacdbxWJiHRh1k1u8MMf/hDXXnut3+urV6+G1WrF8uXLtdr0cSlKj0eM2Qib3YWW3hEUZcRPvhIREdEMKJMb6PCKDxFRqGnW8Zk/f77fU3ffeecddHV14Qc/+EHAubxnA7PJiHmZCahtH8T+jkF2fIiISDPKc3x0OKsbEVGohXTswuOPPw6DwYArr7xSk/JdLpfyv+PhfpDpvgid4CBYOUQ65iAxB4k5SMwh/Lz3gXtyg1GH/iY34LEoMQeJOXgwC0mLHEI2uUF/fz+2bt2KL37xiygpKZn0/TU1NZg7dy6Sk5OV10ZHR1FbZJ4e3gAAIABJREFUWwsASEtLQ1FRkWqdzz//HO5blk4++WTVsq6uLhw+fBgAUFRUhLS0NGWZ0+lEdXU1ADk+0D2z2/5jExw0NjZiYGAAAFBRUaF6am1fXx8OHjwIAMjPz/e7IXbXrl0QQiAuLg4LFy5ULTt06BB6enoAAGVlZapnRgwNDaG+vh4AkJ2djby8PNW6e/bsUab4W7RokWrZjh07lIOkvLwciYmJyjKbzYa6ujoAQHp6OgoLC1Xr7tu3DyMjIzAYDFiyRP0wvc7OTrS2tgIA5s6di9TUVGWZw+FATU0NACA5OdlvHzc0NChjMSsrK1VX/Hp7e9Hc3AwAmDNnDjIzM1Xr7ty5EwAQHx+P0tJS1bLm5mb09vYqn9VqtarWczrll4mCggLk5uaq1q2pqYHD4YDVakV5eblqWWtrKzo7OwEACxYsQEKC55lOR48exf79+wEAGRkZKCgoUK1bV1cHm80Gk8mEyspK1bKOjg60tbUBAIqLi5GSkqIsGxsbw969ewEAKSkpKC4uVq1bX1+PoSHZGV+8eLFqHGt3dzdaWlqUz+o97eOuXbvgcDgAyL8b3yuxTU1N6O/vBwCccMIJiImJUZb19/ejqakJAJCXl4fs7GzVutXV1XA6nYiNjUVZWZlqWUtLC7q7uwEApaWliI/3XD0dHh7GgQMHAABZWVnIz89XrVtbW4vR0VGYzWZUVFSolrW3t+PIkSMAgJKSkimfI3bv3g273Q5APiG6qqpKVe50zhHz5s1TrRtJ5wjfHObPn686R4yOjoK05d4HFosF1oxiAIBNh1d8vHPw/XvUE+YgMQcPZiFpkUPIOj7PPvssRkZGcNVVV03p/Q6HA77zLgghlAbb/UVuqlwul7JuoJ6jd7mlOfKL1P5jV3wcDoey3LdO3uW6v2T7liuEgMVi8VvmdDqPq1z38on4flbvDAOV6/6sBoP/pA7e9Z2o3ED7xjvDQHWc6r6ZqNyJ5ukYL0OHwxHwRriJ9s1kGbr3TaBlE5XrXneycgOZLEPf8serk6/JPuvY2BhcLlfAoavByDBQRlMtd6JzRKDPq9VxOJvPEXa7PeDfMoVOrEW/V3yIiEItZB2fxx9/HBkZGbj44oun9H6z2ez35dtgMChfDrx/UfVeZ7wvO0ajUVk30Bdd73JL0449y6djCC6XgNlsVpb71sm73EBf/iwWC4QQAetrMpmOq1zvf73FxMQov9r6flbvDAOV6/6sgTo+3vWdqNzx9k2gurrLmuq+mahc3zrHxcVheHhYqXugcr3r7W2ifTNZhhaLBU6nM+Cyicp1rztRuTPJMDExUbmiM9ln9TXZZ42JiYHT6dQkQ5fLNe2/m4mOw8TERAwMDIxbrlbH4Ww7RyQmJmJ4eBh2ux1mszng3zJpKzExUfkV0+K+x0eHkxt456BnzEFiDh7MQtIiB82ms/a2a9cuVFVV4cYbb8SDDz7ot3y2TZ/qcLqwaOPrGHO68Pfvr0JhOic4ICJ9mG3n49lEi2yODNjwhfvehMloQP195x9vFYmIdGGm5+OQtGSPP/44AODqq68OxeaOm9lkxLwseU/H/gh+kCkREc1u7skNnC4Bh1N/V32IiEJJ847P6Ogonn76aaxYscLvRu/ZrDTCZ3YjIqLZzz2dNaDP4W5ERKGkecfnT3/6E3p6eiLmao/bwmMzu+07wis+RESkDfcVHwCw2TnBARGRljSf3ODxxx9HQkICLr/8cq03haamJuWmct+pgKerNMczwUGkCWYOkYw5SMxBYg4Scwg/330QYzJizOnS3RUfHosSc5CYgwezkLTIQfOOz9/+9jetN6Ho7+8P2uwP7qFu+4/Imd2MxsiZ6SiYOUQy5iAxB4k5SMwh/Hz3gdWsz44Pj0WJOUjMwYNZSFrkwGl6xjE3PR4xJiNG7E4c7hsJd3WIiChKWfksHyKikAjZc3xC4YQTTghaWWaTEaU5iahpHUBN60BETWkdzBwiGXOQmIPEHCTmEH6++8A9wcGoXV9XfHgsSsxBYg4ezELSIoeo6vjExMQEtbyK/ORjHZ9+nFeZG9SytRTsHCIVc5CYg8QcJOYQfr77wD3Bgd6GuvFYlJiDxBw8mIWkRQ4c6jaBivwUAEBN60CYa0JERNEq5ljHh7O6ERFpix2fCVTkJwMAalr7w1wTIiKKVrGWY0PddHbFh4go1KJqqFt/fz+EEDAYDEhJSTnu8k7IS4bBABwZGEXX0CgyE61BqKX2gp1DpGIOEnOQmIPEHMLPdx94hrrp64oPj0WJOUjMwYNZSFrkEFUdn6amJmXau6qqquMuL8FqRklGAhq6hlHTOoCzF2YFoZbaC3YOkYo5SMxBYg4Scwg/331gtehzcgMeixJzkJiDB7OQtMiBQ90msYjD3YiISEN6ndyAiCjUouqKT15envKE12CpyE/Bq7vaImqCAy1yiETMQWIOEnOQmEP4+e4DvQ5147EoMQeJOXgwC0mLHKKq45OdnR30MivnyCs+eyKo46NFDpGIOUjMQWIOEnMIP9994H6Oj01nQ914LErMQWIOHsxC0iIHDnWbhHtK68auYQyNOsJcGyIiijaxFn1e8SEiCjV2fCaRnhCDvJRYAMDetsi56kNERJHBfcWH9/gQEWmLHZ8pcD/Pp/owJzggIqLgsrqv+OhsqBsRUahF1T0+1dXVGBsbQ0xMDCorK4NW7qL8FGzb2xExExxolUOkYQ4Sc5CYg8Qcws93H+h1cgMeixJzkJiDB7OQtMghqq74OJ1OuFwuOJ3BbTwqlCmtI6Pjo1UOkYY5SMxBYg4Scwg/332g16FuPBYl5iAxBw9mIWmRQ1Rd8YmNjYXJZILFYglque6Oz/4jgxh1OJVGarbSKodIwxwk5iAxB4k5hJ/vPnBf8bHZ9fUlh8eixBwk5uDBLCQtcoiqjk9ZWZkm5c5JjUNKnAX9I3bsPzKEyjkpmmwnWLTKIdIwB4k5SMxBYg7h57sPYi36vOLDY1FiDhJz8GAWkhY5RNVQN60YDAav4W6c4ICIiILHc4+Pvjo+REShxo7PFLmv8kTKfT5ERBQZPLO66WuoGxFRqLHjM0WRNsEBERFFBr1ObkBEFGpRdY9PS0sLnE4nTCYTCgoKglq2u+Ozt20ATpeAyWgIavnBpGUOkYQ5SMxBYg4Scwg/332g16FuPBYl5iAxBw9mIWmRQ1R1fLq7u2G322GxWIJ+oJRkJiLOYsLRMScau4axIDsxqOUHk5Y5RBLmIDEHiTlIzCH8fPeBMrmBzoa68ViUmIPEHDyYhaRFDhzqNkUmowHleUkAOMEBEREFj16v+BARhVpUXfEpLS2FEAIGgzbD0Cryk/F5cx/2tA7gwqVzNNlGMGidQ6RgDhJzkJiDxBzCz3cfKJMbOPR1xYfHosQcJObgwSwkLXKIqo5PfHy8puVX5EfGzG5a5xApmIPEHCTmIDGH8PPdB8rkBnZ9XfHhsSgxB4k5eDALSYscONRtGryf5SOECHNtiIgoGnCoGxFRaGje8fnHP/6B888/H2lpaYiLi0NpaSl+8pOfaL1ZTSzMSYLJaEDvUTva+m3hrg4REUUBd8dnzOmC08Uf1YiItKLpULc//vGP+Na3voV/+7d/w5NPPonExETU19ejtbVVk+0NDw8rYwETEhKCXn6sxYTS7ETUtg+ipnUA+alxQd9GMGidQ6RgDhJzkJiDxBzCz3cfuGd1A4AxhwtxMaYJ1o4ePBYl5iAxBw9mIWmRg2Ydn8OHD+Oaa67BunXr8PDDDyuvr1q1SqtN4sCBA8q0d1VVVZpsoyI/5VjHpx9fWpSjyTaOVyhyiATMQWIOEnOQmEP4+e4D9xUfQE5woJeOD49FiTlIzMGDWUha5KDZULfHHnsMw8PDuP3227XaRFh47vOZ3RMcEBFRZDCbjMpDsXmfDxGRdjS74vPuu+8iPT0dtbW1uPDCC1FdXY309HSsWbMGDzzwAJKTkydcv6amBnPnzlW9b3R0FLW1tQCAtLQ0FBUVqdYxGo0wGo1wOv2nBO3q6sLhw4cBAEVFRUhLS1OWOZ1OVFdXAwCSkpIwb9481bqNjY0YGJAdnfKcPADAnmMdn76+Phw8eBAAkJ+fj6ysLNW6u3btghACcXFxWLhwoWrZoUOH0NPTAwAo+//s3Xl4G9WhNvBXu7zvjrd4iePYjp0ECIGkJW0IlIYCpdDlAl1oud0o7Qd92lIKNIRLyy1f4d7SjcJNKZR9Ke13SwO0LKGUQgkEEuzES+w43jd5i2xLljTz/XGikUaWJdvxSLL0/p4nTxIfzdGZd8ajOZozZ6qrYbValTK73Y62tjYAQH5+PgoLC1XLHjp0SOkFr127VlVmtVrh8Xjg8Xhgt9uRmup72KrD4UBzczMAIDs7GytXrlQt29LSgunpaeh0Oqxfv15VNjQ0pAxTLCsrQ2ZmplLmdrvR2NgIAEhPT0dFRYVq2fb2dhw/fhwAUF9fD4PB943m6OgoOjs7AQDFxcXIzc1VLXvgwAEAYnaPqqoqVVlnZydGR0cBADU1NbBYLEpZeno6RkdH4fF40N/fj4KCAtWyjY2NcLvdsFgsqKmpUZX19vZiaGgIALB69WrVJdapqSm0trYCAHJycmY9VKu5uRkOhwMGgwH19fWqssHBQfT19QEAysvLkZGRoZTNzMzg8OHDAICMjAyUl5erlm1ra4PdbgcArFu3Dnq973sLm82G7u5uAEBJSQlycnKUstzcXAwMDMDj8aCtrQ2VlZWqejs6OjA+Lp5NVVtbC7PZrJSNj4+jo6MDAFBYWIj8/HzVsg0NDfB4PLBaraiurlaVdXd3w2azARBTUvrPzjI5OYkjR44AAPLy8lBUVKRatqmpCU6nE0ajEXV1daqy/v5+DAwMAAAqKirmfYzIy8vD8PAw3G43Dhw4MOvbo6U6RtTV1cFo9B1aY+0YkZeXh4mJCUxNTeHAgQOorKxUHSOcTidIW3l5ecrTyL0sRj2mZjwJNbNbsBwSEXMQmIMPsxC0yEHToW5TU1P49Kc/jR/84Af42c9+hn379uGWW25BQ0MDXnvttZDzcrvd7lkzp8myDJfLpZQHMhqNc35oS5KkLCtJsz9YQtXrdruV8poC8RDTnrFpjE7OQParN1iHy+VyQZZlmEymWWUej0dZNnBdpXnU6y0PlJKSonQyAtfVP8Ng9XrXNdi28W9vqHrDZRhoqbZNYIbZ2dnKifdcGbrdblUHwivUtgmXoXfbBCsLVa932XD1BhMqw8LCQqWzFWx5/zYFCreuMzMzkCQp6EFpKTIMltF86w3cX4qKijA+Pq60OZBW++F8fpcjeYwoKiqCJEmw2+2QJCno7zJpK7CjD/h1fBLoWT7BckhEzEFgDj7MQtAiB806PpIkweFw4JZbbsENN9wAANi2bRvMZjOuu+46vPTSSzj33HPnbpjROOvkW6fTKScH/t+o+i8T7OQBEFeDvGXBTnTnW296kgllOck4ZptCY+8E6vN8ZcFO/kwmE2RZDlqvwWBQlg1cV//2zlWv/99z1Ru4rv4ZBqvXu67BOj7zrTda2ybU/jJXhv6v8Rdq28yn3rm+oQhVr3fZUPWebIbh1jVQuHU1m83weDyaZChJ0oJ/b2JxP5zP73KsHSMo8sSzfFxwJNAVHyKiSNPJGn29t2XLFrz55pvYv38/Tj31VOXnLS0tqK6uxh133IHrr78egOgkea9QeKWlpQU9+YgF33jkHex5vx8/OL8GX/twZfgFiIiWieV2PI4kLbPZ9tNX0GGbwtNf34LTy7NPuj4ioni22OOxZp9kgfeHeHn7Wcv5Q7SuSNyXwQkOiIhoKYgrPpzcgIhIS5oNdfvkJz+J++67D88995zqis+ePXsAAJs3b17y92xqalJu5g28WX0prS8RHZ/9naOavcfJiFQOsY45CMxBYA4Cc4i+YNvAYhJfBibSPT7cFwXmIDAHH2YhaJGDZh2f8847DxdddBH+4z/+A5IkYfPmzXj77bdx66234sILL8RZZ5215O/pdDrhcrmC3pi8lE4tzYJeB3SPTqNvfBqFGbH1INNI5RDrmIPAHATmIDCH6Au2DbzP8kmkWd24LwrMQWAOPsxC0CIHTcebPfHEE7juuutw33334fzzz8c999yDb3/723j66ac1eT+j0aj80VKqxYj6YnHV562jI5q+12JEKodYxxwE5iAwB4E5RF+wbZCIQ924LwrMQWAOPsxC0CIHzSY3WIjleDPtbc8ewm//cRSfPbMUP75kXbSbQ0S0JJbj8ThStMzm3x/Yh5eaBvGTS9fhsjNKwy9ARJTAYm5yg3i36cSsO/s6Yu+KDxERLS9WU+Jd8SEiijR2fBZpU7l4qnvLgB2jkzNRbg0REXm9/PLLuOqqq1BTU4OUlBQUFxfj4osvxjvvvDPrtfv378e5556L1NRUZGZm4tJLL0V7e3vE26zc45NAkxsQEUUaOz6LlJNqwer8VAC86kNEFEvuuecedHR04Nprr8WePXtw9913Y3BwEJs3b8bLL7+svK6pqQnbtm3DzMwMnnzySdx///1oaWnB1q1bMTQ0FNE2K7O6JdDkBkREkRZXd0319/fD4/HAYDCgoKBA8/fbVJ6NI4N27OsYwXl12r/ffEU6h1jFHATmIDAHIRFy+NWvfoX8/HzVz3bs2IHVq1fj9ttvx/bt2wEAO3fuhMViwbPPPov09HQAwMaNG1FVVYU777wTd9xxhybtC7YNEnFyg0TYF+eDOQjMwYdZCFrkEFdXfAYGBtDX14eBgYGIvN+ZFeI+n7c6Yut5PpHOIVYxB4E5CMxBSIQcAjs9AJCamoq1a9eiq6sLAOB2u/Hss8/ik5/8pNLpAYCysjKcffbZ+OMf/6hZ+4Jtg0Qc6pYI++J8MAeBOfgwC0GLHOKq4xNpm050fBp6xjHpdEe5NURENJfx8XHs378fdXV1AIC2tjZMT09j/fr1s167fv16HDlyBA6HI2Lt83Z8HBzqRkSkmbga6lZRUQFZlqHT6SLyfsWZSSjOTELP2DTe7RzDWVW5EXnfcCKdQ6xiDgJzEJiDkKg5XHPNNZicnMRNN90EALDZbACA7OzsWa/Nzs6GLMsYHR1FYWFhyHobGxtRVlamumrkdDrR1NQEAMjKykJpqXp6arPZDFmW4f80CcuJWd3G7VM4cOAAAKC0tBRZWVnKazweDxoaGgCIaVtXrVqlqvfo0aOYmJgAANTV1amefTE2NoZjx44BAIqKipCXl6da9uDBg5BlGUlJSVizZo2qrKurCyMj4l7W6upqWK1Wpcxut6OtrQ2AuNIWmNehQ4eUJ6+vXbtWVZaRkYGxsTHIsgy73Y7U1FSlzOFwoLm5GYDYHitXrlQt29LSgunpaeh0ulmd16GhIfT29gIQV/AyMzOVMrfbjcbGRgBAeno6KioqVMu2t7crU+TW19fDYDAoZaOjo+js7AQAFBcXIzdX/Znv3W7JycmoqqpSlXV2dmJ0VIwOqampgcViUcpWrFiB/v5+yLKM/v7+WUN6Ghsb4Xa7YbFYZj29vre3V7kfbfXq1UhJSVHKpqam0NraCgDIyclBSUmJatnm5mY4HA4YDAbU19erygYHB9HX1wcAKC8vR0ZGhlI2MzODw4cPAxDbsLy8XLVsW1sb7HY7AGDdunWq6YVtNhu6u7sBACUlJcjJyVHKysrK0NHRAVmW0dbWhsrKSlW9HR0dGB8fBwDU1tbCbDYrZePj4+jo6AAAFBYWzrrq29DQAI/HA6vViurqalVZd3e3cjyoqqpCcnKyUjY5OYkjR44AAPLy8lBUVKRatqmpCU6nE0ajUflSxau/v1+5UlFRUXHSxwiv4eFh9PT0AEjsY4TT6ZyVzXzEVcfHf6eKlDMqsvHHd3vwVsdIzHR8opFDLGIOAnMQmIOQiDn88Ic/xCOPPIJf/OIX2Lhxo6osVAdwPp1Dt9s96+RElmW4XC6lfK7l/PkPdfMuG+xp5aHqdbvdSnlgmyRJUso8ntnD6VwuF2RZhslkmlXm8XhOql5veSCj0aisR+C6+mcYrF7vugbbRv7tDVVvuAwD+a/rUm6bpKQkZZm5MnS73UGfTxJq24TL0LttgpWFqte7bLh6gwmVYXp6upJDsOX92xQo3LrOzMxAkiRVRzZYvYvNMFhG8613vscIL632w+V4jFiMuOr4RMOm8hMdn6O2aDeFiIgC3HrrrfjRj36EH//4x/jmN7+p/Nz7TbP3m15/IyMj0Ol0qisFczEajbNOvnU6nXJyEOyJ40ajcdbJg/eKz4zHd2IR7ER3vvUGtkmv1ytlwU7+TCYTZFkOWq/BYDipev3/nqvewHX1zzBYvd51DdbxmW+98902Xv7rupTbJty6etczXIaLqdd74/hC6vUuG6rek80w3LoGCreuZrMZHo9HkwwlSVrw700s7ofL8RixGDp5sV2mJbScnxR+ZPA4zv2vv8Ni1OP9XR+F2Rj7bSYimstyPh4HuvXWW7Fr1y7s2rULt9xyi6rM7XYjPT0dV155Je655x5V2Y4dO9De3o6WlhbVz7XM5sm3u3D90wdxdnUefvelM066PiKieLbY4/Hy+yQLwel0wuFwLHrc32JU5qUiO8UMp1vC+z3jEXvfUKKRQyxiDgJzEJiDkCg53Hbbbdi1axduvvnmWZ0eQHzzedFFF+GZZ55RfXh2dnbilVdewaWXXqpZ24JtA99Qt8SZ3CBR9sVwmIPAHHyYhaBFDnE11K2pqUm5QWrDhg0ReU+dTodN5Vl4oXEAbx0dwcayrPALaSwaOcQi5iAwB4E5CImQw1133YWdO3dix44duOCCC/Dmm2+qyjdv3gxAXBHatGkTLrzwQtxwww1wOBzYuXMncnNz8Z3vfEez9gXbBt7n+DhciTOddSLsi/PBHATm4MMsBC1yiKuOT7RsKs/GC40D2NcxgqtRGX4BIiLSzJ///GcAwPPPP4/nn39+Vrl3hHdNTQ327t2L73//+/jUpz4Fo9GI7du3484775w1o5HWrKbEu+JDRBRpcdXxycrKgtvtDnrjlZbOrBA3ye7rGIFHkmHQR3ea2GjlEGuYg8AcBOYgJEIOe/funfdrN27ciBdffFG7xgQRbBt4r/gkUscnEfbF+WAOAnPwYRaCFjnEVaKB86BHSm1hGlLMBhx3uNHcfxxri6I7XWy0cog1zEFgDgJzEJhD9AXbBhaTbzrrRMF9UWAOAnPwYRaCFjnE1eQG0WI06HHaiXt79nWMRLk1RES03CiTG7gS54oPEVGkseOzRM6sEE//fusoOz5ERLQwiTjUjYgo0tjxWSKbyk90fDpGFv00WSIiSkzeKz6JNKsbEVGkxdU9Pq2trcpNUFVVVRF97w0rM2E26DF03IljtimU56ZE9P39RTOHWMIcBOYgMAeBOURfsG1gNfmu+MiyvOinki8n3BcF5iAwBx9mIWiRQ1x1fKamppT5viPNajJgw8oM7OsYxVtHR6La8YlmDrGEOQjMQWAOAnOIvmDbwDu5AQDMeCRl6Fs8474oMAeBOfgwC0GLHDjUbQn5D3cjIiKaL+9QN4D3+RARaUUnx8ANKZIk4fjx46qfpaWlQa9fXv2yV5oH8aXf7UNZTjJe/d7Z0W4OEdGCxcvxWAtaZiPLMip+sAcAsO+mc5GXZjnpOomI4tVij8f8JFtCG8uyoNcBx2xTGJhwRLs5RES0TOh0Ok5wQESkMXZ8llC61YTaQvHw0jfbbVFuDRERLSfKs3w41I2ISBPs+CyxD63JAwC8dHgwyi0hIqLlxDezG6/4EBFpQbNZ3fbu3Yuzzw5+n8sbb7yBzZs3L/l7Dg8PQ5Ik6PV65ObmLnn983FubT7u2duGvc2DcHkkmAyR71vGQg6xgDkIzEFgDgJziL65toF3ZrdEueLDfVFgDgJz8GEWghY5aD6d9e233z6rA1RfX6/Je/X09CjT3kVrRzllZRayU8wYmZzBvo4RfKAy8u2IhRxiAXMQmIPAHATmEH1zbQPvFNZOV2J0fLgvCsxBYA4+zELQIgfNOz5VVVWaXN2JVQa9DmdX5+MP+7vx0uHBqHR8iIho+fHd48OhbkREWoirB5iWlpYql8Si6dxab8dnADdfUBvxJ3DHSg7RxhwE5iAwB4E5RN9c28A3q1tiXPHhvigwB4E5+DALQYscNO/4XHPNNbjsssuQnJyMLVu24Ic//CHOOussTd4rKytLk3oXauuaPJgNenTYptA2NInV+akRff9YySHamIPAHATmIDCH6JtrGyhD3RLkig/3RYE5CMzBh1kIWuSgWccnIyMD1157LbZt24acnBwcOXIEP/3pT7Ft2zb85S9/wUc/+tGQyzc2NqKsrAzp6enKz5xOJ5qamgCIMEpLS1XLtLa2YmpqCgCwYcMGVdnw8DB6enoAiB6kf5gejwcNDQ0AxMOPVq1apVr26NGjmJiYAADU1dXBaPTFNjY2hmPHjgEAioqKkJeXh1SLEWeuysZrrcN4+OX3cEltGpKSkrBmzRpVvV1dXRgZGQEAVFdXw2q1KmV2ux1tbW0AgPz8fBQWFqqWPXTokDLuce3ataqyvr4+DA6KWeUqKyuRmurreDkcDjQ3NwMAsrOzsXLlStWyLS0tmJ6ehk6nw/r161VlQ0ND6O3tBQCUlZUhMzNTKXO73WhsbAQApKeno6KiQrVse3u78qCp+vp6GAwGpWx0dBSdnZ0AgOLi4lnjOA8cOAAASE5ORlVVlaqss7MTo6OjAICamhpYLL6H/k1MTODo0aMAgBUrVqCgoEC1bGNjI9xuNywWC2pqalRlvb29GBoaAgCsXr0aKSkpStnU1BRaW1sBADk5OSgpKVEt29zcDIfDAYPBMOt+tsHBQfT19QEAysvLkZGRoZTNzMzg8OHDAMTvT3l5uWrZtrY22O12AMC6detU34DYbDZ0d3cDAEpKSpCTk6OUSZKE999xiBCnAAAgAElEQVR/HwCQmpqKyspKVb0dHR0YHx8HANTW1sJsNitl4+Pj6OjoAAAUFhYiPz9ftWxDQwM8Hg+sViuqq6tVZd3d3bDZxLTuVVVVSE5OVsomJydx5MgRAEBeXh6KiopUyzY1NcHpdMJoNKKurk5V1t/fj4GBAQBARUXFsjxG+Dt48CBkWY6ZY4TT6QRFhzXBJjcgIoo0zTo+p556Kk499VTl/1u3bsUll1yCdevW4frrrw/b8XG73ZBlWfUzWZbhcrmU8mDLeMsDSZKklEnS7A+V+dYb2Cb/ej0e37d059auwGutw/hX9xQuXG2FyWSaVa/H41lwvf7tnWtd/esNXFf/DIPV613XYMPz5ltvrGybcOvqcrngdruDXkINtW3mU6/L5QpaFqpe77Lh6g1mvhkGW96/TYHCrevMzAwkSVJ1ZIPVu9gMg2U033pjZT+cz++yLMsxdYyg6PBd8WHHh4hICxG9xyczMxMXXnghfvOb32B6ehpJSUlzvtZoNM46+dbpdMrJgf83ql4GgyHoyQMA6PV6pSzYiW6oeo1Go1Ie2Cb/ev1P/s6pzcct/9uIZpsL05Ie6WHaO996A9sbbH39cwpcV/+yYPV61zVYx8e/vaHqDZdhIK22jf/J5FwZ+rfbX6htEy5Dk8kEj8cTtCxUvd5lQ9W7mAw9Hk/I/SXU7024dTWbzar656p3MRlKkhT293whxwjvNomVY4R/vbIsL3hdF3uM8Hg8YY8RpC3/jqr/tlOms3YlxlC3uXJINMxBYA4+zELQIgedHOGv977+9a/j3nvvxfT0tDJsQ5IkZRiUV1pa2oJvZjpw4IAytCNwGEs07PjZ39HUfxz//W8bcMmpJeEXWCKxlkO0MAeBOQjMQQiXw1Idj+OR1p9V1z99AE++3Y3vfbQa15y9eknaHMv4OykwB4E5+DALIVQOiz0eR/STbHR0FM8++yxOOeUU1Vj1eHVu7QoAwIuHB6PcEiIiinW+5/gkxhUfIqJI02yo2xVXXIHS0lKcfvrpyM3NRWtrK+666y4MDAzggQce0OQ909LS4Ha7gw4ZiYZzavPxy1eO4NXmIcy4JZiNkelnxloO0cIcBOYgMAeBOUTfXNvA9xyfxLjHh/uiwBwE5uDDLAQtctAs0fXr1+OJJ57Ab37zG9jtdmRnZ+Oss87CQw89hE2bNmnynoEzLUXbhpJM5KZaMGx34q2jIzirKjIPM421HKKFOQjMQWAOAnOIvrm2gdWUWJMbcF8UmIPAHHyYhaBFDpp1fG644QbccMMNWlW/LOj1OmyvycOTb3fjxcMDEev4EBHR8uO74sOhbkREWuDdqho758R9Pi81DXCaWCIimpNvVrfEuOJDRBRp7PhobGtVLsxGPbpGptE6aI92c4iIKEbxOT5ERNqKq7umjh49qtwEVVFREe3mAACSzUZ8sDIHrzQP4cXDA1izIk3z94zFHKKBOQjMQWAOAnOIvrm2gXeomyNBZnXjvigwB4E5+DALQYsc4qrjMzExocz3HUvOqV2BV5qH8NLhQXxjm/bPZojVHCKNOQjMQWAOAnOIvrm2gTLULUGu+HBfFJiDwBx8mIWgRQ4c6hYB59TmAwD2d47CZndGuTVERBSLrMpQt8S44kNEFGlxdcWnrq4OsixDp9NFuykqhRlJqCtKR2PvBF5pHsKnNpZo+n6xmkOkMQeBOQjMQWAO0TfXNki0Kz7cFwXmIDAHH2YhaJFDXHV8YvlBT+fUrkBj7wRePDSgeccnlnOIJOYgMAeBOQjMIfrm2gbK5AYJMqsb90WBOQjMwYdZCFrkwKFuEfKRE9Na/711CJNOd5RbQ0REsYbP8SEi0hY7PhFSX5yO8pxkTM148HxDf7SbQ0REMcZ7xceRIFd8iIgiLa6upY2NjUGSJOj1emRmZka7OSo6nQ6f2liCO//agqff6cYnNRzuFss5RBJzEJiDwBwE5hB9c20D3z0+iXHFh/uiwBwE5uDDLAQtcoirjs+xY8eUae9icUe55LQS3PW3FrzRbkPXyBRWZidr8j6xnkOkMAeBOQjMQWAO0TfXNrAm2ANMuS8KzEFgDj7MQtAiBw51i6DizCR8sDIXAPDM/p4ot4aIiGJJos3qRkQUaXF1xaeoqAgejwcGgyHaTZnTpzaW4B9HhvH0/i58a/tq6PVLP1XhcsghEpiDwBwE5iAwh+ibaxt4JzfwSDJm3BLMxvj+bpL7osAcBObgwywELXKIq45PXl5etJsQ1kfrCpBqMaJrZBr7OkZw5qqcJX+P5ZBDJDAHgTkIzEFgDtE31zZIt5pgMujg8sgYsjtRnJkU4ZZFFvdFgTkIzMGHWQha5BDfXyfFoCSzAReuLwQAPP1Od5RbQ0REsUKv12FFuhUA0D8+HeXWEBHFH3Z8osD7ANO/vN/HZ/oQEZGiMEN0fHrHHFFuCRFR/GHHJwo2lmUpz/R5js/0ISKiEwozxPC2/nF2fIiIllpc3eNz8OBBZdq79evXR7s5c1I/06dLuQK0VJZLDlpjDgJzEJiDwByiL9Q2UK74JMBQN+6LAnMQmIMPsxC0yCGurvjIsqz8iXWXnFYCnQ54s30EXSNTS1r3cspBS8xBYA4CcxCYQ/SF2gbejk9fAgx1474oMAeBOfgwC0GLHOLqik9SUhJMJhOMxthfLe8zff5xZBh/2N+N685ds2R1L6cctMQcBOYgMAeBOURfqG1QcGKoW99E/Hd8uC8KzEFgDj7MQtAiB50cA91JSZJw/Phx1c/S0tKg18fVBalZ/vRuD6574j2szE7Cq989W5Nn+hARLUSiHo/nIxLZHOwew8d/+Try0yx466Zzl6xeIqJ4stjjMT/Josj/mT5vdYxEuzlERBRlBSeGug3ZnXB5pCi3hogovrDjE0V8pg8REfnLTbHAZNBBloGBBBjuRkQUSez4RJl3Rrc9fKYPEVHC0+t1ylUfTmlNRLS04uquqa6uLng8HhgMBqxcuTLazZkX7zN9OmxT2PN+Hz59+sm3eznmoAXmIDAHgTkIzCH6wm2DwvQkdI1MozfOOz7cFwXmIDAHH2YhaJFDXF3xGRkZwfDwMEZGls/9MjqdTuns/O71jiWZsm855qAF5iAwB4E5CMwh+sJtg8JM7xWf+H6WD/dFgTkIzMGHWQha5BDRjs/u3buh0+mQmpoaybeNeZ89sxRJJgMO9U3gH0eGo90cIiKKIu9Qt94EeJYPEVEkRWyoW09PD7773e+iqKgI4+PjmrxHdXU1ZFmGTre8poXOTDbjsjNW4nevd+A3r7Zha1XeSdW3XHNYasxBYA4CcxCYQ/SF2wZFJ57lE+/3+HBfFJiDwBx8mIWgRQ4R6/h8/etfx4c+9CFkZ2fj6aef1uQ9rFarJvVGwr+fVYHfv3EMrx+x4f3ucawryVh0Xcs5h6XEHATmIDAHgTlEX7ht4L3i0xfnQ924LwrMQWAOPsxC0CKHiAx1e/jhh/Hqq6/i17/+dSTeblkqyUrGxzcUAQDu/XtblFtDRLS8HT9+HNdffz3OO+885OXlQafTYdeuXUFfu3//fpx77rlITU1FZmYmLr30UrS3t0e2wX68V3z64vyKDxFRpGne8RkcHMR1112Hn/zkJygpKdH67Za1r35oFQAxtXWnbSrKrSEiWr5sNhvuu+8+OJ1OfOITn5jzdU1NTdi2bRtmZmbw5JNP4v7770dLSwu2bt2KoaGhCLbYx/8hpjNuPsSUiGipaD7U7Rvf+Aaqq6tx9dVXL2i5xsZGlJWVIT09XfmZ0+lEU1MTACArKwulpaWqZZqamuBwiG/ITjnlFFXZ8PAwenp6AAClpaXIyspSyjweDxoaGgAAaWlpWLVqlWrZo0ePYmJiAgBQV1cHo9EX29jYGI4dOwYAKCoqQl6e+v6cgwcPQpZlJCUlYc2aNaqyrq4uZaaK6upq1Bam48Nr8vBqyxB+/XIzLl8j+qX5+fkoLCxULXvo0CG4XC6YTCasXbtWVXbs2DGMjo4CAFavXq2aTMLhcKC5uRkAkJ2dPWt6wJaWFkxPT0On02H9+vWqsqGhIfT29gIAysrKkJmZqZS53W40NjYCANLT01FRUaFatr29HcePHwcA1NfXw2AwKGWjo6Po7OwEABQXFyM3N1e17IEDBwAAycnJqKqqUpV1dnYq61pTUwOLxaKUDQwMoK+vDwBQUFCAgoIC1bKNjY1wu92wWCyoqalRlfX29ionPatXr0ZKSopSNjU1hdbWVgBATk7OrA59c3MzHA4HDAYD6uvrVWWDg4NKm8rLy5GR4RvSODMzg8OHDwMAMjIyUF5erlq2ra0NdrsdALBu3Tro9b7vLWw2G7q7xUNwS0pKkJOTo5RNTEwo316npaWhsrJSVW9HR4dy311tbS3MZrNSNj4+jo6ODgBAYWEh8vPzVcs2NDTA4/HAarWiurpaVdbd3Q2bzQYAqKqqQnJyslI2OTmJI0eOAADy8vJQVFSkWrapqQlOpxNGoxF1dXWqsv7+fgwMDAAAKioq5n2MsNvt6OrqgtPphE6nw4YNG1T1LodjhP9lf7vdjrY2cXV4IccIu92O4eFhjI2NQafTobKyUnWMcDqdiAdlZWUYHR2FTqfD8PAwdu/eHfR1O3fuhMViwbPPPqvsSxs3bkRVVRXuvPNO3HHHHUveNrvdDkmSoNfrg072k5Nihtmgx4xHwuBxB0qykoPUsvyFyyFRMAeBOfgwC0GLHDTt+PzhD3/An//8Z7z77rsLvjHJ7XbPmtpZlmW4XC6lPNDk5OSc00FLkqQsK0mzv0ELVa/b7VbKA+v3r9fj8QStV5ZlmEymWWUej2dWvV/78Cq82jKEPx7ox0eKcpBh0c9Zr3fZQDabTVnHwHX1zzBYvd51Dba9/Nsbqt5wGQbSatv09vYq6zhXhm63W9WB8Aq2bbzCZejdNsHKQtXrXTZcvcGEyrC9vV3JLtjy/m0KFG5dZ2ZmIEmSqiMbrN7FZhgso/nWG7i/tLW1zbmewPI5Riyk3mDrG5hDsN/leDCfzxy3241nn30WX/jCF1Qd6LKyMpx99tn44x//qEnHx7sNTCbTrA44IB5iuiLDgq6RafSNx2/HJ1wOiYI5CMzBh1kIWuSgWcfHbrfjmmuuwbe+9S0UFRVhbGwMgDhRAsS3oCaTSfVNuqphRuOsDy6dTqecHPh/ozofer1eWTbYiW6oeo1Go1Ie2Cb/eoOd/JlMJsiyHLReg8Ewq94tq3KwoSQDB7rH8dejDlyxLmPOev3/nkvguvpnGKxe77oGO2nwb2+oesNlGKyNWmybwLYHq9e/3YGvn6vecBmaTCblgVsLqde7bKh6F5thYP1ztSlQuHU1m83weDyaZChJ0rx/b4LVG+oYEay9y+UYsZB6/f8OxmQyBf1dThRtbW2Ynp6edXUbANavX4+//e1vcDgcUbnRuDDjxENMx+J7ggMiokjSyRp9vdfR0TFruFOgiy++GH/6058gSZIyDMorLS0t5AlcMH19fcoJZ+Cwj+Vkz/t9+MYj+5GZbMI/b9iOZPPCOnnxksPJYg4CcxCYgxAuh6U6HseS4eFh5OXl4ZZbblFNcPDPf/4TH/zgB/HYY4/hsssuUy3zn//5n7jxxhvR29ur5BQsm87OzgUPy25oaFC+BDzttNNmtbWnpwf/9c8RvHpsCj84vwZf+7AYnhpPQy4BMbTaO3x3zZo1CTssu6OjQ8m3qKgoYYdl9/b2or+/X6k3UYdle9sb7hgBxPewbCD0MWJ6elrJyGs+n1WaXfEpKCjAK6+8MuvnP/nJT/Dqq6/iueeem3XQOFnxcjLz0boClOUk45htCk/s68KXPhi6AxkoXnI4WcxBYA4CcxCYw2yhrnKFuwK2mGHZBoMh6HBKwDeEMevEeUPgzG7xMuQSEB0E70lYIg/LzsrKwvDwsNL2YPUmwrDsgoICpcOayMOygfkdI7z/DtamueqNt2PEYmjW8bFardi2bdusnz/wwAMwGAxBy0gw6HX4ytZVuPlPDdj92lF8bnMZTIbl+20rEVEs8n7b7P2219/IyAh0Op3qakEwixmWPZ+hv/mpZgBTs57lE09DLuc7fDreh2XPZ+hvogzLnu/+EijehmVHYz9cjseIxdBsqNtcvvjFL+Lpp59WLl0B8Tm04mQ5XB6cdcfLGLbP4O7LTsHFpxRHu0lElADi8Xg811A3t9uN9PR0XHnllbjnnntUy+zYsQPt7e1oaWlRfhbJbP7a2I+vPvQO1pdk4H+/edaS109EtJwt9ngc8U+yBx54QNXpoeCsJgO++IFyAMBvXm2Pm5mWiIhihdFoxEUXXYRnnnlG9QHa2dmJV155BZdeemnU2laUyYeYEhEtNc2f4xNJoW6QWo4+t7kMv97bhsN9E3iuoR8fWze/sfnxlsNiMQeBOQjMQUikHJ577jlMTk4qnZpDhw7h6aefBgB87GMfQ3JyMm699VZs2rQJF154IW644QY4HA7s3LkTubm5+M53vqNJu+azDbwPMR0+8RBTs3H5XnGbSyLti6EwB4E5+DALQYsc4qrjE+oGqeUoM9mMr2xdhbtfasV/PncY59Tmw2KcPT4yULzlsFjMQWAOAnMQEimHq6++WpmlCACeeuopPPXUUwDE7Ebl5eWoqanB3r178f3vfx+f+tSnYDQasX37dtx5552zZjVaKvPZBv4PMR2YcGBldvw9yyeR9sVQmIPAHHyYhaBFDnHV8Znvs22Wk699eBUe39eJrpFpPPB6hzKtaSjxmMNiMAeBOQjMQUikHLzT24azceNGvPjii9o2xs98toFOp0NBhhWdI1PoG4/Pjk8i7YuhMAeBOfgwC0GLHCI+uUEw8Xgz7VJ6+p1ufPepA0izGLH3e9uQk2oJvxAR0SLweDy3SGfzb/e+gX8dHeEEN0REAZbN5Aa0cJeeWoz64nQcd7rx3y+2hF+AiIiWvcIT9/lwggMioqXBjs8yoNfrcPMF4qauR//ViZaB42GWICKi5a7wxMxu/ez4EBEtCXZ8lonNq3Lw0boVkGTg9j2Ho90cIiLSWNGJKz69Y9NhXklERPMRV5Mb9PX1KU8hLiyc39TPy8kPzq/Fy02D2Ns8hFdbhvDhNcFnHIr3HOaLOQjMQWAOAnOIvvlug4KME1d8JuLzig/3RYE5CMzBh1kIWuQQVx2fwcFBZb7veNxRynNTcOWWcuz+x1H8+C+H8MHKrTAaZl+0i/cc5os5CMxBYA4Cc4i++W6DQuWKT3x2fLgvCsxBYA4+zELQIgcOdVtmvrW9CpnJJrQM2PHE213Rbg4REWmk0O8hpk63J8qtISJa/uLqik9lZSUkSYrraVczkk247pwq7PrzIfzXX1tw0YYipFvV85snQg7zwRwE5iAwB4E5RN98t0F2ihlmox4zbgmDE864e5YP90WBOQjMwYdZCFrkEFcdn9TU1Gg3ISI+u7kMv3/zGNqHJvHLl4/gxo/VqsoTJYdwmIPAHATmIDCH6JvvNtDpdCjMsOKYbQq9Y9Nx1/HhvigwB4E5+DALQYscErsruUyZDHrcfIHo7Ox+rR37O0ej3CIiItKCd7hbvE5wQEQUSez4LFPba1bgE6cUQZKB7z55ANMzHP9NRBRvCk/M7BavExwQEUVSXHV8HA4Hpqen4XAkxgfErR+vR0G6Fe3Dk7jj+Sbl54mWw1yYg8AcBOYgMIfoW8g2UK74jMffs3y4LwrMQWAOPsxC0CKHuLrHp7m5WZn2bsOGDdFujuYykk34v59ajy/c/xYe+GcHPrJ2BT64OjfhcpgLcxCYg8AcBOYQfQvZBsqU1uPxdwLEfVFgDgJz8GEWghY5xNUVn0T0oTV5+NzmUgDA9546gAmHK8otIiKipeId6tYfhx0fIqJIi6srPtnZ2coTXhPJjR+rxWutwzhmm8Kt/3sI121JzBwCJer+EIg5CMxBYA7Rt5BtUJgprvj0xeFQN+6LAnMQmIMPsxC0yEEny7K8ZLUtkiRJOH78uOpnaWlpCT9/+UK83TGCz9z7BiQZuPfzG/HRuoJoN4mIliEej+cWjWxGJmdw2m1/AwA0/2gHLMbEPhEiIgIWfzzmJ1mcOL08G1/9UCUA4MZn3sew3RnlFhER0cnKSjbBYhQf1QPjPK4TEZ0MdnziyLc/UoWagjTYJmdw0x/fRwxczCMiopPgfYgpEJ/D3YiIIokdnzhiMRpw12c2wGTQ4YXGATz8r85oN4mIiE6Sd4KDPk5wQER0UuJqcoOWlha43W4YjUasWbMm2s2JirqiDFx5Wg527xvGLf+vAZW5KfjA6txoNysquD8IzEFgDgJziL6FbgPflNbxdcWH+6LAHATm4MMsBC1yiKsrPtPT05iamsL0dHx9OCzUhZUWbC21QpKBqx/Zj47hyWg3KSq4PwjMQWAOAnOIvoVuA+/MbvE2pTX3RYE5CMzBh1kIWuQQVx0fnU6n/Elker0e3zg9A2tyzBifduHLv387IZ/vw/1BYA4CcxCYQ/QtdBsUnBjq1jsWXx0f7osCcxCYgw+zELTIgdNZx7HBCQc+/svX0T/hwLbqPPz2yk0w6BP7l4iIQuPxeG7RyualwwP49wffRn1xOp791lZN34uIaDmIuems33vvPVxwwQUoLS1FUlISsrOzsWXLFjz88MNavSUFyE+34n++cDqsJj32Ng/hJ88djnaTiIhogQq8s7rF2RUfIqJI06zjMzY2hpUrV+L222/Hnj178Pvf/x7l5eX4/Oc/jx/96EdavS0FWFeSgbs+fQoA4H9eO4on3+6KcouIiGghik4MdbNNzsDh8kS5NUREy1fEh7pt3rwZvb296Oz0TbXMoRXa+++/teDul1phMujw2Fc24/Ty7Gg3iYhiEI/Hc4tWNrIso3bn83C4JLz6vW0oy0nR9P2IiGLdYo/HEZ/OOjc3F4ODg5rUPTQ0BI/HA4PBgLy8PE3eYzkIlsO151ShdfA49rzfj6/8/m088uXNWFuUHuWWaov7g8AcBOYgMIfoW+g2EA8xTcLR4Un0jTvipuPDfVFgDgJz8GEWghY5aN7xkSQJkiRhdHQUTz31FF544QX88pe/DLtcY2MjysrKkJ7uOzl3Op1oamoCAGRlZaG0tFS1TGdnJ7wXsAIDGh4eRk9PDwCgtLQUWVlZSpnH40FDQwMA0VtctWqVatmjR49iYmICAFBXVwej0Rfb2NgYjh07BgAoKiqa9b4HDx6ELMtISkqaNQd5V1cXRkZGAADV1dWwWq1Kmd1uR1tbGwAgPz8fhYWFqmUPHToEl8sFk8mEtWvXzqpXkiQAQFJSElJTU6HX63Dnpzege2QKB3sm8G+/eR0/v6QSZ5+qblNLSwump6eh0+mwfv16VdnQ0BB6e3sBAGVlZcjMzFTK3G43GhsbAQDp6emoqKhQLdve3q70zOvr62EwGJSy0dFR5QpgcXExcnPVzx06cOAAACA5ORlVVVWqss7OToyOjgIAampqYLFYlLLu7m54PGJYiMfjQUFBgWrZxsZGuN1uWCwW1NTUqMp6e3sxNDQEAFi9ejVSUnwnGlNTU2htbQUA5OTkoKSkRLVsc3MzHA4HDAYD6uvrVWWDg4Po6+sDAJSXlyMjI0Mpm5mZweHD4j6sjIwMlJeXq5Zta2uD3W4HAKxbt071rYbNZkN3dzcAoKSkBDk5OUpZT08P3G43AGBiYgKVlZWqejs6OjA+Pg4AqK2thdlsVsrGx8fR0dEBACgsLER+fr5q2YaGBng8HlitVlRXV6vKuru7YbPZAABVVVVITk5WyiYnJ3HkyBEA4ne1qKhItWxTUxOcTieMRiPq6upUZf39/RgYGAAAVFRUzPsY0dvbC5fLpfx7w4YNqnoT5RgRmENlZSVSU1NVGZK2vNvAZDLN+8O8MMN6ouMTP9PbLiaHeMQcBObgwywELXLQvOPzjW98A/feey8AwGw24+c//zm+9rWvhV3O7XYjcBSeLMvKB7b3RG6+JElSlvV2CvyFqtftdivlgW3yr9d7kh1YryzLMJlMs8o8Hs9J1estD8V/XZPNRvzP5zbgs/e9gSOjblz7/9rx+IoC1ZUf77oGmzrQv72BGYbbNv4ZBmujFtsmsO3B6nW73UEvi4baNv7rGmrbBCsLVa932XD1BhMuw8D652pToHDrOjMzA0mSVB3ZYPUuNsNgGc233lDHiGDrm4jHCJfLFfR3mWKPMsFBnD3Lh4gokjTv+Nx444348pe/jMHBQfz5z3/GN7/5TUxOTuK73/1u6IYZjbNOvnU6nXJy4P+NqldSUtKc31bq9Xpl2WAnuqHqNRqNSnlgm/zrDXbyZzKZIMty0HoNBsNJ1ev/t7/MzEzlG/zAdc1IMuM/tufjlr1DaLW5cMXuN/Go37A377oG6/j4tzew3nDbxj/DQFptmxUrVihXBubK0L/d/kJtG/9l5qrXe2l2IfV6lw1V72IyLCsrU67ahFvXQOHW1Ww2w+PxaJKhJEkL/r0JtR+WlZWht7cXTqcz6H6WKMeIsrIy2Gw2TExMQK/XB/1dJm2VlZVBkqQF3RvkneCgezR+rvgsJod4xBwE5uDDLAQtcoj45AZXX301du/ejd7eXuWyFW+mjbwJhwuf/+1bONA1hsxkEx758pmoK8oIvyARxTUej+cWzWyeb+jH1x9+B7mpFrzxg+0wGbg9iChxxdxzfOZyxhlnwO12o729PdJvTX7SrSY89O9n4JSVmRibcuGzu/+Fxt7xaDeLiIiCOKc2H7mpFgzbnXjx0EC0m0NEtCxFvOPzyiuvQK/Xz7o5mCIv3WrC7wM6Pwe6xqLdLCIiCmAy6PGZ08VEKo++1Rnm1UREFIxm9/h89atfRXp6Os444wysWLECw8PDeOqpp/DEE0/ge9/7niazVHgnRNDpdEHHyyeKheTg7fx84bdv4b2uMXzm3jfw009vwMc3FIVcbjng/iAwB4E5CHjoXj4AAB8lSURBVMwh+ha7DS7bVIpf723Da63D6LRNoTQnOfxCMYz7osAcBObgwywELXLQLM0tW7bgd7/7HR588EGMjY0hNTUVGzZswEMPPYTPfe5zmrxnY2OjMu1d4FS1iWShOXiHvf2fx97FK81D+D+PvYvm/gl85yPV0OuX743O3B8E5iAwB4E5RN9it0FpTjK2VuXitdZhPL6vE9fvqAm/UAzjvigwB4E5+DALQYscNBvq9qUvfQl///vfMTQ0BJfLhdHRUezdu1ezTg+dnDSrCbuv3ISvfVgMQfzVK2346kPvwO5c2LThRESknc+eKZ5N9eTb3XB55p66noiIZour62fp6elwu90JfVkQWHwOBr0OPzi/FtUr0nDDM+/jxcMD+OSv/4ndV56OldnLb0gF9weBOQjMQWAO0Xcy2+Cc2hXIS7Ng6LiY5OD8dYXhF4pR3BcF5iAwBx9mIWiRQ8Snsw6G06fGnnc7R/G1h97B4HEnspJN+PVnN2JLZU60m0VEGuPxeG6xks1PX2jCr15pw9aqXDz072dG9L2JiGLBspnOmpaHU0uz8L/fPAvrSzIwOuXC5377L/z0hSY43bOfEE9ERJFz2aZS6HRQJjkgIqL5YceH5lSQYcWTX9uCS08rhkeS8atX2nDxL19HQw+f90NEFC0rs5OxtUrMjPrYPk5tTUQ0X+z4UEhWkwH/9ZlTcM9nT0N2ihlN/cfxiV+9jp+92MIba4mIouSKM1YCAJ56uwszbh6LiYjmI67ummpvb1dugkrkB6RqkcP56wqxqSIbP/xTA55r6MfPXmzF3w4N4K7PbEBNQfqSvMdS4/4gMAeBOQjMIfqWYhuoJjk4PICPLcNJDrgvCsxBYA4+zELQIoe4uuJz/PhxTExMzLrZKdFolUNuqgW//uxp+PnlpyIz2YTG3glc9It/4L/+2hyT015zfxCYg8AcBOYQfUuxDUwGPT5zegkA4LG3ludwN+6LAnMQmIMPsxC0yCGuOj6kPZ1Oh49vKMJfv/0hnFu7Ai6PjJ+/fATbfroXD795jMPfiIgixH+Sg2O2yWg3h4go5sXVdNYej2/GMYPBsCRtW44ilYMsy3i+oR93PN+EjhMzC63KTcH1O2rw0boV0Ol0mr33fHB/EJiDwByEcDnEypTNsSgWP6u+cP9b+HvLEK7eVonv76g5qboijb+TAnMQmIMPsxBC5bDY43FcdXwoOlweCY+91Ym7X2yFbXIGALCxLAs3fqwGG8uyo9w6IloIHo/nFovZPN/Qj68//A5yU834x/e3w2pK3JMkIkocfI4PRY3JoMcXtpRj7/e24VvbV8Nq0uOdY6P45D1v4DP3voEXGvvhkaLevyYiijvn1OZjRboFw/YZXPXAPhx3uKLdJCKimMUrPrTk+scd+O+/teAP+7vhPtHhKc1Oxhc/UI5Pn16CNKspyi0kornweDy3WM3mn23D+MqDb2NyxoP64nT87otnIC/NEtU2ERFpiUPdAIyOjkKSJOj1emRlZS1lE5eVWMmhb3waD71xDI++1YmxKfEtZKrFiM+cvhJf2FKG8twUTd8/VnKINuYgMAchXA6xenIfC2L5s+r97nF88XdvwTY5g7KcZDx01ZkozUlekrq1wt9JgTkIzMGHWQihcljs8TiunuPT2dkJl8sFk8mU0DtKrORQmJGE63fU4Fvbq/DMu924/x9H0TY0iftfP4r7Xz+KDSUZuGhDES7aUIQV6dYlf/9YySHamIPAHATmEH1abIN1JRl4+uoP4PO//ReO2aZw6T3/xINXbUJdUcaS1K8F7osCcxCYgw+zELTIgV/hkeaSzAZ89swy/O3bH8aDV52BbdV5MOh1ONA9jh/95TA2/+dLuOy+N/DIv45h9MTkCEREtDAVuSl45uoPoKYgDcN2Jy6790280WaLdrOIiGJGXA11Gx4eVi6J5ebmLmUTl5XlkMOw3Yk97/fhf9/rxdvHRpWfG/U6nFaahbOqcnFWVS7WF2fAaFhc/3w55BAJzEFgDkK4HDjUbW7L5bNqwuHClx98G28dHYHZoMfNF9biUxtLkGyOrUEe/J0UmIPAHHyYhRAqB97jQ8tW9+gUnj0oOkGH+iZUZWlWIz5QmYOzqvLwgcocVOSkQK+P7vOBiOIZj8dzW07ZOFweXPv4u3ihcQAAkGYx4hOnFuOKM0tRW5ge5dYREZ0cdnwoLnTapvDakSH8o3UYrx8ZxoTDrSpPsxqxviQD64ozsaEkA+tXZqIowxr1h6USxYtEPB7b7XbcfPPNePLJJzEyMoKamhrccMMNuOyyy1SvW27ZeCQZv3v9KB568xiOnXjINACcWpqJK84oxYXri5Bk5nN/iGj5YceH4o5HkvF+zzj+0TqE11qH8V7XGJxuadbrclPNWLMiDZV5qViVl4JVealYlZuC4swkXh0iWqBEPB6fd9552LdvH37yk59gzZo1ePTRR7F792488sgjuOKKK5TXLddsJEnGP9tsePStY/hr44DymIFUixGnrMzEupIMrC/OwLqSDBRnJvGLJCKKeez4UNxzeSS0DBzHwe7xE3/G0Nx/XPkQD2Qx6lGek4KiTCsKM5NQmH7i7wwrCjKsyE+zINVi5Ic8kZ9EOx7v2bMHF1xwAR599FFcfvnlys/PO+88NDY2orOzEwaDuCoSD9kMHnfgqbe78fi+TnSNTM8qz04xY11xBqoL0lCYYT3xRxw3c1Mt/DKJiGICOz4ADhw4oEx7t2HDhqVs4rKSSDk4XB4c7pvAkUE72ocn0T5kR/vQJDpsk3B5wu/aZoMeWSkmZCWbkZ1iRlaKGVnJJqRZTUi1GJFmNSLFbESq1Yg0ixHJFiMsRj2sJgOsJj2sRgOsJgMsRn3MnhAk0v4QCnMQwuUQDyf3C/GVr3wFjz/+OEZHR2E0+m7+f+yxx3DFFVfg9ddfxwc+8AEA8fVZJUkyDvVN4GD3ON7vGcP7PeNo6pv7iyQAMBl0yE+zIjvFjIwkEzKSTEg/8XdGkglpViOSzQYkm8VxMdlsRJLJgCSzOEaajXqYDSf+NurR+P5BuN1u/k7GwP4QC5iDD7MQQuXA5/hQQrKaDDi1NAunlqrnd3d7JLz4xrvoGnNgbEYHQ1ou+sen0TfuEH/GpjE548GMR8LAhBMDE86TbotRr4PJoIfRoIPZoFf+bTLoYdDrYNDpoNfrYNADBp0OBr0Oep34o9NB/FsP6CD+r9Pp4O1K6XSADlCuTvl3sdQXrGZ3viYmxiFJMgx6HdIPvH3S6xlOqO6ff1t1Aa+c68JbqGWgC/rPoFfxxkZHIckSDHo9Mg+9G/a95nibIMssvMO75F3kIBXmp1lxw/k1S/1OcaehoQG1tbWqTg8ArF+/Xin3dnziiV6vQ31xBuqLMwCUAhBfJDX3H8fBnnF0DE+ib3wavWMO9I87MHjcAZdHRs/YNHrGZl8pWgwdAKMeMOh1MP+xXzlWKsdMvQ56HZRjpe9n4ufBjp967zHyxGt0fv/GiWOr973FcdV7vPX+XKf8PvmOvzpVm5V/z3H8CVwmHP+HNGY3vTfv5eLNiFY5xOZ3kiGNjojPK71Oj6zm+N4nkkwG/PiSdRF7v7jq+CQnJ8Ptds/6AEs0zAEwGvSoXJGOspxkGI1GVFVVzXrN9IwHI1MzGJ2cwcjkDEanTvw9OQO70wO70wW70y3+7XBh0unB5IwbDpcEp8sDh9ujuqrklmS4JQ/giuSaLlCPI9otiA3HlubELZatyksJ2vHh8UHNZrNh1apVs36enZ2tlIfS2NiIsrIypKf7ZkpzOp1oamoCAGRlZaG0tFS1jCzL0Ol0cLvVk7cAYvrWnp4eAEBpaanqoX0ejwcNDQ0AxDebge0+evQoJibEzJh1dXWqbTw2NoZjx44BAIqKipCXl6da9uDBg5BlGUlJSfj85jWqsq6uLgwO2zA67UFybjGmPTqMT7swPu3C0PgkuvptsM9I8OhNkA0mTM94MDXjgcPlwcSUAw63BJcHcEky/C8oyQBckvi5I0gWCaljKvxrEgFz8InzLFLNenxmlQSTyYS1a9eqyvR6vXKstNvtSE1NVcqczsV9YR1Xn3zBTm4TEXMQwuWQZDag2JyE4sykRb+HR5LhcIkPeJdHhssjnfij/rdHkiHJ4m/vH7ckQ5ZlyAAkWZwQyLIMWRb/9w5ClQHldcoPAHh/4v+6SJlrgKwcohVzLzP3C0Otk3998iKWCduOIHXP12IHEIfKb6Eyk8xBf87jw2yhvp0P98292+2etY/IsgyXy6WUB7JYLJicnAxanyRJyrKSNHsyl1D1ut1upTywTf71ejyeoPXKsgyTyTSrzOPxQPa4kWkG6lZmICnJd8ycmJhAS4v4QqWgoAAlJSWqZQOHqngkGTNuCTNuCR1d3ejtH4RHlrGyrBxJySlweSR4JBn2KQeOtLVDkoG09HTk5a+AR5YhnTh+dnZ1weF0AtChvKJCOX5KsoyxsXHYbCOQAeTm5SElOUUcU0+sS1dXF2QAVmsS8vLzlV9YGcDAwCAcDgdkACUlJartb5+cxIhtBACQmZWJ1NQ0VdZdXV0AALPZjBUrVqhysNlsmJyaUnIyGX05TzumMTw8DABIT0tHRkaGatme3h5IkgSj0YjCgkLl5zLEunqH++Tn58Ni8f3ez8zMYGBgEACQmpqKrKxMVb39/f1wudzQ6XQoKSlWlU1MHMf4+DgAIDc3F0lJVqXM4/agt68PAJCcnIScnBzVsoODQ8pJaUlJsTpD+yRGR8Wz+7KyspCamuJbH1lGd7fo9FssFuTnqzvnNpsNU1PiS6uiwkIYjL4ZCaenHUqGGRkZSE9PUy3b3d1zYv82oqCgQFU2OjoGu90OAFixIh9msy9Dp3MGg4Miw7S0NGRmqrdNX18/3G43DAY9ioqKVGXj4xPKFxF5ebmwWn0Zulxu9Pf3n8gwGTk52aplBwYGMTMjHui+cqX6d8put2N0dAyA+IImJSVZKZMkWfnixGq1Ii9P/eyb4eFhTE+L39eioiIY/J6TODU1rXzRk5mZgbS04BmK/TtfVTYyMqoc0woKCmAy+boXDocTQ0NDAIJnODTQrxybAmVlZSk5BR4PF3unTlx1fIgizaDXIcViRIqFv0pEy1FOTk7QqzojI+IE13vlZy5G4+wJUnQ6ndKBCHZlzWg0Bu1gAOIbTm9ZsLHq8603sE3+9XonawisV5bloPUaDIaTqtf/b4NehySzuO8nP90KOMTJYGVequrbXIfDgZRpcVKcnZ2BlSvVJ8EtpglMT09Dp9Nh/Xr1CefQkAW9vaJjWFZWgMxM3wm/2+1GY7I4GU1PT0dFRZlq2fZ2330D9fVlqnUaHR1FZ6foNBYXF816oOKBA2K55ORkVFWpr8Z1dhqVE/6amnJYLBalbGJiAkePivauWLFi1ol5Y+M03G43LBYLamrU9fb29mJoSLRx9epSpKT4OhJTU1NobRUnzzk5ObM6pc3NbjgcDhgMBtTXV6rKBgcH0dcntnV5eYmqMzYzM4PDh0UHJCMjA+Xl5apl29qgdCTWrVul2o9tNhu6u8UJa0lJsarTJEkS3n9fnDynpqaislLdpo4Og9IZq60tV3VQxsfH0dEhMiwsLER+vvrEvKFhGh6PB1arFdXV6nq7u7ths4n9vqqqDMnJvo7E5OQkjhwRGebl5c3q3DQ1ueB0OmE0GlFXp663v78fAwNi3SsqVga5Kiw6IMGuCre2Spg60VHesEFdr7gqLP5dWloS5KqwyDD4VWG931XhiiBXhcX+Hfyq8KRyVXjNGnWburq6lGNmdXWZqpNnt9vR1iY6Nvn5+SgsLFQte+iQU/lyJJD/sSfweLjYianianIDIiI6OYl2PP7qV7+Kxx57bNbkBo8//jguv/xyTSY3ICKik7PY47FmR+uXX34ZV111FWpqapCSkoLi4mJcfPHFeOedd7R6SyIiogW55JJLYLfb8Yc//EH18wcffBBFRUU488wzo9QyIiJaapqNz7nnnntgs9lw7bXXYu3atRgaGsJdd92FzZs344UXXsD27duX/D07OzuVm3YDLxsmEuYgMAeBOQjMQWAOaueffz4+8pGP4Oqrr8bExARWr16Nxx57DM8//zwefvjhoMO3Tha3gcAcBOYgMAcfZiFokYNmHZ9f/epXs8ZY7tixA6tXr8btt9+uScdndHRUGSeYyDsKcxCYg8AcBOYgMIfZnnnmGdx0003YuXMnRkZGUFNTg8ceewyXXXaZJu/HbSAwB4E5CMzBh1kIWuSgWccnsNMDiJvV1q5dq8x8QkREFG2pqam4++67cffdd0e7KUREpKGITm4wPj6OsrIybN++Hc8884zy82A3KHV2di742QjNzc2YnhYzjZxyyimqslh4NsKaNbOfjeCbBaM6yCwYbQDmmgXjkNILDpz3vKurS5mlaPXq1bNmymlubgYgZitauXKlatmWlha/mXLWq8qGhobQ29sLACgrK5s9U05jIwDvTDkVqmXb29v9ZsqpDzJTTicAoLi4OMhMOQcAeGfKUU/F29nZ6TdTTo1qphybzaZ0sgsKCoLMlNPoN1OO+nknYqYcMf3i6tWrg8yU0wpgrplymv1myqlXlYmZcsQ0oOXl5UFmyjkMYK6Zctr8ZspZF2SmnG4AYgpW/5lypqenlW2elpYWZKacDr+ZcmqDzJTTAWCumXIa/GbKqVaViZlyxH5YVVUVZKacIwDmmimnyW+mnDpVmZgpZwAAUFFRMe9jhNPpREdHh7J/Bz4FOlGOEU6nE4ODg7DZbNDpdKisrFQdI6anp5VpVL14A7+wVJMbOJ1O5Vk+/sesRMMcBOYgMAcfZiGEymGxx+OIzsF7zTXXYHJyEjfddFPY1y7m2QiSJAX9ubcsFp+NcDL1zjXvuf+D8YLNex6qXu+6Bpsm0L+9oeoNl2EgrbaN0WhUlpkrQ7fbHfSXJNS2CZehd9sEKwtVr3fZcPUGEypDi8Wi5BBsef82BQq3rjMzM5AkKeh9EEuRYbCM5ltv4P5isVh4jIDIIdwxgrSVyCcy/piDwBwE5uDDLAQtcohYx+eHP/whHnnkEfziF7/Axo0bw76ez0ZY2LMR5qo32Lznoer1rmuwjs98642VbRNuXb3rGS7DxdTr8XiCloWq17tsqHpPNsNw6xoo3LqazWZ4PB5NMvQ+sG+x9cbKfrgcjxFERETxKCJD3W699Vbs2rULP/7xj3HjjTfOKuezEYiIYgOPx3NjNkREsSFmh7p5Oz27du0K2ukBgg+tCDbUJBz/ANLS0ha8fLxgDgJzEJiDwByEcDkEO/Zy+JvAz6qlxRwE5iAwBx9mIYTKYbGfVZpe8bntttuwc+dO3HzzzbjtttvmfJ3b7cbk5KRWzSAiopOQkpISdCheouFnFRFR7JrPZ5Vmn2R33XUXdu7ciR07duCCCy7Am2++qSrfvHmzVm9NRERERESkotkVn23btuHVV1+ds9z/bfktGhFR7OIVH4GfVUREsWs+n1URfY7PXPhhQkQUu9jxEfhZRUQUu5ZNx0eSpFk3Kel0Ok6rSkQUYbIsz7pBVK/Xc+Yy8LOKiChWLPazKiY6PkRERERERFriV3hERERERBT32PEhIiIiIqK4FxcdH7vdjuuuuw5FRUWwWq045ZRT8Pjjj0e7WZo6fvw4rr/+epx33nnIy8uDTqfDrl27gr52//79OPfcc5GamorMzExceumlaG9vj2yDNfDyyy/jqquuQk1NDVJSUlBcXIyLL74Y77zzzqzXxmsGAPDee+/hggsuQGlpKZKSkpCdnY0tW7bg4YcfnvXaeM4hmN27d0On0yE1NXVWWbxmsXfvXuW+k8A/gY8VePHFF7FlyxYkJycjNzcXX/ziFzE4OBillsc/flbxs4qfVfysCoafVZH7rIqLjs+ll16KBx98ELfccguee+45bNq0CZdffjkeffTRaDdNMzabDffddx+cTic+8YlPzPm6pqYmbNu2DTMzM3jyySdx//33o6WlBVu3bsXQ0FAEW7z07rnnHnR0dODaa6/Fnj17cPfdd2NwcBCbN2/Gyy+/rLwunjMAgLGxMaxcuRK33377/2/vXkKiev8wgD/VKFbiddKYUoMiyUZRIovALCS0MEjCIsIkSKK0G5mSFWnYZVELC6xcuCjNYioJa8CMJqGQLtTCwI3dEAPHtMwGrQa/v0V/z99xZvT3A2emOef5wCx837N4z4PnPLyOnAOz2Yxr165hwYIFyMvLQ2VlpXKc2nMYr7u7G8XFxTAYDE5zWsjizJkzaGtrc/gYjUZlvrW1FevXr0d0dDTu3buHqqoqPHr0CBkZGfj586cPV65e7Cp2FbuKXTUeu8rLXSV+7sGDBwJAbty44TC+bt06MRgMYrfbfbQyzxoZGZGRkREREent7RUAcvLkSafjcnNzRa/Xy8DAgDL28eNHCQgIkJKSEm8t1yN6enqcxgYHByU6OloyMjKUMTVnMJEVK1ZITEyM8rPWcsjOzpaNGzdKfn6+zJ4922FOzVlYLBYBICaTacLjli9fLgkJCfL7929l7NmzZwJAqqurPb1MzWFXsavGYlf9H7uKXTWRqe4qv//Gp7GxEcHBwcjNzXUY37lzJz5//oznz5/7aGWe9W8eoWq323H//n1s3rwZISEhynhcXBzWrl2LxsZGTy/To6KiopzGgoODkZCQgK6uLgDqz2Aier1eeZ691nKoq6tDa2srqqurnea0loUr3d3dePnyJfLy8hzeebBq1SosXrxYExl4G7vKPbVfk+yqibGr2FXueKKr/H7j8/btWyxZssTphUVJSUnKvFa9e/cOQ0NDShZjJSUlobOzE8PDwz5YmecMDAzg9evXWLp0KQBtZTAyMgK73Y7e3l5UV1ejubkZpaWlALSVg9VqxcGDB3Hu3DnMnz/faV4rWRQWFkKn0yEkJASZmZl4+vSpMjd6X3SXgZbvm57CrnJPK9fkWOwqdhW76g9vd5Xfb3z6+voQERHhND461tfX5+0l/TVGz91dPiKCr1+/entZHlVYWAibzYZjx44B0FYGe/fuRUBAAKKionDo0CFcvHgRu3fvBqC9HOLj47Fnzx6X82rPIjQ0FAcOHMDVq1dhsVhQVVWFrq4urFmzBs3NzQAmz0DL901PYVe5p/Zr0hV2FbuKXeWbrtJNfsjfb6Kv0flGbe3kc+LECdTX1+PSpUtYtmyZw5wWMigrK8OuXbtgtVrR1NSEoqIi2Gw2FBcXK8eoPYc7d+6gqakJb968mfR81JpFSkoKUlJSlJ/T0tKQk5ODxMRElJSUIDMzU5lzd57+fP5/M7X+zk0VreTDrmJXsat811V+v/GJjIx0uePr7+8H4HqXqBWRkZEAXP8lsb+/H9OmTUNYWJi3l+URFRUVqKysxOnTp1FUVKSMaymD2NhYxMbGAgA2bNgAADh69Cjy8/M1kcOPHz9QWFiIffv2wWAw4Nu3bwCAX79+AfjzRKGAgABNZDFeWFgYsrOzceXKFQwNDU2agZbvm57CrnJPS9cku4pdxa5yzxtd5ff/6paYmIiOjg7Y7XaH8fb2dgBweCSe1ixcuBAzZ85Ushirvb0dixYtQlBQkA9WNrUqKipQXl6O8vJylJWVOcxpJQNXUlNTYbfb8f79e03k8OXLF/T09ODChQsIDw9XPg0NDbDZbAgPD8f27ds1kYUrIgLgz1/IRu+L7jLQ8n3TU9hV7mnlmmRXucauYleN5fGu+s/PgfvLmM1mASA3b950GM/KylL1I0LHmugRoVu2bJGoqCj5/v27Mvbp0ycJDAyU0tJSL67SM06dOiUA5Pjx426PUXsG7uTl5cn06dPFarWKiPpzGBoaEovF4vTJzMyUoKAgsVgs0t7eLiLqz2K8/v5+mTdvniQnJytjqampYjQaHe6RbW1tAkAuX77si2WqGruKXcWuco1dxa4a5Y2u8vuNj8if9yCEh4dLTU2NPH78WAoKCgSA1NXV+XppHmU2m8VkMkltba0AkNzcXDGZTGIymcRms4mISEdHhwQHB8vq1avFbDbL3bt3xWg0isFgUG4y/ur8+fMCQLKysqStrc3pM0rNGYiIFBQUyOHDh+XWrVvy5MkTuX37tmzdulUAyJEjR5Tj1J6DO67ejaDmLLZt2yalpaViMpnEYrFITU2NxMfHi06nk5aWFuU4i8UiOp1OcnJypKWlRerr6yUmJkaMRqMMDw/78AzUi13FrmJXsavcYVd5p6tUsfEZHByU/fv3y9y5cyUwMFCSkpKkoaHB18vyuLi4OAHg8vPhwwfluFevXklGRobMmjVLQkJCZNOmTdLZ2em7hU+R9PR0t+c//stMtWYgIlJbWytpaWmi1+tFp9NJWFiYpKeny/Xr152OVXMO7rgqExH1ZnH27FlJTk6W0NBQmTFjhsyZM0dycnLkxYsXTsc+fPhQVq5cKUFBQRIRESE7duxw+bJFmhrsKnYVu4pd5Q67yjtdNU3kf/9MR0REREREpFJ+/3ADIiIiIiKiyXDjQ0REREREqseNDxERERERqR43PkREREREpHrc+BARERERkepx40NERERERKrHjQ8REREREakeNz5ERERERKR63PgQEREREZHqceNDRERERESqx40PERERERGp3j8PgnlbouylTwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"P = np.diag([500., 49.])\n",
"Ms, Ps = run(count=50, R=10, Q=0.01, P=P)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is still a lot to learn, but we have implemented a Kalman filter using the same theory and equations as published by Rudolf Kalman! Code very much like this runs inside of your GPS, airliners, robots, and so on. \n",
"\n",
"The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (labelled *Track*). After the initial settling in period the filter should track the dog's position very closely. The yellow shaded portion between the black dotted lines shows 1 standard deviations of the filter's variance, which I explain in the next paragraph.\n",
"\n",
"The next two plots show the variance of $x$ and of $\\dot x$. I have plotted the diagonals of $\\mathbf P$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf P[0,0]$ is the variance of $x$, and $\\mathbf P[1,1]$ is the variance of $\\dot x$. You can see that we quickly converge to small variances for both. \n",
"\n",
"The covariance matrix $\\mathbf P$ tells us the *theoretical* performance of the filter *assuming* everything we tell it is true. Recall that the standard deviation is the square root of the variance, and that approximately 68% of a Gaussian distribution occurs within one standard deviation. If at least 68% of the filter output is within one standard deviation the filter may be performing well. In the top chart I have displayed the one standard deviation as the yellow shaded area between the two dotted lines. To my eye it looks like perhaps the filter is slightly exceeding that bounds, so the filter probably needs some tuning.\n",
"\n",
"In the univariate chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filters with this code merely by altering our assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and acceleration in 3D space. We can do that with the code in this chapter.\n",
"\n",
"I want you to get a better feel for how the Gaussians change over time, so here is a 3D plot showing the Gaussians every 7th epoch (time step). Every 7th separates them enough so can see each one independently. The first Gaussian at $t=0$ is to the left."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from kf_book.book_plots import set_figsize, figsize\n",
"from kf_book.nonlinear_plots import plot_gaussians\n",
"\n",
"P = np.diag([3., 1.])\n",
"np.random.seed(3)\n",
"Ms, Ps = run(count=25, R=10, Q=0.01, P=P, do_plot=False)\n",
"with figsize(x=9, y=5):\n",
" plot_gaussians(Ms[::7], Ps[::7], (-5,25), (-5, 5), 75)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Saver Class\n",
"\n",
"In the `run()` method I wrote boilerplate code to save the results of the filter\n",
"```python\n",
" xs, cov = [], []\n",
" for z in zs:\n",
" kf.predict()\n",
" kf.update(z)\n",
" xs.append(kf.x)\n",
" cov.append(kf.P)\n",
"\n",
" xs, cov = np.array(xs), np.array(cov)\n",
"```\n",
"\n",
"There's an easy way to avoid this. `filtery.common` provides the `Saver` class which will save all attributes in the Kalman filter class each time `Saver.save()` is called. Let's see it in action and then we will talk about it more."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"from filterpy.common import Saver\n",
"kf = pos_vel_filter([0, .1], R=R, P=P, Q=Q, dt=1.) \n",
"s = Saver(kf)\n",
"for i in range(1, 6):\n",
" kf.predict()\n",
" kf.update([i])\n",
" s.save() # save the current state"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `Saver` object now contains lists of all the attributes of the KalmanFilter object. `kf.x` is the current state estimate of the filter. Therefore `s.x` contains the saved state estimate that was computed inside the loop:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[array([0.531, 0.304]),\n",
" array([1.555, 0.763]),\n",
" array([2.784, 1.036]),\n",
" array([3.944, 1.105]),\n",
" array([5.015, 1.086])]"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s.x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see all the available attributes with the `keys` attribute:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['alpha',\n",
" 'likelihood',\n",
" 'log_likelihood',\n",
" 'mahalanobis',\n",
" 'dim_x',\n",
" 'dim_z',\n",
" 'dim_u',\n",
" 'x',\n",
" 'P',\n",
" 'Q',\n",
" 'B',\n",
" 'F',\n",
" 'H',\n",
" 'R',\n",
" '_alpha_sq',\n",
" 'M',\n",
" 'z',\n",
" 'K',\n",
" 'y',\n",
" 'S',\n",
" 'SI',\n",
" '_I',\n",
" 'x_prior',\n",
" 'P_prior',\n",
" 'x_post',\n",
" 'P_post',\n",
" '_log_likelihood',\n",
" '_likelihood',\n",
" '_mahalanobis',\n",
" 'inv']"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s.keys"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are many attributes there that we haven't discussed yet, but many should be familar.\n",
"\n",
"At this point you could write code to plot any of these variables. However, it is often more useful to use `np.array` instead of lists. Calling `Saver.to_array()` will convert the lists into `np.array`. There is one caveat: if the shape of any of the attributes changes during the run, the `to_array` will raise an exception since `np.array` requires all of the elements to be of the same type and size. \n",
"\n",
"If you look at the keys again you'll see that `z` is one of the choices. This is promising; apparently the measurement `z` is saved for us. Let's plot it against the estimate."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"s.to_array()\n",
"book_plots.plot_measurements(s.z);\n",
"plt.plot(s.x[:, 0]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While I've demonstrated this with the `KalmanFilter` class, it will work with all filter classes implemented by `FilterPy`. It will probably work with any class you write as well, as it inspects the object to retrieve the attribute names. We will use this class throughout the book to keep the code readable and short. Using the `Saver` will slow down your code because a lot happens behind the scenes, but for learning and exploring the convience cannot be beat."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Kalman Filter Equations\n",
"\n",
"We are now ready to learn how `predict()` and `update()` perform their computations. \n",
"\n",
"A word about notation. I'm a programmer, and I am used to code that reads\n",
"\n",
"```python\n",
"x = x + 1\n",
"``` \n",
"\n",
"That is not an equation as the sides are not equal, but an *assignment*. If we wanted to write this in mathematical notation we'd write\n",
"$$x_k = x_{k-1} + 1$$\n",
"\n",
"Kalman filter equations are littered with subscripts and superscripts to keep the equations mathematically consistent. I find this makes them extremely hard to read. In most of the book I opt for subscriptless assignments. As a programmer you should understand that I am showing you assignments which implement an algorithm that is to be executed step by step. I'll elaborate on this once we have a concrete example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Prediction Equations\n",
"\n",
"The Kalman filter uses these equations to compute the *prior* - the predicted next state of the system. They compute the prior mean ($\\bar{\\mathbf x}$) and covariance ($\\bar{\\mathbf P}$) of the system.\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathbf{\\bar x} &= \\mathbf{Fx} + \\mathbf{Bu}\\\\\n",
"\\mathbf{\\bar P} &= \\mathbf{FPF}^\\mathsf T + \\mathbf Q\n",
"\\end{aligned}$$\n",
"\n",
"$\\underline{\\textbf{Mean}}$\n",
"\n",
"$\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu}$\n",
"\n",
"As a reminder, the linear equation $\\mathbf{Ax} = \\mathbf b$ represents a system of equations, where $\\mathbf A$ holds the coefficients set of equations, $\\mathbf x$ is the vector of variables. Performing the multiplication $\\mathbf{Ax}$ computes the right hand side values for that set of equations, represented by $\\mathbf b$.\n",
"\n",
"If $\\mathbf F$ contains the state transition for a given time step, then the product $\\mathbf{Fx}$ computes the state after that transition. Easy! Likewise, $\\mathbf B$ is the control function, $\\mathbf u$ is the control input, so $\\mathbf{Bu}$ computes the contribution of the controls to the state after the transition. Thus, the prior $\\mathbf{\\bar x}$ is computed as the sum of $\\mathbf{Fx}$ and $\\mathbf{Bu}$.\n",
"\n",
"The equivalent univariate equation is\n",
"\n",
"$$\\bar\\mu = \\mu + \\mu_{move}$$\n",
"\n",
"If you perform the matrix multiplication $\\mathbf{Fx}$ it generates this equation for $x$.\n",
"\n",
"Let's make this explicit. Recall the value for $\\mathbf F$ from the last chapter:\n",
"\n",
"$$\\mathbf F = \\begin{bmatrix}1&\\Delta t \\\\ 0&1\\end{bmatrix}$$\n",
"\n",
"Thus $\\mathbf{\\bar x} = \\mathbf{Fx}$ corresponds to the set of linear equations:\n",
"\n",
"$$\\begin{cases}\n",
"\\begin{aligned}\n",
"\\bar x &= 1x + &\\Delta t\\, \\dot x \\\\\n",
"\\bar{\\dot x} &=0x + &1\\, \\dot x\n",
"\\end{aligned}\n",
"\\end{cases}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\underline{\\textbf{Covariance}}$\n",
"\n",
"$\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q$\n",
"\n",
"This equation is not as easy to understand so we will spend more time on it. \n",
"\n",
"In univariate version of this equation is:\n",
"\n",
"$$\\bar\\sigma^2 = \\sigma^2 + \\sigma^2_{move}$$\n",
"\n",
"We add the variance of the movement to the variance of our estimate to reflect the loss of knowlege. We need to do the same thing here, except it isn't quite that easy with multivariate Gaussians. \n",
"\n",
"We can't simply write $\\mathbf{\\bar P} = \\mathbf P + \\mathbf Q$. In a multivariate Gaussians the state variables are *correlated*. What does this imply? Our knowledge of the velocity is imperfect, but we are adding it to the position with\n",
"\n",
"$$\\bar x = \\dot x\\Delta t + x$$\n",
"\n",
"Since we do not have perfect knowledge of the value of $\\dot x$ the sum $\\bar x = \\dot x\\Delta t + x$ gains uncertainty. Because the positions and velocities are correlated we cannot simply add the covariance matrices. For example, if $\\mathbf P$ and $\\mathbf Q$ are diagonal matrices the sum would also be diagonal. But we know position is correlated to velocity so the off-diagonal elements should be non-zero. \n",
"\n",
"The correct equation is\n",
"\n",
"$$\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q$$\n",
"\n",
"Expressions in the form $\\mathbf{ABA}^\\mathsf T$ are common in linear algebra. You can think of it as *projecting* the middle term by the outer term. We will be using this many times in the rest of the book. I admit this may be a 'magical' equation to you. Let's explore it.\n",
"\n",
"When we initialize $\\mathbf P$ with\n",
"\n",
"$$\\mathbf P = \\begin{bmatrix}\\sigma^2_x & 0 \\\\ 0 & \\sigma^2_v\\end{bmatrix}$$\n",
"\n",
"\n",
"the value for $\\mathbf{FPF}^\\mathsf T$ is:\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathbf{FPF}^\\mathsf T &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
"\\begin{bmatrix}\\sigma^2_x & 0 \\\\ 0 & \\sigma^2_{v}\\end{bmatrix}\n",
"\\begin{bmatrix}1&0\\\\\\Delta t&1\\end{bmatrix} \\\\\n",
"&= \\begin{bmatrix}\\sigma^2_x&\\sigma_v^2\\Delta t\\\\ 0 & \\sigma^2_{v}\\end{bmatrix}\n",
"\\begin{bmatrix}1&0\\\\\\Delta t&1\\end{bmatrix} \\\\\n",
"&= \\begin{bmatrix}\\sigma^2_x + \\sigma_v^2\\Delta t^2 & \\sigma_v^2\\Delta t \\\\\n",
"\\sigma_v^2\\Delta t & \\sigma^2_{v}\\end{bmatrix}\n",
"\\end{aligned}$$\n",
"\n",
"The initial value for $\\mathbf P$ had no covariance between the position and velocity. Position is computed as $\\dot x\\Delta t + x$, so there is a correlation between the position and velocity. The multiplication $\\mathbf{FPF}^\\mathsf T$ computes a covariance of $\\sigma_v^2 \\Delta t$. The exact value is not important; you just need to recognize that $\\mathbf{FPF}^\\mathsf T$ uses the process model to automatically compute the covariance between the position and velocity!\n",
"\n",
"Another way to think of this is to reflect on the $\\mathbf{Fx}$ multiplication. That projected $\\mathbf x$ forward in time. $\\mathbf {FP}$ might seem to be the equivalent operation, but $\\mathbf P$ is a matrix while $\\mathbf x$ is a vector. The trailing $\\mathbf F^\\mathsf T$ term ensures that we multiply by both the rows and columns of $\\mathbf F$. In the second line of the computation of $\\mathbf{FPF}^\\mathsf T$ we have the value for $\\mathbf{FP}$. You can see that it is an upper triangular matrix because we haven't fully incorporated $\\mathbf F$ into the multiplication.\n",
"\n",
"If you have some experience with linear algebra and statistics, this may help. The covariance due to the prediction can be modeled as the expected value of the error in the prediction step, given by this equation. \n",
"\n",
"$$\\begin{aligned}\n",
"\\bar{\\mathbf P} &= \\mathbb E[(\\mathbf{Fx - \\bar \\mu})(\\mathbf{Fx - \\bar\\mu})^\\mathsf T]\\\\\n",
" &= \\mathbf F\\, \\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]\\, \\mathbf F^\\mathsf T\n",
"\\end{aligned}$$\n",
"\n",
"Of course, $\\mathbb E[\\mathbf{(x- \\bar\\mu)(x- \\bar\\mu)}^\\mathsf T]$ is just $\\mathbf P$, giving us\n",
"\n",
"$$\\bar{\\mathbf P} = \\mathbf{FPF}^\\mathsf T$$\n",
"\n",
"Let's look at its effect. Here I use $\\mathbf F$ from our filter and project the state forward 6/10ths of a second. I do this five times so you can see how $\\mathbf{\\bar P}$ continues to change. "
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dt = 0.6\n",
"x = np.array([0., 5.])\n",
"F = np.array([[1., dt], [0, 1.]])\n",
"P = np.array([[1.5, 0], [0, 3.]])\n",
"plot_covariance_ellipse(x, P, edgecolor='r')\n",
"\n",
"for _ in range(5):\n",
" x = np.dot(F, x)\n",
" P = np.dot(F, P).dot(F.T)\n",
" plot_covariance_ellipse(x, P, edgecolor='k', ls='dashed')\n",
"book_plots.set_labels(x='position', y='velocity')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see that with a velocity of 5 the position correctly moves 3 units in each 6/10ths of a second step. At each step the width of the ellipse is larger, indicating that we have lost information about the position due to adding $\\dot x\\Delta t$ to x at each step. The height has not changed - our system model says the velocity does not change, so the belief we have about the velocity cannot change. As time continues you can see that the ellipse becomes more and more tilted. Recall that a tilt indicates *correlation*. $\\mathbf F$ linearly correlates $x$ with $\\dot x$ with the expression $\\bar x = \\dot x \\Delta t + x$. The $\\mathbf{FPF}^\\mathsf T$ computation correctly incorporates this correlation into the covariance matrix.\n",
"\n",
"Here is an animation of this equation that allows you to change the design of $\\mathbf F$ to see how it affects shape of $\\mathbf P$. The `F00` slider affects the value of F[0, 0]. `covar` sets the intial covariance between the position and velocity($\\sigma_x\\sigma_{\\dot x}$). I recommend answering these questions at a minimum\n",
"\n",
"* what if $x$ is not correlated to $\\dot x$? (set F01 to 0, the rest at defaults)\n",
"* what if $x = 2\\dot x\\Delta t + x_0$? (set F01 to 2, the rest at defaults)\n",
"* what if $x = \\dot x\\Delta t + 2x_0$? (set F00 to 2, the rest at defaults)\n",
"* what if $x = \\dot x\\Delta t$? (set F00 to 0, the rest at defaults)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "df9f68b8fa9e483a8faa25afa63896b7",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(IntSlider(value=1, continuous_update=False, description='F00', max=2), FloatSlider(value…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ipywidgets import interact\n",
"from kf_book.book_plots import IntSlider, FloatSlider\n",
"\n",
"def plot_FPFT(F00, F01, F10, F11, covar): \n",
" plt.figure()\n",
" dt = 1.\n",
" x = np.array((0, 0.))\n",
" P = np.array(((1, covar), (covar, 2)))\n",
" F = np.array(((F00, F01), (F10, F11)))\n",
" plot_covariance_ellipse(x, P)\n",
" plot_covariance_ellipse(x, np.dot(F, P).dot(F.T), ec='r')\n",
" plt.gca().set_aspect('equal')\n",
" plt.xlim(-4, 4)\n",
" plt.ylim(-4, 4)\n",
" #plt.title(str(F))\n",
" plt.xlabel('position')\n",
" plt.ylabel('velocity')\n",
" \n",
"interact(plot_FPFT, \n",
" F00=IntSlider(value=1, min=0, max=2), \n",
" F01=FloatSlider(value=1, min=0, max=2, description='F01(dt)'),\n",
" F10=FloatSlider(value=0, min=0, max=2),\n",
" F11=FloatSlider(value=1, min=0, max=2),\n",
" covar=FloatSlider(value=0, min=0, max=1));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(If you are reading this in a static form: instructions to run this online are here: https://git.io/vza7b). Or, go to binder using the link below, and open this notebook from there.\n",
"\n",
"http://mybinder.org/repo/rlabbe/Kalman-and-Bayesian-Filters-in-Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Update Equations\n",
"\n",
"The update equations look messier than the predict equations, but that is mostly due to the Kalman filter computing the update in measurement space. This is because measurements are not *invertible*. For example, consider a sensor that gives the range to a target. It is impossible to convert a range into a position - an infinite number of positions in a circle will yield the same range. On the other hand, we can always compute the range (measurement) given a position (state).\n",
"\n",
"Before I continue, recall that we are trying to do something very simple: choose a new estimate chosen somewhere between a measurement and a prediction, as in this chart:\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equations will be complicated because the state has multiple dimensions, but this operations is what we are doing. Don't let the equations distract you from the simplicity of this idea.\n",
"\n",
"$\\underline{\\textbf{System Uncertainty}}$\n",
"\n",
"$\\textbf{S} = \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R$\n",
"\n",
"To work in measurement space the Kalman filter has to project the covariance matrix into measurement space. The math for this is $\\mathbf{H\\bar PH}^\\mathsf T$, where $\\mathbf{\\bar P}$ is the *prior* covariance and $\\mathbf H$ is the measurement function.\n",
"\n",
"\n",
"You should recognize this $\\mathbf{ABA}^\\mathsf T$ form - the prediction step used $\\mathbf{FPF}^\\mathsf T$ to update $\\mathbf P$ with the state transition function. Here, we use the same form to update it with the measurement function. The linear algebra is changing the coordinate system for us. \n",
"\n",
"Once the covariance is in measurement space we need to account for the sensor noise. This is very easy - we just add matrices. The result is variously called the *system uncertainty* or *innovation covariance*.\n",
"\n",
"If you ignore the $\\mathbf H$ term this equation is the equivalent to the denominator in the univariate equation for the Kalman gain:\n",
"\n",
"$$K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2}$$\n",
"\n",
"Compare the equations for the system uncertainty and the covariance\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R\\\\\n",
"\\mathbf{\\bar P} &= \\mathbf{FPF}^\\mathsf T + \\mathbf Q\n",
"\\end{aligned}$$\n",
"\n",
"In each equation $\\mathbf P$ is put into a different space with either the function $\\mathbf H$ or $\\mathbf F$. Then we add the noise matrix associated with that space.\n",
"\n",
"$\\underline{\\textbf{Kalman Gain}}$\n",
"\n",
"$\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}$\n",
"\n",
"Look back at the residual diagram. Once we have a prediction and a measurement we need to select an estimate somewhere between the two. If we have more certainty about the measurement the estimate will be closer to it. If instead we have more certainty about the prediction then the estimate will be closer to it. \n",
"\n",
"In the univariate chapter we scaled the mean using this equation\n",
"\n",
"$$\n",
"\\mu =\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_\\mathtt{z}^2 \\bar\\mu} {\\bar\\sigma^2 + \\sigma_\\mathtt{z}^2}$$\n",
"\n",
"which we simplified to\n",
"\n",
"$$\\mu = (1-K)\\bar\\mu + K\\mu_\\mathtt{z}$$\n",
"\n",
"which gave us\n",
"\n",
"$$K = \\frac {\\bar\\sigma^2} {\\bar\\sigma^2 + \\sigma_z^2}$$\n",
"\n",
"$K$ is the *Kalman gain*, and it is a real number between 0 and 1. Ensure you understand how it selects a mean somewhere between the prediction and measurement. The Kalman gain is a *percentage* or *ratio* - if K is .9 it takes 90% of the measurement and 10% of the prediction. \n",
"\n",
"For the multivariate Kalman filter $\\mathbf K$ is a vector, not a scalar. Here is the equation again: $\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of finding the reciprocal. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n",
"\n",
"$$\\begin{aligned} \\mathbf K &\\approx \\frac{\\mathbf{\\bar P}\\mathbf H^\\mathsf T}{\\mathbf{S}} \\\\\n",
"\\mathbf K &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{prediction} + \\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\n",
"\\end{aligned}$$\n",
"\n",
"The Kalman gain equation computes a ratio based on how much we trust the prediction vs the measurement. We did the same thing in every prior chapter. The equation is complicated because we are doing this in multiple dimensions via matrices, but the concept is simple. The $\\mathbf H^\\mathsf T$ term is less clear, I'll explain it soon. If you ignore that term the equation for the Kalman gain is the same as the univariate case: divide the uncertainty of the prior with the of the sum of the uncertainty of the prior and measurement.\n",
"\n",
"$\\underline{\\textbf{Residual}}$\n",
"\n",
"$\\mathbf y = \\mathbf z - \\mathbf{H\\bar{x}}$\n",
"\n",
"This is an easy one as we've covered this equation while designing the measurement function $\\mathbf H$. Recall that the measurement function converts a state into a measurement. So $\\mathbf{Hx}$ converts $\\mathbf x$ into an equivalent measurement. Once that is done, we can subtract it from the measurement $\\mathbf z$ to get the residual - the difference between the measurement and prediction.\n",
"\n",
"The univariate equation is\n",
"\n",
"$$y = z - \\bar x$$\n",
"\n",
"and clearly computes the same thing, but only in one dimension.\n",
"\n",
"$\\underline{\\textbf{State Update}}$\n",
"\n",
"$\\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky}$\n",
"\n",
"We select our new state to be along the residual, scaled by the Kalman gain. The scaling is performed by $\\mathbf{Ky}$, which both scales the residual and converts it back into state space with the $\\mathbf H^\\mathsf T$ term which is in $\\mathbf K$. This is added to the prior, yielding the equation: $\\mathbf x =\\mathbf{\\bar x} + \\mathbf{Ky}$. Let me write out $\\mathbf K$ so we can see the entire computation:\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathbf x &= \\mathbf{\\bar x} + \\mathbf{Ky} \\\\\n",
"&= \\mathbf{\\bar x} + \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1}\\mathbf y \\\\\n",
"&\\approx \\mathbf{\\bar x} + \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\mathbf H^\\mathsf T\\mathbf y\n",
"\\end{aligned}$$\n",
"\n",
"Perhaps a better way to *see* the ratio is to rewrite the estimate equation:\n",
"\n",
"$$\\begin{aligned}\n",
"\\mathbf x &= \\mathbf{\\bar x} + \\mathbf{Ky} \\\\\n",
"&= \\mathbf{\\bar x} +\\mathbf K(\\mathbf z - \\mathbf{H\\bar x}) \\\\\n",
"&= (\\mathbf I - \\mathbf{KH})\\mathbf{\\bar x} + \\mathbf{Kz}\n",
"\\end{aligned}$$\n",
"\n",
"The similarity between this and the univariate form should be obvious:\n",
"$$\\mu = (1-K)\\bar\\mu + K\\mu_\\mathtt{z}$$\n",
"\n",
"$\\underline{\\textbf{Covariance Update}}$\n",
"\n",
"$\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P}$\n",
"\n",
"$\\mathbf{I}$ is the identity matrix, and is the way we represent $1$ in multiple dimensions. $\\mathbf H$ is our measurement function, and is a constant. We can think of the equation as $\\mathbf P = (1-c\\mathbf K)\\mathbf P$. $\\mathbf K$ is our ratio of how much prediction vs measurement we use. If $\\mathbf K$ is large then $(1-\\mathbf{cK})$ is small, and $\\mathbf P$ will be made smaller than it was. If $\\mathbf K$ is small, then $(1-\\mathbf{cK})$ is large, and $\\mathbf P$ will be relatively larger. This means that we adjust the size of our uncertainty by some factor of the Kalman gain.\n",
"\n",
"This equation can be numerically unstable and I don't use it in FilterPy. The subtraction can destroy symmetry and lead to floating point errors over time. Later I'll share more complicated but numerically stable forms of this equation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### An Example not using FilterPy\n",
"\n",
"FilterPy hides the details of the implementation from us. Normally you will appreciate this, but let's implement the last filter without FilterPy. To do so we need to define our matrices as variables, and then implement the Kalman filter equations explicitly.\n",
"\n",
"Here we initialize our matrices:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"dt = 1.\n",
"R_var = 10\n",
"Q_var = 0.01\n",
"x = np.array([[10.0, 4.5]]).T\n",
"P = np.diag([500, 49])\n",
"F = np.array([[1, dt],\n",
" [0, 1]])\n",
"H = np.array([[1., 0.]])\n",
"R = np.array([[R_var]])\n",
"Q = Q_discrete_white_noise(dim=2, dt=dt, var=Q_var)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from numpy import dot\n",
"from scipy.linalg import inv\n",
"\n",
"count = 50\n",
"track, zs = compute_dog_data(R_var, Q_var, count)\n",
"xs, cov = [], []\n",
"for z in zs:\n",
" # predict\n",
" x = dot(F, x)\n",
" P = dot(F, P).dot(F.T) + Q\n",
" \n",
" #update\n",
" S = dot(H, P).dot(H.T) + R\n",
" K = dot(P, H.T).dot(inv(S))\n",
" y = z - dot(H, x)\n",
" x += dot(K, y)\n",
" P = P - dot(K, H).dot(P)\n",
" \n",
" xs.append(x)\n",
" cov.append(P)\n",
"\n",
"xs, cov = np.array(xs), np.array(cov)\n",
"plot_track(xs[:, 0], track, zs, cov, plot_P=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results are identical to the FilterPy version. Which you prefer is up to you. I prefer not polluting my namespace with variables such as `x`, `P`, and so on; `dog_filter.x` is, to me, more readable.\n",
"\n",
"More importantly, this example requires you to remember and program the equations for the Kalman filter. Sooner or later you will make a mistake. FilterPy's version ensures that your code will be correct. On the other hand, if you make a mistake in your definitions, such as making $\\mathbf H$ a column vector instead of a row vector, FilterPy's error message will be harder to debug than this explicit code. \n",
"\n",
"FilterPy's KalmanFilter class provides additional functionality such as smoothing, batch processing, faded memory filtering, computation of the maximum likelihood function, and more. You get all of this functionality without having to explicitly program it."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Summary\n",
"\n",
"We have learned the Kalman filter equations. Here they are all together for your review. There was a lot to learn, but I hope that as you went through each you recognized it's kinship with the equations in the univariate filter. In the *Kalman Math* chapter I will show you that if we set the dimension of $\\mathbf x$ to one that these equations revert back to the equations for the univariate filter. This is not \"like\" the univariate filter - it is a multidimensional implementation of it.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{Predict Step}\\\\\n",
"\\mathbf{\\bar x} &= \\mathbf{F x} + \\mathbf{B u} \\\\\n",
"\\mathbf{\\bar P} &= \\mathbf{FP{F}}^\\mathsf T + \\mathbf Q \\\\\n",
"\\\\\n",
"\\text{Update Step}\\\\\n",
"\\textbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R \\\\\n",
"\\mathbf K &= \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1} \\\\\n",
"\\textbf{y} &= \\mathbf z - \\mathbf{H \\bar x} \\\\\n",
"\\mathbf x &=\\mathbf{\\bar x} +\\mathbf{K\\textbf{y}} \\\\\n",
"\\mathbf P &= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P}\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"I want to share a form of the equations that you will see in the literature. There are many different notation systems used, but this gives you an idea of what to expect.\n",
"\n",
" $$\n",
"\\begin{aligned}\n",
"\\hat{\\mathbf x}_{k\\mid k-1} &= \\mathbf F_k\\hat{\\mathbf x}_{k-1\\mid k-1} + \\mathbf B_k \\mathbf u_k \\\\\n",
"\\mathbf P_{k\\mid k-1} &= \\mathbf F_k \\mathbf P_{k-1\\mid k-1} \\mathbf F_k^\\mathsf T + \\mathbf Q_k \\\\ \t\n",
"\\tilde{\\mathbf y}_k &= \\mathbf z_k - \\mathbf H_k\\hat{\\mathbf x}_{k\\mid k-1}\\\\\n",
"\\mathbf{S}_k &= \\mathbf H_k \\mathbf P_{k\\mid k-1} \\mathbf H_k^\\mathsf T + \\mathbf R_k \\\\\n",
"\\mathbf K_k &= \\mathbf P_{k\\mid k-1}\\mathbf H_k^\\mathsf T \\mathbf{S}_k^{-1}\\\\\n",
"\\hat{\\mathbf x}_{k\\mid k} &= \\hat{\\mathbf x}_{k\\mid k-1} + \\mathbf K_k\\tilde{\\mathbf y}_k\\\\\n",
"\\mathbf P_{k|k} &= (I - \\mathbf K_k \\mathbf H_k) \\mathbf P_{k|k-1}\n",
"\\\\\\end{aligned}\n",
"$$\n",
"\n",
"This notation uses the Bayesian $a\\mid b$ notation, which means $a$ given the evidence of $b$. The hat means estimate. Thus $\\hat{\\mathbf x}_{k\\mid k}$ means the estimate of the state $\\mathbf x$ at step $k$ (the first k) given the evidence from step $k$ (the second k). The posterior, in other words. $\\hat{\\mathbf x}_{k\\mid k-1}$ means the estimate for the state $\\mathbf x$ at step $k$ given the estimate from step $k - 1$. The prior, in other words. \n",
"\n",
"This notation, copied from [Wikipedia](https://en.wikipedia.org/wiki/Kalman_filter#Details) [[1]](#[wiki_article]), allows a mathematician to express himself exactly. In formal publications presenting new results this precision is necessary. As a programmer I find it fairly unreadable. I am used to thinking about variables changing state as a program runs, and do not use a different variable name for each new computation. There is no agreed upon format in the literature, so each author makes different choices. I find it challenging to switch quickly between books and papers, and so have adopted my admittedly less precise notation. Mathematicians may write scathing emails to me, but I hope programmers and students will rejoice at my simplified notation.\n",
"\n",
"The **Symbology** Appendix lists the notation used by various authors. This brings up another difficulty. Different authors use different variable names. $\\mathbf x$ is fairly universal, but after that it is anybody's guess. For example, it is common to use $\\mathbf{A}$ for what I call $\\mathbf F$. You must read carefully, and hope that the author defines their variables (they often do not).\n",
"\n",
"If you are a programmer trying to understand a paper's equations, I suggest starting by removing all of the superscripts, subscripts, and diacriticals, replacing them with a single letter. If you work with equations like this every day this is superfluous advice, but when I read I am usually trying to understand the flow of computation. To me it is far more understandable to remember that $P$ in this step represents the updated value of $P$ computed in the last step, as opposed to trying to remember what $P_{k-1}(+)$ denotes, and what its relation to $P_k(-)$ is, if any, and how any of that relates to the completely different notation used in the paper I read 5 minutes ago."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercise: Show Effect of Hidden Variables\n",
"\n",
"In our filter velocity is a hidden variable. How would a filter perform if we did not use velocity in the state?\n",
"\n",
"Write a Kalman filter that uses the state $\\mathbf x=\\begin{bmatrix}x\\end{bmatrix}$ and compare it against a filter that uses $\\mathbf x=\\begin{bmatrix}x & \\dot x\\end{bmatrix}^\\mathsf T$."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Solution\n",
"\n",
"We've already implemented a Kalman filter for position and velocity, so I will provide the code without much comment, and then plot the result."
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from math import sqrt\n",
"from numpy.random import randn\n",
"\n",
"def univariate_filter(x0, P, R, Q):\n",
" f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)\n",
" f.x = np.array([[x0]])\n",
" f.P *= P\n",
" f.H = np.array([[1.]])\n",
" f.F = np.array([[1.]])\n",
" f.B = np.array([[1.]])\n",
" f.Q *= Q\n",
" f.R *= R\n",
" return f\n",
"\n",
"def plot_1d_2d(xs, xs1d, xs2d):\n",
" plt.plot(xs1d, label='1D Filter')\n",
" plt.scatter(range(len(xs2d)), xs2d, c='r', alpha=0.7, label='2D Filter')\n",
" plt.plot(xs, ls='--', color='k', lw=1, label='track')\n",
" plt.title('State')\n",
" plt.legend(loc=4)\n",
" plt.show()\n",
" \n",
"def compare_1D_2D(x0, P, R, Q, vel, u=None):\n",
" # storage for filter output\n",
" xs, xs1, xs2 = [], [], []\n",
"\n",
" # 1d KalmanFilter\n",
" f1D = univariate_filter(x0, P, R, Q)\n",
"\n",
" #2D Kalman filter\n",
" f2D = pos_vel_filter(x=(x0, vel), P=P, R=R, Q=0)\n",
" if np.isscalar(u):\n",
" u = [u]\n",
" pos = 0 # true position\n",
" for i in range(100):\n",
" pos += vel\n",
" xs.append(pos)\n",
"\n",
" # control input u - discussed below\n",
" f1D.predict(u=u)\n",
" f2D.predict()\n",
" \n",
" z = pos + randn()*sqrt(R) # measurement\n",
" f1D.update(z)\n",
" f2D.update(z)\n",
" \n",
" xs1.append(f1D.x[0])\n",
" xs2.append(f2D.x[0])\n",
" plt.figure()\n",
" plot_1d_2d(xs, xs1, xs2)\n",
"\n",
"compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=1.) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Discussion\n",
"\n",
"The filter that incorporates velocity into the state produces much better estimates than the filter that only tracks position. The univariate filter has no way to estimate the velocity or change in position, so it lags the tracked object. \n",
"\n",
"In the univarate Kalman filter chapter we had a control input `u` to the predict equation:\n",
"\n",
"```python\n",
" def predict(self, u=0.0):\n",
" self.x += u\n",
" self.P += self.Q\n",
"```\n",
"\n",
"Let's try specifying the control input:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=1., u=1.) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here the performance of the two filters are similar, and perhaps the univariate filter is tracking more cloesly. But let's see what happens when the actual velocity `vel` is different from the control input `u`:"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"compare_1D_2D(x0=0, P=50., R=5., Q=.02, vel=-2., u=1.) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we are tracking a robot which we are also controlling the univariate filter can do a very good job because the control input allows the filter to make an accurate prediction. But if we are tracking passively the control input is not much help unless we can make an accurate *apriori* guess as to the velocity. This is rarely possible."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How Velocity is Calculated\n",
"\n",
"I haven't explained how the filter computes the velocity, or any hidden variable. If we plug in the values we calculated for each of the filter's matrices we can see what happens.\n",
"\n",
"First we need to compute the system uncertainty.\n",
"\n",
"$$\\begin{aligned}\n",
"\\textbf{S} &= \\mathbf{H\\bar PH}^\\mathsf T + \\mathbf R \\\\\n",
"&= \\begin{bmatrix} 1 & 0\\end{bmatrix}\n",
"\\begin{bmatrix}\\sigma^2_x & \\sigma_{xv} \\\\ \\sigma_{xv} & \\sigma^2_v\\end{bmatrix}\n",
"\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix} + \\begin{bmatrix}\\sigma_z^2\\end{bmatrix}\\\\\n",
"&= \\begin{bmatrix}\\sigma_x^2 & \\sigma_{xv}\\end{bmatrix}\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix}+ \\begin{bmatrix}\\sigma_z^2\\end{bmatrix} \\\\\n",
"&= \\begin{bmatrix}\\sigma_x^2 +\\sigma_z^2\\end{bmatrix}\n",
"\\end{aligned}$$\n",
"\n",
"Now that we have $\\mathbf S$ we can find the value for the Kalman gain:\n",
"$$\\begin{aligned}\n",
"\\mathbf K &= \\mathbf{\\bar PH}^\\mathsf T \\mathbf{S}^{-1} \\\\\n",
"&= \\begin{bmatrix}\\sigma^2_x & \\sigma_{xv} \\\\ \\sigma_{xv} & \\sigma^2_v\\end{bmatrix}\n",
"\\begin{bmatrix} 1 \\\\ 0\\end{bmatrix}\n",
"\\begin{bmatrix}\\frac{1}{\\sigma_x^2 +\\sigma_z^2}\\end{bmatrix} \\\\\n",
"&= \\begin{bmatrix}\\sigma^2_x \\\\ \\sigma_{xv}\\end{bmatrix}\n",
"\\begin{bmatrix}\\frac{1}{\\sigma_x^2 +\\sigma_z^2}\\end{bmatrix} \\\\\n",
"&= \\begin{bmatrix}\\sigma^2_x/(\\sigma_x^2 +\\sigma_z^2) \\\\ \\sigma_{xv}/(\\sigma_x^2 +\\sigma_z^2)\\end{bmatrix}\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"In other words, the Kalman gain for $x$ is \n",
"\n",
"$$K_x = \\frac{VAR(x)}{VAR(x)+VAR(z)}$$\n",
"\n",
"This should be very familiar to you from the univariate case. \n",
"\n",
"The Kalman gain for the velocity $\\dot x$ is\n",
"$$K_{\\dot x} = \\frac{COV(x, \\dot x)}{VAR(x)+VAR(z)}$$\n",
"\n",
"What is the effect of this? Recall that we compute the state as \n",
"\n",
"$$\\begin{aligned}\\mathbf x \n",
"&=\\mathbf{\\bar x}+\\mathbf K(z-\\mathbf{Hx)} \\\\\n",
"&= \\mathbf{\\bar x}+\\mathbf Ky\\end{aligned}$$\n",
"\n",
"Here the residual $y$ is a scalar. Therefore it is multiplied into each element of $\\mathbf K$. Therefore we have\n",
"\n",
"$$\\begin{bmatrix}x \\\\ \\dot x\\end{bmatrix}=\\begin{bmatrix}\\bar x \\\\ \\bar{\\dot x}\\end{bmatrix} + \\begin{bmatrix}K_x \\\\ K_{\\dot x}\\end{bmatrix}y$$\n",
"\n",
"Which gives this system of equations: \n",
"\n",
"$$\\begin{aligned}x& = \\bar x + yK_x\\\\\n",
"\\dot x &= \\bar{\\dot x} + yK_{\\dot x}\\end{aligned}$$\n",
"\n",
"The prediction $\\bar x$ was computed as $x + \\bar x \\Delta t$. If the prediction was perfect then the residual will be $y=0$ (ignoring noise in the measurement) and the velocity estimate will be unchanged. On the other hand, if the velocity estimate was very bad then the prediction will be very bad, and the residual will be large: $y >> 0$. In this case we update the velocity estimate with $yK_{\\dot x}$. $K_{\\dot x}$ is proportional to $COV(x,\\dot x)$. Therefore the velocity is updated by the error in the position times the value proportional to the covariance between the position and velocity. The higher the correlation the larger the correction. \n",
"\n",
"To bring this full circle, $COV(x,\\dot x)$ are the off-diagonal elements of $\\mathbf P$. Recall that those values were computed with $\\mathbf{FPF}^\\mathsf T$. So the covariance of position and velocity is computed during the predict step. The Kalman gain for the velocity is proportional to this covariance, and we adjust the velocity estimate based on how inaccurate it was during the last epoch times a value proportional to this covariance. \n",
"\n",
"In summary, these linear algebra equations may be unfamiliar to you, but computation is actually very simple. It is essentially the same computation that we performed in the g-h filter. Our constants are different in this chapter because we take the noise in the process model and sensors into account, but the math is the same."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Adjusting the Filter\n",
"\n",
"Let's start varying our parameters to see the effect of various changes. This is a very normal thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. Designing a Kalman filter is as much art as science. We are modeling a physical system using math, and models are imperfect.\n",
"\n",
"Let's look at the effects of the measurement noise $\\mathbf R$ and process noise $\\mathbf Q$. We will want to see the effect of different settings for $\\mathbf R$ and $\\mathbf Q$, so I have given the measurements a variance of 225 meters squared. That is very large, but it magnifies the effects of various design choices on the graphs, making it easier to recognize what is happening. Our first experiment holds $\\mathbf R$ constant while varying $\\mathbf Q$."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
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