{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Smoothing" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "from __future__ import division, print_function\n", "import book_format\n", "book_format.load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It has probably struck you by now that the performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement deviates far from the current track, like so (I'll only consider 1 dimension for simplicity):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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D2dkZvr6+eO6556DRaPr+LoiIiIhowCiL7/Q3Z7350DKYnGu1WkRGRmLjxo1wdHS861fT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\ndvGCnU1bvWVUV+5f0uLMb3KeVSzOqU6WipaY/tJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, 10.1, 9.9, 10.2, 10.0, 9.9, 11.4]\n", "plt.plot(data);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After a long period of near steady state, we have a very large change. Assume that change is larger than the aircraft's maneuvering envelope. Nonetheless the Kalman filter incorporates that new measurement into the filter based on the current Kalman gain. It cannot reject the noise because the measurement could reflect the initiation of a turn. Granted it is unlikely that we are turning so abruptly, but it is impossible to say whether \n", " \n", "* The aircraft started a turn awhile ago, but the previous measurements were noisy and didn't show the change.\n", " \n", "* The aircraft is turning, and this measurement is very noisy\n", " \n", "* The measurement is very noisy and the aircraft has not turned\n", "\n", "\n", "Now, suppose the following measurements are:\n", "\n", " 11.3 12.1 13.3 13.9 14.5 15.2\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7Jzja3xjMXa4OX1HhcvllnCpIRbumRf+YEV6jkBD7LLxd/Y3/RxORqBi0iYho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\nvb/0AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n", "plt.plot(data + data2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given these future measurements we can infer that yes, the aircraft initiated a turn. \n", "\n", "On the other hand, suppose these are the following measurements." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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I0tm09MQ7d+4AAHx9dX/q9PHxQUbG/T8Qz507h/fffx8nT55sVmlLcnJyywIl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\nHyzLIrf6HPS22higV42gZz1v+BOJiCt7ufoREiMzDOrV8tZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n", "plt.plot(data + data3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Overview of How They Work\n", "\n", "The Kalman filter is a **recursive** filter - it's estimate at step `k` is partially based on its estimate from step `k-1`. But this means that the estimate from step `k-1` is partially based on step `k-2`, and so on back to the first measurement. Hence, the estimate at step `k` depends on *all* of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n", "\n", "Smoothing filters incorporate future measurements into the estimate for step `k`. The measurement from `k+1` will have the most effect, `k+2` will have less effect, `k+3` less yet, and so on. \n", "\n", "This topic is called **smoothing**, but I think that is a misleading name. I could smooth the data above by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Types of Smoothers\n", "\n", "There are three broad classes of Kalman smoothers that produce better tracking in these situations.\n", "\n", "* Fixed Interval Smoothing\n", "\n", "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed interval smoother will collect all the data than estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", "\n", "\n", "* Fixed Lag Smoothing\n", "\n", "Fixed lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will ingest the first 3 measurements but not output a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurements 1 through 4 into account. When the 5th measurement comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account. This is useful when you need recent data but can afford a bit of lag. For example, perhaps you are using machine vision to monitor a manufacturing process. If you can afford a few seconds delay in the estimate a fixed lag smoother will allow you to produce very accurate and smooth results.\n", "\n", "\n", "* Fixed Point Smoothing\n", "\n", "Fixed point smoothers start out as a normal Kalman filter. But once they get to measurement 4 (say) it then looks backwards and revises the filter output for the previous measurement(s). So, at step 5 the filter will produce a result for 5, and update the result for measurement 4 taking measurement 5 into account. When measurement 6 comes in the filter produces the result for 6, and then goes back and revises 4 using the measurements from 5 and 6. It will revise the output for measurement 5 as well. This process continues, with all previous outputs being revised each time a new input comes in. This filter can be used to fill in gaps. For example, suppose you did not get a sensor reading at step `k`. Instead of just using the prediction from step `k-1` you can continue using data collected at steps `k+1`, `k+2`, and so on to refine the estimate. \n", "\n", "\n", "The choice of these filters depends on your needs and how much memory and processing time you can spare. Fixed point smoothing requires storage of all measurements, and is very costly to compute because the output is for every time step is recomputed for every measurement. On the other hand, the filter does produce a decent output for the current measurement, so this filter can be used for real time applications.\n", "\n", "Fixed lag smoothing only requires you to store a window of data, and processing requirements are modest because only that window is processed for each new measurement. The drawback is that the filter's output always lags the input, and the smoothing is not as pronounced as is possible with fixed interval smoothing.\n", "\n", "Fixed interval smoothing produces the most smoothed output at the cost of having to be batch processed. Most algorithms use some sort of forwards/backwards algorithm that is only twice as slow as a recursive Kalman filter. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fixed Point Smoothing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "not done" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fixed Interval Smoothing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several fixed lag smoothers available in the literature. I have chosen to implement the smoother invented by Rauch, Tung, and Striebel because of its ease of implementation and efficiency of computation. This smoother is commonly known as an RTS smoother, and that is what we will call it\n", "\n", "Derivation of the RTS smoother runs to several pages of densely packed math, and to be honest I have never read it through. I'm certainly not going to inflict it on you. I don't think anyone but thesis writers really need to understand the derivation. Instead I will briefly present the algorithm, equations, and then move directly to implementation and demonstration of the smoother.\n", "\n", "The RTS smoother works by first running the Kalman filter in a batch mode, computing the filter output for each step. Given the filter output for each measurement along with the covariance matrix corresponding to each output the RTS runs over the data backwards, incorporating it's knowledge of the future into the past measurements. When it reaches the first measurement it is done, and the filtered output incorporates all of the information in a maximally optimal form.\n", "\n", "The equations for the RTS smoother are very straightforward and easy to implement. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future. Here is it very important to distinguish between past, present, and future so I have used subscripts to denote whether the data is from the future or not.\n", "\n", " Predict Step\n", " \n", "$$\\begin{aligned}\n", "\\mathbf{P} &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n", "\\end{aligned}$$\n", "\n", " Update Step\n", " \n", "$$\\begin{aligned}\n", "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F} \\hspace{2 mm}\\mathbf{P}^{-1} \\\\\n", "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{x+1} - \\mathbf{FX}_k) \\\\\n", "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{K+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n", "\\end{aligned}$$\n", "\n", "As always, the hardest part of the implementation is correctly accounting for the subscripts. A basic implementation without comments or error checking would be:\n", "\n", " def rts_smoother(Xs, Ps, F, Q):\n", " n, dim_x, _ = Xs.shape\n", " \n", " # smoother gain\n", " K = zeros((n,dim_x, dim_x))\n", " x, P = Xs.copy(), Ps.copy()\n", "\n", " for k in range(n-2,-1,-1):\n", " P_pred = dot(F, P[k]).dot(F.T) + Q\n", "\n", " K[k] = dot(P[k], F.T).dot(inv(P_pred))\n", " x[k] += dot(K[k], x[k+1] - dot(F, x[k]))\n", " P[k] += dot(K[k], P[k+1] - P_pred).dot(K[k].T)\n", " return (x, P, K)\n", " \n", "This implementation mirrors the implementation provided in FilterPy. It assumes that the Kalman filter is being run externally in batch mode, and the results of the state and covariances are passed in via the `Xs` and `Ps` variable.\n", "\n", "Here is an example. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JCTB5srVb0fv99a9qcaaWQjmo5eMffbRn24QKkLPvg5RsFVC+Zggv27+L95Ua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MyJiIiIiBwAG3MiIiIiIgfAxpyIiIiIyAGwMSciIiIicgBszImIiIiIHAAbcyIiIiIi\nB8DGnIiIiIjIAfw/yKe9sJAKqEsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy import random\n", "import matplotlib.pyplot as plt\n", "from filterpy.kalman import KalmanFilter\n", "import book_plots as bp\n", "\n", "def plot_rts(noise, Q=0.001, show_velocity=False):\n", " random.seed(123)\n", " fk = KalmanFilter(dim_x=2, dim_z=1)\n", "\n", " fk.x = np.array([0., 1.]) # initial state (location and velocity)\n", "\n", " fk.F = np.array([[1., 1.],\n", " [0., 1.]]) # state transition matrix\n", "\n", " fk.H = np.array([[1., 0.]]) # Measurement function\n", " fk.P = 10. # covariance matrix\n", " fk.R = noise # state uncertainty\n", " fk.Q = Q # process uncertainty\n", "\n", " # create noisy data\n", " zs = np.asarray([t + random.randn()*noise for t in range (40)])\n", "\n", " # filter data with Kalman filter, than run smoother on it\n", " mu, cov, _, _ = fk.batch_filter(zs)\n", " M,P,C = fk.rts_smoother(mu, cov)\n", "\n", " # plot data\n", " if show_velocity:\n", " index = 1\n", " print('gu')\n", " else:\n", " index = 0\n", " if not show_velocity:\n", " bp.plot_measurements(zs, lw=1)\n", " plt.plot(M[:, index], c='b', label='RTS')\n", " plt.plot(mu[:, index], c='g', linestyle='--', label='KF output')\n", " if not show_velocity:\n", " plt.plot([0, len(zs)], [0, len(zs)], 'k', linewidth=2, label='track') \n", " plt.legend(loc=4)\n", " plt.show()\n", " \n", "plot_rts(7.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I've injected a lot of noise into the signal to allow you to visually distinguish the RTS output from the ideal output. In the graph above we can see that the Kalman filter, drawn as the green dotted line, is reasonably smooth compared to the input, but it still wanders from from the ideal line when several measurements in a row are biased towards one side of the line. In contrast, the RTS output is both extremely smooth and very close to the ideal output.\n", "\n", "With a perhaps more reasonable amount of noise we can see that the RTS output nearly lies on the ideal output. The Kalman filter output, while much better, still varies by a far greater amount." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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krk7CthBCCCFES6uoQNm2jQxXV3Q6HTqdjmPHjpmqXd1dCG/rj0+EI54BzqaA/TNbK3t8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\nfykp5K1ezSY3d96ZtYLTh7dB4U3tYQdXa7xb1sOrpTMW1iY4WDagc0A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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rts(noise=1.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, we must understand that this smoothing is predicated on the system model. We have told the filter that that what we are tracking follows a constant velocity model with very low process error. When the filter *looks ahead* it sees that the future behavior closely matches a constant velocity so it is able to reject most of the noise in the signal. Suppose instead our system has a lot of process noise. For example, if we are tracking a light aircraft in gusty winds its velocity will change often, and the filter will be less able to distinguish between noise and erratic movement due to the wind. We can see this in the next graph. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tXZgw7O+M7D8ejdq0lv2if0OfbjD/K/j3XTBrBk37gliwKLMG88zMTO69914y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jWLgQMHsnv3btq2bVtl2+7du9fqE/1z5/RVTevWrSs8FxUVxYYNG2ofsAlatWpl9NjPzw9fX19D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\nQgghhBBCOAApzIUQQgghhHAA/wfB3XEY3QWHVgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rts(noise=7., Q=.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This underscores the fact that these filters are not *smoothing* the data in colloquial sense of the term. The filter is making an optimal estimate based on previous measurements, future measurements, and what you tell it about the behavior of the system and the noise in the system and measurements.\n", "\n", "Let's wrap this up by looking at the velocity estimates of Kalman filter vs the RTS smoother." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gu\n" ] }, { "data": { "image/png": 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awXtVKIoCvaKHHnr46Y01bmd4VzMWrpLbf+2fhidvToXRMLRabZR/ALBYS68I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\n9WqXY6SlpWn7IhoQj+d0B/oDwYGe7gU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rts(7.,show_velocity=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The improvement in the velocity, which is an hidden variable, is even more dramatic. \n", "\n", "Since we are plotting velocities let's look at what the the 'raw' velocity is, which we can compute by subtracting subsequent measurements. We see below that the noise swamps the signal, causing the computed values to be essentially worthless. I show this to reiterate the importance of using Kalman filters to compute velocities, accelerations, and even higher order values. I use a Kalman filter even when my measurements are so accurate that I am willing to use them unfiltered if I am also interested in the velocities and/or accelerations. Even a very small error in a measurement gets magnified when computing velocities. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fixed Lag Smoothing\n", "\n", "The RTS smoother presented above should always be your choice of algorithm if you can run in batch mode because it incorporates all available data into each estimate. Not all problems allow you to do that, but you may still be interested in receiving smoothed values for previous estimates. The number line below illustrates this concept." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from smoothing_internal import *\n", "with book_format.figsize(y=3.):\n", " show_fixed_lag_numberline()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At step $k$ we can estimate $x_k$ using the normal Kalman filter equations. However, we can make a better estimate for $x_{k-1}$ by using the measurement received for $x_k$. Likewise, we can make a better estimate for $x_{k-2}$ by using the measurements recevied for $x_{k-1}$ and $x_{k}$. We can extend this computation back for an arbitrary $N$ steps.\n", "\n", "Derivation for this math is beyond the scope of this book; Dan Simon's *Optimal State Estimation* [2] has a very good exposition if you are interested. The essense of the idea is that instead of having a state vector $\\mathbf{x}$ we make an augmented state containing\n", "\n", "$$\\mathbf{x} = \\begin{bmatrix}\\mathbf{x}_k \\\\ \\mathbf{x}_{k-1} \\\\ \\vdots\\\\ \\mathbf{x}_{k-N+1}\\end{bmatrix}$$\n", "\n", "This yields a very large covariance matrix that contains the covariance between states at different steps. FilterPy's class `FixedLagSmoother` takes care of all of this computation for you, including creation of the augmented matrices. All you need to do is compose it as if you are using the `KalmanFilter` class and then call `smooth()`, which implements the predict and update steps of the algorithm. \n", "\n", "Each call of `smooth` computes the estimate for the current measurement, but it also goes back and adjusts the previous `N-1` points as well. The smoothed values are contained in the list `FixedLagSmoother.xSmooth`. If you use `FixedLagSmoother.x` you will get the most recent estimate, but it is not smoothed and is no different from a standard Kalman filter output." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "standard deviation fixed lag: 2.61624417392\n", "standard deviation kalman: 3.56221928461\n" ] }, { "data": { "image/png": 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XX2bXrl38/PPP5ObmApCdnU2LFrYPgjt27ODhhx82afP396/xDcHtt99e42g6WH4N/TFu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\nfPhwtc/v3UVAh3oLkZP1DQBg0YIoRAz+Ho4OdlW+Vn5+IXb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import FixedLagSmoother, KalmanFilter\n", "import numpy.random as random\n", "\n", "fls = FixedLagSmoother(dim_x=2, dim_z=1, N=8)\n", "\n", "fls.x = np.array([0., .5])\n", "fls.F = np.array([[1.,1.],\n", " [0.,1.]])\n", "\n", "fls.H = np.array([[1.,0.]])\n", "fls.P *= 200\n", "fls.R *= 5.\n", "fls.Q *= 0.001\n", "\n", "kf = KalmanFilter(dim_x=2, dim_z=1)\n", "kf.x = np.array([0., .5])\n", "kf.F = np.array([[1.,1.],\n", " [0.,1.]])\n", "kf.H = np.array([[1.,0.]])\n", "kf.P *= 200\n", "kf.R *= 5.\n", "kf.Q *= 0.001\n", "\n", "N = 4 # size of lag\n", "\n", "nom = np.array([t/2. for t in range (0, 40)])\n", "zs = np.array([t + random.randn()*5.1 for t in nom])\n", "\n", "for z in zs:\n", " fls.smooth(z)\n", " \n", "kf_x, _, _, _ = kf.batch_filter(zs)\n", "x_smooth = np.array(fls.xSmooth)[:, 0]\n", "\n", "\n", "fls_res = abs(x_smooth - nom)\n", "kf_res = abs(kf_x[:, 0] - nom)\n", "\n", "plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n", "plt.plot(x_smooth, label='FLS')\n", "plt.plot(kf_x[:, 0], label='KF', ls='--')\n", "plt.legend(loc=4)\n", "\n", "print('standard deviation fixed lag:', np.mean(fls_res))\n", "print('standard deviation kalman:', np.mean(kf_res))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I have set `N=8` which means that we will incorporate 8 future measurements into our estimates. This provides us with a very smooth estimate once the filter converges, at the cost of roughly 8x the amount of computation of the standard Kalman filter. Feel free to experiment with larger and smaller values of `N`. I chose 8 somewhat at random, not due to any theoretical concerns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n", "\n", "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n", "\n", "http://arc.aiaa.org/doi/abs/10.2514/3.3166" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }