{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Designing Nonlinear Kalman Filters"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from __future__ import division, print_function"
]
},
{
"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": [
"** Author's note: I was initially planning to have a design nonlinear chapter that compares various approaches. This may or may not happen, but for now this chapter has no useful content and I suggest not reading it. **"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a silly example; we can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Kalman Filter with Air Drag"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I will dispense with the step 1, step 2, type approach and proceed in a more natural style that you would use in a non-toy engineering problem. We have already developed a Kalman filter that does excellently at tracking a ball in a vacuum, but that does not incorporate the effects of air drag into the model. We know that the process model is implemented with $\\textbf{F}$, so we will turn our attention to that immediately.\n",
"\n",
"Notionally, the computation that $\\textbf{F}$ computes is\n",
"\n",
"$$x' = Fx$$\n",
"\n",
"With no air drag, we had\n",
"\n",
"$$\n",
"\\mathbf{F} = \\begin{bmatrix}\n",
"1 & \\Delta t & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 & 0 \\\\\n",
"0 & 0 & 1 & \\Delta t & \\frac{1}{2}{\\Delta t}^2 \\\\\n",
"0 & 0 & 0 & 1 & \\Delta t \\\\\n",
"0 & 0 & 0 & 0 & 1\n",
"\\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"which corresponds to the equations\n",
"\n",
"$$ \n",
"\\begin{aligned}\n",
"x &= x + v_x \\Delta t \\\\\n",
"v_x &= v_x \\\\\n",
"\\\\\n",
"y &= y + v_y \\Delta t + \\frac{a_y}{2} {\\Delta t}^2 \\\\\n",
"v_y &= v_y + a_y \\Delta t \\\\\n",
"a_y &= a_y\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the section above we know that our new Euler equations must be\n",
"\n",
"$$ \n",
"\\begin{aligned}\n",
"x &= x + v_x \\Delta t \\\\\n",
"v_x &= v_x \\\\\n",
"\\\\\n",
"y &= y + v_y \\Delta t + \\frac{a_y}{2} {\\Delta t}^2 \\\\\n",
"v_y &= v_y + a_y \\Delta t \\\\\n",
"a_y &= a_y\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Realistic 2D Position Sensors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The position sensor in the last example are not very realistic. In general there is no 'raw' sensor that provides (x,y) coordinates. We have GPS, but GPS already uses a Kalman filter to create a filtered output; we should not be able to improve the signal by passing it through another Kalman filter unless we incorporate additional sensors to provide additional information. We will tackle that problem later. \n",
"\n",
"Consider the following set up. In an open field we put two transmitters at a known location, each transmitting a signal that we can detect. We process the signal and determine how far we are from that signal, with some noise. First, let's look at a visual depiction of that."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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