{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Nonlinear Filtering" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%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\n", "\n", "The Kalman filter that we have developed uses linear equations, and so the filter can only handle linear problems. But the world is nonlinear, and so the classic filter that we have been studying to this point can have very limited utility. \n", "\n", "There can be nonlinearity in the process model. Suppose we want to track an object falling through the atmosphere. The acceleration of the object depends on the drag it encounters. Drag depends on air density, and the air density decreases with altitude. In one dimension this can be modelled with the nonlinear differential equation\n", "\n", "$$\\ddot x = \\frac{0.0034ge^{-x/22000}\\dot x^2}{2\\beta} - g$$\n", "\n", "A second source of nonlinearity comes from the measurements. For example, radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n", "\n", "$$x=\\sqrt{\\mathtt{slant}^2 - \\mathtt{altitude}^2}$$\n", "\n", "These facts were not lost on the early adopters of the Kalman filter. Soon after Dr. Kalman published his paper people began working on how to extend the Kalman filter for nonlinear problems. \n", "\n", "It is almost true to state that the only equation anyone knows how to solve is $\\mathbf{Ax}=\\mathbf{b}$. We only really know how to do linear algebra. I can give you any linear set of equations and you can either solve it or prove that it has no solution. \n", "\n", "Anyone with formal education in math or physics has spent years learning various analytic ways to solve integrals, differential equations and so on. Yet even trivial physical systems produce equations that cannot be solved analytically. I can take an equation that you are able to integrate, insert a $\\log$ term, and render it insolvable. This leads to jokes about physicists stating \"assume a spherical cow on a frictionless surface in a vacuum...\". Without making extreme simplifications most physical problems do not have analytic solutions.\n", "\n", "How do we do things like model airflow over an aircraft in a computer, or predict weather, or track missiles with a Kalman filter? We retreat to what we know: $\\mathbf{Ax}=\\mathbf{b}$. We find some way to linearize the problem, turning it into a set of linear equations, and then use linear algebra software packages to compute an approximate solution. \n", "\n", "Linearizing a nonlinear problem gives us inexact answers, and in a recursive algorithm like a Kalman filter or weather tracking system these small errors can sometimes reinforce each other at each step, quickly causing the algorithm to spit out nonsense. \n", "\n", "What we are about to embark upon is a difficult problem. There is not one obvious, correct, mathematically optimal solution anymore. We will be using approximations, we will be introducing errors into our computations, and we will forever be battling filters that *diverge*, that is, filters whose numerical errors overwhelm the solution. \n", "\n", "In the remainder of this short chapter I will illustrate the specific problems the nonlinear Kalman filter faces. You can only design a filter after understanding the particular problems the nonlinearity in your problem causes. Subsequent chapters will then teach you how to design and implement different kinds of nonlinear filters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Problem with Nonlinearity\n", "\n", "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multiply them we get another Gaussian as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin$ as an output.\n", "\n", "What I mean by linearity may be obvious, but there are some subtleties. The mathematical requirements are twofold:\n", "\n", "* additivity: $f(x+y) = f(x) + f(y)$\n", "* homogeneity: $f(ax) = af(x)$\n", "\n", "\n", "This leads us to say that a linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if I sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if the amplifier outputs a nonzero signal such as a hum for a zero input the additive relationship no longer holds. This is because linearity requires that $amp(voice) = amp(voice + 0)$. This clearly should give the same output, but if amp(0) is nonzero, then\n", "\n", "\n", "\\begin{aligned}\n", "amp(voice) &= amp(voice + 0) \\\\\n", "&= amp(voice) + amp(0) \\\\\n", "&= amp(voice) + non\\_zero\\_value\n", "\\end{aligned}\n", "\n", "\n", "which is clearly nonsense. Hence, an apparently linear equation such as\n", "\n", "$$L(f(t)) = f(t) + 1$$\n", "\n", "is not linear because $L(0) = 1$. Be careful!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Intuitive Look at the Problem\n", "\n", "I particularly like the following way of looking at the problem, which I am borrowing from Dan Simon's *Optimal State Estimation* [[1]](#[1]). Consider a tracking problem where we get the range and bearing to a target, and we want to track its position. The reported distance is 50 km, and the reported angle is 90$^\\circ$. Assume that the errors in both range and angle are distributed in a Gaussian manner. Given an infinite number of measurements what is the expected value of the position?\n", "\n", "I have been recommending using intuition to gain insight, so let's see how it fares for this problem. We might reason that since the mean of the range will be 50 km, and the mean of the angle will be 90$^\\circ$, that the answer will be x=0 km, y=50 km.\n", "\n", "Let's plot that and find out. Here are 3000 points plotted with a normal distribution of the distance of 0.4 km, and the angle having a normal distribution of 0.35 radians. We compute the average of the all of the positions, and display it as a star. Our intuition is displayed with a large circle." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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