{ "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": { "image/png": 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\n", 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