{ "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": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "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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