{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Unscented Kalman Filter" ] }, { "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": [ "In the last chapter we discussed the difficulties that nonlinear systems pose. This nonlinearity can appear in two places. It can be in our measurements, such as a radar that is measuring the slant range to an object. Slant range requires you to take a square root to compute the x,y coordinates:\n", "\n", "$$x=\\sqrt{\\text{slant}^2 - \\text{altitude}^2}$$\n", "\n", "The nonlinearity can also occur in the process model - we may be tracking a ball traveling through the air, where the effects of air drag lead to nonlinear behavior. The standard Kalman filter performs poorly or not at all with these sorts of problems.\n", "\n", "In the last chapter I showed you a plot like this. I have altered the equation somewhat to emphasize the effects of nonlinearity." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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