{ "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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