{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Designing Kalman Filters" ] }, { "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": [ "In the last chapter we worked with 'textbook' problems. These are problems that are easy to state, program in a few lines of code, and teach. Real world problems are rarely this simple. In this chapter we will work with more realistic examples, and learn how to evaluate filter performance.\n", "\n", "We will begin by tracking a robot in a 2D space, such as a field or warehouse. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n", "\n", "We will then move to a nonlinear problem. The world is nonlinear, but the Kalman filter is linear. Sometimes you can get away with using it for mildly nonlinear problems, sometimes you can't. I'll show you examples of both. This will set the stage for the remainder of the book, where we learn techniques for nonlinear problems. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking a Robot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This first attempt at tracking a robot will closely resemble the 1D dog tracking problem of previous chapters. Instead of a sensor that outputs position in a hallway, we now have a sensor that supplies a noisy measurement of position in a 2D space. At each time $t$ it will provide an $(x,y)$ coordinate pair of the noisy measurement of the sensor's position in the field.\n", "\n", "Implementation of code to interact with real sensors is beyond the scope of this book, so as before we will program simple simulations of the sensors. We will develop several of these sensors as we go, each with more complications, so as I program them I will just append a number to the function name. \n", "\n", "So let's start with a very simple sensor, one that simulates tracking an object traveling in a straight line. It is initialized with the initial position, velocity, and noise standard deviation. Each call to read() updates the position by one time step and returns the new measurement." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from numpy.random import randn\n", "\n", "class PosSensor(object):\n", " def __init__(self, pos=(0, 0), vel=(0, 0), noise_std=1.):\n", " self.vel = vel\n", " self.noise_std = noise_std\n", " self.pos = [pos[0], pos[1]]\n", " \n", " def read(self):\n", " self.pos[0] += self.vel[0]\n", " self.pos[1] += self.vel[1]\n", " \n", " return [self.pos[0] + randn() * self.noise_std,\n", " self.pos[1] + randn() * self.noise_std]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A quick test to verify that it works as we expect." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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