{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Smoothing"
]
},
{
"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": [
"The performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement deviates far from the current track, like so (I'll only consider 1 dimension for simplicity):"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"