{
"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": [
"%matplotlib inline\n",
"from __future__ import division, print_function"
]
},
{
"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",
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