{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Table of Contents](./table_of_contents.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Smoothing"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 3,
"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": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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