Control Kalman Filter - Simple (youtube example)

Control Kalman Filter - Simple (youtube example).ipynb

{
  "cells": [
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from IPython.display import YouTubeVideo\nimport pandas as pd\nimport numpy as np",
      "execution_count": 10,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "YouTubeVideo('SIQJaqYVtuE',height=315, width=560)",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
          "data": {
            "text/plain": "<IPython.lib.display.YouTubeVideo at 0x7f7fd32fa198>",
            "text/html": "\n        <iframe\n            width=\"560\"\n            height=\"315\"\n            src=\"https://www.youtube.com/embed/SIQJaqYVtuE\"\n            frameborder=\"0\"\n            allowfullscreen\n        ></iframe>\n        ",
            "image/jpeg": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "\nmeasurements = [75,71,70,74,74,74]\ndf = pd.DataFrame(data={'measurement':measurements,\n                        'measurement_error_constant':[4]*len(measurements)})\ndf['estimate'] = np.nan\ndf['kalman_gain'] = np.nan\ndf['estimate_error'] = np.nan\n",
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def get_estimates(target_series, inital_guess, inital_error, measurement_error_constant):\n    dframe = target_series.to_frame()\n    dframe['measurement_error_constant'] = measurement_error_constant\n    dframe['estimate'] = np.nan\n    dframe['kalman_gain'] = np.nan\n    dframe['estimate_error'] = np.nan\n    current = 0\n\n    for timestamp,row in dframe.iterrows():\n        previous = current - 1\n        print(f'current:{current}')\n        print(f'previous:{previous}')\n\n        if current != 0:\n            previous_estimate_error =dframe.iloc[previous]['estimate_error']\n            previous_estimate = dframe.iloc[previous]['estimate']\n        else:\n            previous_estimate_error = 2\n            previous_estimate = 68\n        print(f'previous_estimate_error: {previous_estimate_error};  previous_estimate: {previous_estimate}')\n        measurement = dframe.iloc[current]['measurement']\n        measurement_error = dframe.iloc[current]['measurement_error_constant']\n        kalman_gain = previous_estimate_error / (previous_estimate_error + measurement_error)\n        print(f'kalman gain = {previous_estimate_error}/({previous_estimate_error}+{measurement_error}) = {kalman_gain}')\n        estimate = previous_estimate + kalman_gain*(measurement-previous_estimate)\n        print(f'new estimate = {previous_estimate} + {kalman_gain}*({measurement}-{previous_estimate}) = {estimate}')\n        estimate_error = (1-kalman_gain)*previous_estimate_error   \n\n        dframe.loc[current,'kalman_gain'] = kalman_gain\n        dframe.loc[current,'estimate'] = estimate\n        dframe.loc[current,'estimate_error'] = estimate_error\n        current +=1\n    return dframe",
      "execution_count": 22,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
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      "cell_type": "code",
      "source": "get_estimates(df['measurement'],inital_guess=68, inital_error=2,measurement_error_constant=4)",
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": "current:0\nprevious:-1\nprevious_estimate_error: 2;  previous_estimate: 68\nkalman gain = 2/(2+4.0) = 0.3333333333333333\nnew estimate = 68 + 0.3333333333333333*(75.0-68) = 70.33333333333333\ncurrent:1\nprevious:0\nprevious_estimate_error: 1.3333333333333335;  previous_estimate: 70.33333333333333\nkalman gain = 1.3333333333333335/(1.3333333333333335+4.0) = 0.25\nnew estimate = 70.33333333333333 + 0.25*(71.0-70.33333333333333) = 70.5\ncurrent:2\nprevious:1\nprevious_estimate_error: 1.0;  previous_estimate: 70.5\nkalman gain = 1.0/(1.0+4.0) = 0.2\nnew estimate = 70.5 + 0.2*(70.0-70.5) = 70.4\ncurrent:3\nprevious:2\nprevious_estimate_error: 0.8;  previous_estimate: 70.4\nkalman gain = 0.8/(0.8+4.0) = 0.16666666666666669\nnew estimate = 70.4 + 0.16666666666666669*(74.0-70.4) = 71.0\ncurrent:4\nprevious:3\nprevious_estimate_error: 0.6666666666666666;  previous_estimate: 71.0\nkalman gain = 0.6666666666666666/(0.6666666666666666+4.0) = 0.14285714285714285\nnew estimate = 71.0 + 0.14285714285714285*(74.0-71.0) = 71.42857142857143\ncurrent:5\nprevious:4\nprevious_estimate_error: 0.5714285714285714;  previous_estimate: 71.42857142857143\nkalman gain = 0.5714285714285714/(0.5714285714285714+4.0) = 0.125\nnew estimate = 71.42857142857143 + 0.125*(74.0-71.42857142857143) = 71.75\n",
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "execution_count": 24,
          "data": {
            "text/plain": "   measurement  measurement_error_constant   estimate  kalman_gain  \\\n0           75                           4  70.333333     0.333333   \n1           71                           4  70.500000     0.250000   \n2           70                           4  70.400000     0.200000   \n3           74                           4  71.000000     0.166667   \n4           74                           4  71.428571     0.142857   \n5           74                           4  71.750000     0.125000   \n\n   estimate_error  \n0        1.333333  \n1        1.000000  \n2        0.800000  \n3        0.666667  \n4        0.571429  \n5        0.500000  ",
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>measurement</th>\n      <th>measurement_error_constant</th>\n      <th>estimate</th>\n      <th>kalman_gain</th>\n      <th>estimate_error</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>75</td>\n      <td>4</td>\n      <td>70.333333</td>\n      <td>0.333333</td>\n      <td>1.333333</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>71</td>\n      <td>4</td>\n      <td>70.500000</td>\n      <td>0.250000</td>\n      <td>1.000000</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>70</td>\n      <td>4</td>\n      <td>70.400000</td>\n      <td>0.200000</td>\n      <td>0.800000</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>74</td>\n      <td>4</td>\n      <td>71.000000</td>\n      <td>0.166667</td>\n      <td>0.666667</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>74</td>\n      <td>4</td>\n      <td>71.428571</td>\n      <td>0.142857</td>\n      <td>0.571429</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>74</td>\n      <td>4</td>\n      <td>71.750000</td>\n      <td>0.125000</td>\n      <td>0.500000</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
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      "execution_count": null,
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