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Created November 22, 2019 11:28
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gh-tutorial.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "gh-tutorial.ipynb",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "aPU2I0q6q4oM",
"colab_type": "text"
},
"source": [
"## Kalman filter\n",
"\n",
"カルマンフィルターを学ぼう。\n",
"\n",
"\n",
"#### ズバリ、キーワードは**noise**です\n",
"\n",
"ざっとやった雰囲気から先にカルマンフィルターのイメージを超ざっくり説明すると\n",
"\n",
"> 回帰においてtargetに幅を持たせたアルゴリズム\n",
"\n",
"> estimationとpredictionの二つを逐次的に重み付けながらblendする点が大きな特徴\n",
"\n",
"と言ってもこれだけではやはりわからないので実験込みでみていこう\n",
"\n",
"---\n",
"\n",
"**ちなみに、このブックではカルマンフィルターには触れません**\n",
"\n",
"**最終的な目標がカルマンフィルターになります**\n",
"\n",
"\n",
"## $\\alpha$-$\\beta$ filter"
]
},
{
"cell_type": "code",
"metadata": {
"id": "Abc_Dhvgk5oA",
"colab_type": "code",
"colab": {}
},
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "Et4t87l_pzNV",
"colab_type": "text"
},
"source": [
"ひとまずfilterというものを理解するために次の体重のデータを使って振る舞いをみよう\n",
"\n",
"例えばpredictionが150.6になったとする、しかし、実際にはmeasurementが158.1だったとしよう\n",
"\n",
"predictionとmeasurement共にnoiseが乗っていると考えるとその間のestimateという値を考えたほうが良さそう\n",
"\n",
"(ちなみにカルマンフィルターのKGはこれらに逐次$(0,1)$の重みを与える)\n",
"\n",
"分数のところは適当で、次のような式がたまたま閃いたとしよう\n",
"\n",
"$$ estimation = prediction + \\frac{4}{10} (measurement - prediction) $$\n",
"\n",
"\n",
"> predictionとestimationの違いなんやねん!って思いましたよね、僕もです。\n",
"\n",
"> 未来の値がprediction、現在の予測がestimation(noise考慮の予測と思ってもいい)です、時間軸がどこにあるかです\n",
"\n",
"> もっと雑に言えばイコールです\n",
"\n",
"\n",
"weightは1 lb/dayずつ増えると仮定する(prediction)"
]
},
{
"cell_type": "code",
"metadata": {
"id": "NhXEQUj9h2lw",
"colab_type": "code",
"outputId": "97077631-dae0-4f8a-a5ee-b4f3b6b58e66",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 607
}
},
"source": [
"weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
"\n",
"time_step = 1.0 # day\n",
"scale_factor = 4.0/10 # random テキトウ\n",
"\n",
"def predict_using_gain_guess(estimated_weight, gain_rate, do_print=False): \n",
" # storage for the filtered results\n",
" estimates, predictions = [estimated_weight], []\n",
"\n",
" # most filter literature uses 'z' for measurements\n",
" for i, z in enumerate(weights): \n",
" # predict new position\n",
" predicted_weight = estimated_weight + gain_rate * time_step\n",
"\n",
" # update filter \n",
" estimated_weight = predicted_weight + scale_factor * (z - predicted_weight)\n",
"\n",
" # save and log\n",
" estimates.append(estimated_weight)\n",
" predictions.append(predicted_weight)\n",
" if do_print:\n",
" print('previous estimate: {:.2f} prediction: {:.2f} estimate: {:.2f}'.format(estimates[i], predicted_weight, estimated_weight))\n",
" return estimates, predictions\n",
"\n",
"initial_estimate = 160.\n",
"gain_rate = 1 # 1 lb/day\n",
"estimates, predictions = predict_using_gain_guess(\n",
" estimated_weight=initial_estimate, gain_rate=gain_rate, do_print=True)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.ylim(156, 173)\n",
"plt.xlabel('days', fontsize=18)\n",
"plt.ylabel('weight[lb]', fontsize=18)\n",
"plt.plot(range(len(weights)+1), estimates, label='Estimates', color='skyblue', marker='o')\n",
"plt.plot(range(1, len(weights)+1), predictions, label='Prediction', color='red', marker='^', linestyle='dashed')\n",
"plt.scatter(range(1, len(weights)+1), weights, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": [
"previous estimate: 160.00 prediction: 161.00 estimate: 159.80\n",
"previous estimate: 159.80 prediction: 160.80 estimate: 162.16\n",
"previous estimate: 162.16 prediction: 163.16 estimate: 162.02\n",
"previous estimate: 162.02 prediction: 163.02 estimate: 161.77\n",
"previous estimate: 161.77 prediction: 162.77 estimate: 162.50\n",
"previous estimate: 162.50 prediction: 163.50 estimate: 163.94\n",
"previous estimate: 163.94 prediction: 164.94 estimate: 166.80\n",
"previous estimate: 166.80 prediction: 167.80 estimate: 167.64\n",
"previous estimate: 167.64 prediction: 168.64 estimate: 167.75\n",
"previous estimate: 167.75 prediction: 168.75 estimate: 169.65\n",
"previous estimate: 169.65 prediction: 170.65 estimate: 170.87\n",
"previous estimate: 170.87 prediction: 171.87 estimate: 172.16\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d896fb70>"
]
},
"metadata": {
"tags": []
},
"execution_count": 2
},
{
"output_type": "display_data",
"data": {
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lS0RFRWE2m4uscVSnTh169OjB1q1bCQsLo02bNjg5OTF8+HA6depUBXcETz75JPPmzeO+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\nAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "avFa-IQKuLhB",
"colab_type": "text"
},
"source": [
"この時点でもういい感じではないか?\n",
"\n",
"\n",
"そして、上の式は実はたまたま閃かずとも導出できるのである\n",
"\n",
"- estimationを$x^*_n$\n",
"- predictionを$\\hat{x}_n$\n",
"- measurementを$z_n$\n",
"\n",
"とします。\n",
"$$x^* = \\frac{1}{N}\\sum_{n=1}^{N}{ (z_n ) } $$\n",
"とすると\n",
"\n",
"$$\\frac{1}{N}\\sum_{n=1}^{N}{ (z_n ) } = \\frac{1}{N}\\sum_{n=1}^{N-1}{ (z_n ) + z_N} $$\n",
"\n",
"$$\\frac{1}{N}\\sum_{n=1}^{N-1}{ (z_n ) + z_N} = \\frac{N-1}{N}\\frac{1}{N-1} \\sum_{n=1}^{N-1}{ (z_n ) } + \\frac{1}{N} z_N $$\n",
"\n",
"$$ \\frac{N-1}{N}\\frac{1}{N-1} \\sum_{n=1}^{N-1}{ (z_n ) } + \\frac{1}{N} z_N = \\frac{N-1}{N} \\hat{x}_{n-1} + \\frac{1}{N} z_N $$\n",
"\n",
"$$ \\frac{N-1}{N} \\hat{x}_{n-1} + \\frac{1}{N} z_N = \\hat{x}_{n-1} + \\frac{1}{N}(z_N - \\hat{x}_{n-1} ) $$\n",
"\n",
"\n",
"となり、つまり\n",
"\n",
"$$x^* = \\hat{x}_{n-1} + \\frac{1}{N}(z_N - \\hat{x}_{n-1} ) $$\n",
"\n",
" です\n",
"\n",
"gain_rateを変えてみる、例えば1.0 lb/day減るとすると"
]
},
{
"cell_type": "code",
"metadata": {
"id": "hBK7n-gXiNTw",
"colab_type": "code",
"outputId": "c29d684a-2d03-46dd-de25-8514236d9135",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 607
}
},
"source": [
"initial_estimate = 160.\n",
"gain_rate = -1 # -1 lb/day\n",
"estimates, predictions = predict_using_gain_guess(\n",
" estimated_weight=initial_estimate, gain_rate=gain_rate, do_print=True)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.ylim(156, 173)\n",
"plt.xlabel('days', fontsize=18)\n",
"plt.ylabel('weight[lb]', fontsize=18)\n",
"plt.plot(range(len(weights)+1), estimates, label='Estimates', color='skyblue', marker='o')\n",
"plt.plot(range(1, len(weights)+1), predictions, label='Prediction', color='red', marker='^', linestyle='dashed')\n",
"plt.scatter(range(1, len(weights)+1), weights, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": [
"previous estimate: 160.00 prediction: 159.00 estimate: 158.60\n",
"previous estimate: 158.60 prediction: 157.60 estimate: 160.24\n",
"previous estimate: 160.24 prediction: 159.24 estimate: 159.66\n",
"previous estimate: 159.66 prediction: 158.66 estimate: 159.16\n",
"previous estimate: 159.16 prediction: 158.16 estimate: 159.74\n",
"previous estimate: 159.74 prediction: 158.74 estimate: 161.08\n",
"previous estimate: 161.08 prediction: 160.08 estimate: 163.89\n",
"previous estimate: 163.89 prediction: 162.89 estimate: 164.69\n",
"previous estimate: 164.69 prediction: 163.69 estimate: 164.78\n",
"previous estimate: 164.78 prediction: 163.78 estimate: 166.67\n",
"previous estimate: 166.67 prediction: 165.67 estimate: 167.88\n",
"previous estimate: 167.88 prediction: 166.88 estimate: 169.17\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5c7b6d8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
},
{
"output_type": "display_data",
"data": {
"image/png": 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yZUuysrJ46623WL58Of/+978ZM2ZMxfkrVqzgiiuuICIigvHjx9OxY0dycnLY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\nuCHMO2tqeWL5FvLTQ74ZRGFmt7toq22M8lZsrSQHjO+byZf6ZZPdw+Z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/+8eTJvmRga99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\niYiIiIiIxKFkSUREREREJI7/DxLI/KvEKFckAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "K5O9E1wCuT20",
"colab_type": "text"
},
"source": [
"measurementsから大きく解離してしまってよろしくない、\n",
"\n",
"今の例だと体重は毎日平均多分$\\pm 1$lbだとこちらが勝手に予想した、\n",
"\n",
"そもそもこれがよくないんじゃないか、しかも実際の予測においてこの値はわからないことがほとんどのはず\n",
"\n",
"ではどうする?\n",
"\n",
"逐次的にデータが得られるのであれば最もらしいgain_rateもその都度計算すれば良いのでは?\n",
"\n",
"例えばday1で計算してみると\n",
"\n",
"$$ (160+1) + \\frac{4}{10}(158 - 161) = 159.8 $$\n",
"\n",
"翌日のmeasurementは164.2なのでその差分(gain_weight)は$164.2 - 159.8 = 4.4$\n",
"\n",
"だからといって毎日4.4ずつ増えるわけではない、例えばday0では何も食べなかったならおそらく翌日は-1などの方が打倒だろう\n",
"\n",
"そこで連続した2日のデータから新たなgainを次のように求めることにとりあえずする\n",
"\n",
"$$ gain := gain + \\frac{1}{3} \\frac{(measurement - prediction)}{1day} $$\n",
"\n",
"今回はデータが簡単で直感的なので実際株価予測などする際は、色々考えてモデリングする必要がありそう"
]
},
{
"cell_type": "code",
"metadata": {
"id": "hx8azZaMpp0K",
"colab_type": "code",
"outputId": "66158602-846e-4496-9618-920babe4ba77",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 412
}
},
"source": [
"weight = 160. # initial guess\n",
"gain_rate = -1.0 # initial guess\n",
"\n",
"time_step = 1.\n",
"weight_scale = 4./10 # random guess\n",
"gain_scale = 1./3 # random guess\n",
"estimates = [weight]\n",
"predictions = []\n",
"\n",
"for z in weights:\n",
" # prediction step\n",
" weight = weight + gain_rate*time_step\n",
" predictions.append(weight)\n",
" \n",
" # update step \n",
" residual = z - weight\n",
" \n",
" gain_rate = gain_rate + gain_scale * (residual/time_step)\n",
" weight = weight + weight_scale * residual\n",
" \n",
" estimates.append(weight)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.ylim(156, 173)\n",
"plt.xlabel('days', fontsize=18)\n",
"plt.ylabel('weight[lb]', fontsize=18)\n",
"plt.plot(range(len(weights)+1), estimates, label='Estimates', color='skyblue', marker='o')\n",
"plt.plot(range(1, len(weights)+1), predictions, label='Prediction', color='red', marker='^', linestyle='dashed')\n",
"plt.scatter(range(1, len(weights)+1), weights, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5c01860>"
]
},
"metadata": {
"tags": []
},
"execution_count": 4
},
{
"output_type": "display_data",
"data": {
"image/png": 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9X3zxRafH69Wrl9I0Tc2fP9+hPSsrS3Xs2FGZTCZ1/Phxe3t8fLwC1JAhQ5TV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\nJEmSpA6GJUmSJEnq8C9JCyoIxbTU4QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "sAGnxf7N2PxW",
"colab_type": "text"
},
"source": [
"おー、いい感じにできた。機械学習では重みを更新する作業があるけどそれと同じようなことをやっていることがわかった\n",
"\n",
"\n",
"ところで今やっていたことは**$\\alpha$-$\\beta$ filter**というものらしい\n",
"- https://en.wikipedia.org/wiki/Alpha_beta_filter\n",
"\n",
"![g-h 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%0A)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kIx3YvfO3Xxr",
"colab_type": "text"
},
"source": [
"色々用語などがあるようなのでそれもメモしよう\n",
"\n",
"- System(plant): estimateするもの\n",
"- The state of the system: systemの実際値、ほぼ観測できない\n",
"- The measurement: systemの値\n",
"- The state estimate: estimateの状態(値)\n",
"\n",
"正直よくわからなかった、みなさんもわからなくてもとりあえず無視していいと思う\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "0tjsQ6aWAcTy",
"colab_type": "text"
},
"source": [
"## 懐かしき高校物理\n",
"\n",
"今時刻$T$でA君が$x_T$にいるとする\n",
"\n",
"そこで時刻$T+1$のAさんの位置は速さが$v$だとすると\n",
"\n",
"$$ x_{t+1} = x_0 + vt $$\n",
"\n",
"となります。これを用いてg-hフィルタをかくと下のようになる\n",
"\n",
"つまり、"
]
},
{
"cell_type": "code",
"metadata": {
"id": "NhkiAV_6yWQk",
"colab_type": "code",
"outputId": "fef81368-ac06-4279-ab5f-f7f9a8bdc0b8",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 412
}
},
"source": [
"def g_h_filter(data, x0, dx, g, h, dt=1.):\n",
" x_est = x0\n",
" results = []\n",
" for z in data:\n",
" # prediction step\n",
" x_pred = x_est + (dx*dt)\n",
" dx = dx\n",
"\n",
" # update step\n",
" residual = z - x_pred\n",
" dx = dx + h * (residual) / dt\n",
" x_est = x_pred + g * residual\n",
" results.append(x_est)\n",
" return np.array(results)\n",
"\n",
"\n",
"data = g_h_filter(data=weights, x0=160., dx=1., g=6./10, h=2./3, dt=1.)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.ylim(156, 173)\n",
"plt.xlabel('days', fontsize=18)\n",
"plt.ylabel('weight[lb]', fontsize=18)\n",
"plt.plot(range(1, len(weights)+1), data, label='Filter', color='skyblue', marker='o', linestyle='dashed')\n",
"plt.scatter(range(1, len(weights)+1), weights, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5b898d0>"
]
},
"metadata": {
"tags": []
},
"execution_count": 5
},
{
"output_type": "display_data",
"data": {
"image/png": 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ynn/+efbu3cvYsWOZOXMmN910E+eff/5APE0RGWHW1bWwrLqRiAWMoT4cY1l1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\n6vEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "qh37iPXU8AXb",
"colab_type": "text"
},
"source": [
"ポイントはgはmeasurementとpredictionの関係を重み付ているということ\n",
"\n",
"\n",
"\n",
"### g-hの変化が及ぼす影響をみてみる\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "LKIdLWwF6YOD",
"colab_type": "code",
"outputId": "05b268fd-1e41-418e-f30f-3cc2388fa045",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 412
}
},
"source": [
"from numpy.random import randn\n",
"def gen_data(x0, dx, count, noise_factor):\n",
" return [x0 + dx*i + randn()*noise_factor for i in range(count)]\n",
"\n",
"measurements = gen_data(0, 1, 30, 1)\n",
"data = g_h_filter(data=measurements, x0=0., dx=1., dt=1., g=.2, h=0.02)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(measurements)+1), data, label='Filter', color='skyblue', marker='o', linestyle='dashed')\n",
"plt.scatter(range(1, len(measurements)+1), measurements, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5b047b8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 6
},
{
"output_type": "display_data",
"data": {
"image/png": 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IZFDXaWxP8OKOJn68sZa/7G3hhDwvE7wulhT6cR1WO8FlYEmhP/WFRA6Tzpmi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\naZ97diOaAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "FNB5IfvM9Rgs",
"colab_type": "text"
},
"source": [
"初期条件をひどくしてみる"
]
},
{
"cell_type": "code",
"metadata": {
"id": "eee3s85S9KGd",
"colab_type": "code",
"outputId": "129c3437-6afc-4532-b3cb-e19858caa532",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 412
}
},
"source": [
"zs = gen_data(x0=5., dx=2., count=100, noise_factor=10)\n",
"data = g_h_filter(data=zs, x0=100., dx=2., dt=1., g=0.2, h=0.02)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data, label='Filter', color='skyblue', marker='o', linestyle='dashed')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5a7b710>"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
},
{
"output_type": "display_data",
"data": {
"image/png": 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XBAYQ1eeibq8EZGihhpGWTkfJgStLNKzGjx+P2tpaWCwWqNVqWK1WPPbYY/j7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\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "iHJ6TQyH90iR",
"colab_type": "text"
},
"source": [
"noiseを大きくしてみる\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "nuPn9yPq8SF-",
"colab_type": "code",
"outputId": "5a205e9b-f6ed-4d13-e1b9-306daa285168",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 412
}
},
"source": [
"zs = gen_data(x0=5., dx=2., count=100, noise_factor=100)\n",
"data = g_h_filter(data=zs, x0=5., dx=2., g=0.2, h=0.02)\n",
"\n",
"plt.figure(figsize=(14, 6))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data, label='Filter', color='skyblue', marker='o', linestyle='dashed')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d59e9908>"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
"image/png": 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KgGxsbJRSSnnddddJrVYrDxw4MHL7BRdcIMvLy6XL5ZJr166VAOT69esjnmPZsmVSCCEf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\nAAAABEAwBQAAAAAB/H+HeTuYrQoCpwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "oVoSjDkZ_YNY",
"colab_type": "text"
},
"source": [
"gの変化を見る"
]
},
{
"cell_type": "code",
"metadata": {
"id": "u0bXGubX96Ng",
"colab_type": "code",
"outputId": "8f5f602b-e742-423b-afda-719aaf226673",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 578
}
},
"source": [
"np.random.seed(100)\n",
"zs = gen_data(x0=5., dx=5., count=50, noise_factor=50)\n",
"data1 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.1, h=0.01)\n",
"data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.4, h=0.01)\n",
"data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.8, h=0.01)\n",
"\n",
"plt.figure(figsize=(16, 9))\n",
"plt.xlim(20, 40)\n",
"plt.ylim(50, 250)\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data1, label='g=0.1', color='skyblue', marker='o', linestyle='dashed')\n",
"plt.plot(range(1, len(zs)+1), data2, label='g=0.4', color='red', marker='^')\n",
"plt.plot(range(1, len(zs)+1), data3, label='g=0.8', color='green', marker='*')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d5961710>"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
},
{
"output_type": "display_data",
"data": {
"image/png": 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pp55i+/btXHPNNVaPX0REROquiIgI0tPTi5Wlp6cTERFho4hqh3Vx60jPTrfK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\n5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z7M4yMe54EpD9D2q7bsOrmLWXfMYvHQxQR42M4EhNiwWPZk7uFA9oHKvygmBgYPFpUb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\nB0s5lP2D/VnSAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j0vtuIH0Belz",
"colab_type": "text"
},
"source": [
"```\n",
"def g_h_filter(data, x0, dx, g, h, dt=1.):\n",
" x_est = x0\n",
" results = []\n",
" for z in data:\n",
" # prediction step\n",
" x_pred = x_est + (dx*dt)\n",
" dx = dx\n",
"\n",
" # update step\n",
" residual = z - x_pred\n",
" dx = dx + h * (residual) / dt\n",
" x_est = x_pred + g * residual\n",
" results.append(x_est)\n",
" return np.array(results)\n",
"```\n",
"\n",
"を見返し、グラフよりgが大きいほどmeasurementに引っ張られることがわかる\n",
"\n",
"次にvelocityがある時点でなくなる例を考える、上の事実を明らかに"
]
},
{
"cell_type": "code",
"metadata": {
"id": "4r7ybvnT_Z5L",
"colab_type": "code",
"outputId": "5e5aa515-91c1-477f-a89b-74b20070fa2b",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 575
}
},
"source": [
"zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n",
"for i in range(50):\n",
" zs.append(14)\n",
"\n",
"data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.1, h=0.01)\n",
"data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.5, h=0.01)\n",
"data3 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.9, h=0.01)\n",
"\n",
"plt.figure(figsize=(16, 9))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data1, label='g=0.1', color='orange', marker='<', linestyle='dashed')\n",
"plt.plot(range(1, len(zs)+1), data2, label='g=0.5', color='red', marker='^')\n",
"plt.plot(range(1, len(zs)+1), data3, label='g=0.9', color='skyblue', marker='*')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d3e318d0>"
]
},
"metadata": {
"tags": []
},
"execution_count": 16
},
{
"output_type": "display_data",
"data": {
"image/png": 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+PBJLQprn/XsbNmwYI0eOJC4ujqFDh/Lkk0+ycuVKevfuTVpaWolfb+1ac83s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\nAABDEmgBAAAY0n8DeLwGn7eFAjUAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "k7dd314JDgbh",
"colab_type": "text"
},
"source": [
"次はhの変化をみる"
]
},
{
"cell_type": "code",
"metadata": {
"id": "3rza-QdBCSje",
"colab_type": "code",
"outputId": "2f875ab4-5c7c-4261-c96e-f473be85158a",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 575
}
},
"source": [
"zs = np.linspace(0, 1, 50)\n",
"\n",
"data1 = g_h_filter(data=zs, x0=0, dx=0., dt=1., g=.2, h=0.05)\n",
"data2 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.05)\n",
"data3 = g_h_filter(data=zs, x0=0, dx=2., dt=1., g=.2, h=0.5)\n",
"\n",
"plt.figure(figsize=(16, 9))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data1, label='h=0.05', color='orange', marker='<', linestyle='dashed')\n",
"plt.plot(range(1, len(zs)+1), data2, label='h=0.05', color='red', marker='^')\n",
"plt.plot(range(1, len(zs)+1), data3, label='h=0.5', color='skyblue', marker='*')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 17,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d3dbcb00>"
]
},
"metadata": {
"tags": []
},
"execution_count": 17
},
{
"output_type": "display_data",
"data": {
"image/png": 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5tVWnVi0YNQo++gh++MHuNCIiIiLVyh1zbEePHg3AzJkzi83fTU1NZcGCBQQF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\nQAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "xbeTP2koFi1e",
"colab_type": "code",
"outputId": "ceb3e734-e8ff-43be-c481-e900a688df36",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 575
}
},
"source": [
"zs = gen_data(x0=5., dx=.2, count=100, noise_factor=100)\n",
"data = g_h_filter(data=zs, x0=5., dx=.2, dt=1., g=0., h=0.)\n",
"\n",
"plt.figure(figsize=(16, 9))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data, label='g=0', color='orange', marker='x', linestyle='dashed')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 18,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d3d32dd8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 18
},
{
"output_type": "display_data",
"data": {
"image/png": 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Ckg0YMMDMzEaPHm2ZmZm2ZMmSuvr3vvc969Gjh23evNmKiopMko0ZM6bBNk444QRzztm4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\nMDjCMAAAAIMjDAMAADA4/x8LL7eFjMGJjgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "St46FReOFi44",
"colab_type": "code",
"outputId": "aa29db62-04fc-4758-9cef-5588f014a19e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 575
}
},
"source": [
"zs = gen_data(x0=5, dx=-2, count=100, noise_factor=5)\n",
"data = g_h_filter(data=zs, x0=5., dx=2., dt=1., g=.005, h=0.001)\n",
"\n",
"plt.figure(figsize=(16, 9))\n",
"plt.xlabel('x', fontsize=18)\n",
"plt.ylabel('y', fontsize=18)\n",
"plt.plot(range(1, len(zs)+1), data, label='g=0.005', color='orange', marker='x', linestyle='dashed')\n",
"plt.scatter(range(1, len(zs)+1), zs, label='Measurements', color='black', marker='o')\n",
"plt.grid('on')\n",
"plt.legend(fontsize=20)"
],
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fa4d3cb1278>"
]
},
"metadata": {
"tags": []
},
"execution_count": 19
},
{
"output_type": "display_data",
"data": {
"image/png": 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Tp0512n7o0CFz8cUXm8DAQLNnz56i7YcPHzb79+8v1Zft27ebiIgI07lzZ6ft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\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "YIZQr14htvRv",
"colab_type": "text"
},
"source": [
"## References\n",
"\n",
"- https://www.kalmanfilter.net/alphabeta.html\n",
"- https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/01-g-h-filter.ipynb"
]
}
]
}
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