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@balzer82
Last active September 12, 2023 13:39
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Alpha-Beta-Filter in Python
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{
"cells": [
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"import seaborn as sns\n",
"sns.set_style('whitegrid')\n",
"sns.set_context('poster')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Alpha Beta Filter\n",
"\n",
"Beispiel: Tracking einer Fahrzeugposition, wenn diese fehlerhaft gemessen wird (z.B. durch GPS)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"position = np.linspace(0, 100, 101) # wahre Position\n",
"messfehler = 20*np.random.randn(len(position))\n",
"messung = position + messfehler # fehlerhafte Messungen"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. $x_k = x_{k-1} + \\Delta T \\cdot v_{k-1}$ (Positionsschätzung)\n",
"2. $v_k = v_{k-1}$ (oder Geschwindigkeitsmessung)\n",
"3. $r_k = messung_k - x_k$ (Residuum)\n",
"4. $x_k = x_k + \\alpha \\cdot r_k$\n",
"5. $v_k = v_k + \\frac{\\beta}{\\Delta T}r_k$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"x=[]\n",
"v=[]\n",
"r=[]\n",
"x_k = 0.0\n",
"v_k = 10.0\n",
"dt = 1.0\n",
"\n",
"alpha = 0.10\n",
"beta = 0.005\n",
"\n",
"for k in range(len(messung)):\n",
" x_k = x_k + dt*v_k\n",
" v_k = 1.0\n",
" r_k = messung[k] - x_k\n",
" x_k = x_k + alpha*r_k\n",
" v_k = v_k + (beta/dt)*r_k\n",
" \n",
" x.append(x_k)\n",
" v.append(v_k)\n",
" r.append(r_k)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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c2UaeHq5//P3vVz9rx/6cmU6re7jpr4/1yDNI5mpUr6bG3d9Rowa2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\nrwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ac2a950>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, label=u'Position geschätzt')\n",
"plt.plot(position, label=u'wahre Position (unbekannt)', c='g')\n",
"plt.scatter(range(len(messung)), messung, c='k', alpha=0.4, label=u'Positionsmessung')\n",
"plt.xlabel('Zeit [s]')\n",
"plt.ylabel('Position [m]')\n",
"plt.legend(loc=4)\n",
"plt.title(r'Alpha-Beta-Tracker mit $\\alpha$=%.2f und $\\beta$=%.4f' % (alpha, beta))\n",
"plt.tight_layout()\n",
"plt.savefig('Alpha-Beta-Tracking-Fahrzeug-Position-GPS-Messung.png', dpi=150)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimale Alpha-Beta-Parameter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\lambda = \\cfrac{\\sigma_w T^2}{\\sigma_v}$\n",
"\n",
"Lambda ist der so genannte 'maneuvering index', im Grunde das Verhältnis von Prozess-Rauschen (wie schnell kann das Auto seine Geschwindigkeit innerhalb eines Zeitschritts ändern?) und Mess-Rauschen (wie falsch kann das GPS messen?).\n",
"\n",
"$\\alpha_\\text{opt} = \\frac{1}{8}\\left(-\\lambda^2 - 8\\lambda + (\\lambda+4) \\sqrt{\\lambda^2+8\\lambda}\\right)$\n",
"\n",
"$\\beta_\\text{opt} = \\frac{1}{4}\\left(\\lambda^2 + 4\\lambda -\\lambda \\sqrt{\\lambda^2 + 8\\lambda} \\right)$"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sigma_v = np.var(messfehler)\n",
"sigma_w = 2.0*dt # 2m/s2 Beschleunigung"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maneuvering Index 0.004\n",
"Least Square Optimal: alpha=0.09, beta=0.004\n"
]
}
],
"source": [
"lamb = (sigma_w*dt**2.0) / sigma_v\n",
"print('Maneuvering Index %.3f' % lamb)\n",
"\n",
"alpha_opt = 1/8.0*(-lamb**2.0 - 8.0*lamb + (lamb+4)*np.sqrt(lamb**2.0 + 8.0*lamb))\n",
"beta_opt = 1/4.0*(lamb**2.0 + 4.0*lamb - lamb*np.sqrt(lamb**2.0 + 8.0*lamb))\n",
"\n",
"print('Least Square Optimal: alpha=%.2f, beta=%.3f' % (alpha_opt, beta_opt))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fragen? [@Balzer82](http://twitter.com/balzer82)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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