diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb index 647359d..8e6b950 100644 --- a/Designing_Kalman_Filters.ipynb +++ b/Designing_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:9253d1b89f39ca3b6e9087392e93410a4b889d4de3c48de04660d0c028948c29" + "signature": "sha256:6790e915a872d1db0a6db2a07a08d735d2be341faf2b0c3720abe5b9628ae04e" }, "nbformat": 3, "nbformat_minor": 0, @@ -244,7 +244,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -336,9 +336,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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ef58fTQCA2ONfG4RUVlYW7xIQIdOy8/ulpiarZ93V1f2fXZmWH44jO7ORnz3R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\nPTWCHWEAAADYEo0wQmJWylx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ib7Y/J4pq8MTGdHyyLw8z+4Xh3z6F6DN5NBTffw9bVJSzy3Mo9ie5Cq78EhER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\nqcnqEoCbIpswGfmEXfDcMAAAADgGwy8ch701mIp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r4RUivkbFr/gcza2JWSk32x7rrl0EPfIIEf37E/jSS2A0XDr/h+1FPPzddu4c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\nFG+h4ldM48O1OYzrFU2I3Ub/PVt574k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5Ol6AdsXYuPbTBlrvXoQ7yo7tmA3l2jVUiwf2li1Ap0d1u0FVUd0qqG5UVQW3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\nKRitWxjRdztvDzMBifuaGQwwbJiNAQMsbNsWk6Dvb2CgSoMGqb/5rFg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B31StH99/byAq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m/5RNlCjhomrV1Benaalf34mXl8qyZaak7ZddLujf35s33rBRvHjqs8heRQqm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\n7MkFX5DrhfBOxoXIDI8Vfvv3759Z5yGEEJnm+HENb7xhwc9P5auvYql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NM3PqlJZFi2Iw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Ynjhz2c/H7X/xLe3XhPOIi9oj5xTRtStXd3Gjw5il5D6vF4rx9punsWg/7agXtnVcNqNXjvvTDu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\nWjUlvyIiI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Ps0tAlKirrGRnu7VunVNvvVVYJ18PkYm1BTV1rKx8+qlDSUkhtW3Lq0uw7tpC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\n6ZRWrizSU0+Vqn17nkEBQE0wYwxEKa9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Nl4hsomvX2Adas5u6Llrkw/z58UWsqGlsgFMg8OabUDZtius56oQJiNxyi0Uj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\nUiT95S9BVWEBAM+4cfCMHw+ItetWQ3ltZmVZeYbt2vleMGfZMhl//av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J7NULIMzQ+QUANEhu7mG9/d7n+rA0TsM8+3TlLaOMuRsbgMhB5xcAEFQHfvhJ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\n2CQXAAAEFJ1foBHq1OktL5d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zdeuq/Yptm66ZI7sa1emtSdRmZxHkZx2s/AIAgiq7wK25X2bpk01eXZbeRjOv\nOl0pKUnhHhYAi6LzCwAICr99ek9tppSE6FjlBRA56PwCAMInL0/7duXo7QMudm8AEJHo/MIPvSez\nkZ/ZTM3P9uuvynvgEb3w12d166r9ineat09vQ5maHX5DftbByi8AoN5itmxR7gsv663CRsrsdrH6\nn5Osmee2s8yEF4B56PwCAOol+1ChFjwwU5kdzla/Dqka2vMEJr0AQo7OLwAgqI7+IFu/4UM1sys3\npwBgDjq/8EPvyWzkZ7aIzM/jUcwvvyi7wK3pq3dozILN5Z3eP51lnU5vTSIyO9Qa+VkHK78AgMoV\nFCj2jTd0aPYcvTr4Fi1v0YXdGwAYj84vAKAC2759in3xRR16Z5FeHXyLMtucpv5djtfQDOoNACIP\nnV8AQIMU3jRGM3oN0fLbnlP/zs00i0kvgChC5xd+6D2ZjfzMFs78jnR6rx96j5wXna9ZV59qqX16\nG4prz2zkZx2s/AKAFfl8su3ZI1/Lln63IabTCyCa0fkFACvxeuVcvFhx06fr17RWennCQ+WTXjq9\nAExE5xcAULmSEiVde62y3T7930336SNvY/X/fcsyJr0ArILOL/zQezIb+ZktaPmVlqpg/J/1eNfL\ndf2waYptd6JmDe1EpzeAuPbMRn7WwcovAES5nEK35q78UR+fcb36ndZKs7q1YMILwLLo/AJAlKpw\nG+JTUjWM2xADiEJ0fgHA4ti9AQCqRucXfug9mY38zNaQ/I7s0ztmwWbF//5BNjq9ocO1Zzbysw5W\nfgHAcJWt9Db55SeVxbcK99AAIOLQ+QUAQx076T2yT6/r9dcV98QTylu9WkpMDPcwASCo6PwCQJSr\nrtPr/Oc/Ff/II8pftIiJLwBUgs4v/NB7Mhv5ma26/Grq9DqXLlXC1KnKnz9fZSefHKoh43dce2Yj\nP+uoceX30Ucf1aJFi9SkSRMtXrxYktSpUyd16NBBktSjRw9NnTo1uKMEAAurze4NjpUrlXDbbSqY\nM0dlnTuHaaQAEPlq7PyuW7dOTqdTd999d/nkt3v37lq3bl21b0znFwAapqpOb2ViNm1STG6uSs85\nJ8SjBIDwCnjnt3v37tq5c2eDBgUAqL367NNb1rmzykI0PgAwWb06v263W0OGDNHIkSP11VdfBXpM\nCDN6T2YjP3NlF7g15Z0v2KfXUFx7ZiM/66jXbg8rV65UamqqNmzYoPHjxyszM1Mul8vvvLFjxyo9\nPV2SlJym7DpsAAAciUlEQVScrIyMDPXu3VvSf/+Rccwxxxxb/fj9Fau1er9TPxTFKSPRp5vb5CnR\nnaeU3/fpDff4OK7d8RGRMh6OyS9ajzds2KDc3FxJUlZWlkaPHq26qNU+vzt37tSYMWPKO79HGzZs\nmB599FGddNJJFR6n8wsA1atLp7eczyf7d9/J/s03cl93XWgGCgARLOj7/B46dEhxcXGKi4vTzp07\ntXfvXrVs2bKubwMAllXnTq/HI8eaNXIuXSrn0qVSWZlKbrstdAMGgChS4+T3vvvuU2Zmpg4dOqQL\nLrhAw4cP1+LFi+VyuWS32/XQQw8pLi4uFGNFiKxatar8zwswD/lFrtpMev3yc7uV3LWrylq3lqd/\nfxW8+abKOnWSbLYQjx414dozG/lZR42T32nTpmnatGkVHhs3blzQBgQA0abWK72+SlpoLpfyPv9c\nvpSU4A8UACygVp3f+qDzC8Dqauz0er2yf/mlXL/XGYqmTZOnf//wDRgADBT0zi8AoHo1rfTav/pK\nsa+8ImdmpsqOP16efv1U+Oyz8nbvHsZRA4A11GufX0S3Y7d9gVnIL3yyC9yavnpHjfv02g4flrdb\nN+V/+KHyP/1UxVOnynvGGVJMDPkZjOzMRn7WwcovADSQ30rvVZ2U+uN3ilnyuTxXXeV3fun556v0\n/PPDMFIAAJ1fAKinCpPek1M0Iu9HNVu2RM5//1u+xES5r7xSxXffHe5hAkBUo/MLAEHmt9I7pINO\n6Hm6vG3bytOvn4oXLlRZ+/bhHiYAoBJ0fuGH3pPZyC94snNyNX3ldv9Ob2Kscr/4QgXvv6+SCRMa\nNPElP3ORndnIzzpY+QWAqng8sq9dqwOrvtDbB11afnwnDWjh1KyhPfz36U1MDM8YAQB1QucXACoR\n++KLynv6eb3S/0Ytb9dDA47zashFXZSSxs0mACCS0PkFgNry+aT8fKlx4woPZxe4Nbft+fp48lnq\n37GpZh57cwoAgLHo/MIPvSezkV/1bDt3yvX220oYM0bJp56qxDvuKH+uwj69KY00a1jnSvfpDSby\nMxfZmY38rIOVXwCWELNjh5KuvFK23FyV9u4tzwUXqPjOO1V20kk13pENABA96PwCiC4FBVJSkv/j\npaWyb94sb+fOUsxvf/Q6dtI7lHoDABiHzi8AaykuluOLL+RYuVLOlStl37xZuevWyZeaWvE8h0Pe\nU0+VVMk+vaz0AoBl0PmFH3pPZrNSfgkTJyqlfXvFP/igJKnob3/ToR9+8J/4/q5Cp/fofXojaOJr\npfyiDdmZjfysg5VfAMYqvuUWHb7/fr/dGo7FSi8A4Ag6vwAiX1GRFB9f55fR6QWA6EfnF0D0KClR\n3P/9n1zvvqu81aslR+3+L4uVXgBAVej8wg+9J7NFS372//xHjS+8UPb165X/z3/WauJ7bKd3ZgR2\nemsSLflZEdmZjfysg5VfAJElL0/xDz4o17/+pcMPPyzPFVdINlu1L2GlFwBQW3R+AUQU+9dfK/bV\nV1V0//3ypaRUey6dXgAAnV8ARvOefroO1/CLMyu9AID6ovMLP/SezBbN+ZmwT29DRXN+0Y7szEZ+\n1sHKL4CwiPnpJzmXL1fJLbfUeC4rvQCAQKHzCyC0PB7FPvus4p55RsV33KGSsWOrPJVOLwCgJnR+\nAUQs+9dfK2HiRPmaNVP+hx+q7IQTKj2PlV4AQLDQ+YUfek9mi9T8nAsXKumaa1QyfrwK5s+vdOJr\nhU5vTSI1P9SM7MxGftbByi+AkCi96CLlrVolX9Omfs+x0gsACBU6vwDChk4vAKCh6PwCCC+fT7aD\nB+Vr0qTKU46e9PY7hZVeAEDo0PmFH3pPZgtnfjG//KKkYcMUf9ddlT5fWaf3T2dZq9NbE64/c5Gd\n2cjPOlj5BRAYhYVqfN558lx4oQ4/+2yFp+j0AgAiBZ1fAAHj/Pe/Ff+Xv6i0d28VPfCA9sY2otML\nAAgqOr8AwsbTt688556rvH88o9fWZuvjvbtY6QUARBQ6v/BD78ls4cwvu8Ct6esP6sa2AxSf0tiS\n+/Q2FNefucjObORnHaz8AmgwOr0AAFPQ+QVQb3Xap9fnU8Kdd8o9ZIhKzz03tAMFAEQtOr8Agq5e\nK702mzwXX6zEW26R56KLVHTffdXuBQwAQDDQ+YUfek9mC2Z+le3TW5dOr+eyy5S7Zo18iYlq3KuX\nXPPmSb6g/PHJWFx/5iI7s5GfdbDyC6BGAe30Nm6sokcekXv4cCX8+c+y7d6tkokTAztgAACqQOcX\nQJWOvQ3xsK4B3qfX65Xcbik+PnDvCQCwFDq/ABrs2EnvzKGddFxDJr15eYrJzlZZu3YVH7fbmfgC\nAEKKzi/80HsyW0PyO7rTG+eI0cyhnfSns1rVe+Ibs3mz4u+8U8mnnSbXe+/Ve1xWwvVnLrIzG/lZ\nByu/AAK70uv1yvnvfyv2pZdk37xZJaNGKW/NGvlatAjsoAEAqAc6v4CFHTvpHdq1WcPqDZLk8Sjx\nhhvkufJKua+4QnK5AjNYAAAqQecXQI0C3uk9mtOpwrfeCsx7AQAQYDV2fh999FGde+65GjhwYPlj\nS5YsUd++fdW3b1+tWLEiqANE6NF7Mlt1+QWs01taKud778m5ZEkDR4tjcf2Zi+zMRn7WUePkt0+f\nPnrhhRfKj91ut5544gm9/fbbevXVV/Xwww8HdYAAGi5Qk17bvn2Ke/JJJXfrptgXXpAvNjZIIwYA\nIDhqrD10795dO3fuLD/+9ttv1b59ezX5/bakzZs31+bNm9WxY8fgjRIh1bt373APAQ1wdH4BqzcU\nFCjhr3+Vc8kSeS6/XAVvvSVv164BHDWO4PozF9mZjfyso86d35ycHKWlpWnOnDlKTk5WWlqasrOz\nmfwCESTgnd7ERJWeeaaKHnhAvt9/8QUAwET13ud3xIgR6t+/vyTJZrMFbEAIP3pP5sopdGvKO18E\nbJ/ecjab3DfeyMQ3BLj+zEV2ZiM/66jzym+zZs2Uk5NTfnxkJbgyY8eOVXp6uiQpOTlZGRkZ5X9W\nOPKPjGOOOW748fsrVmv1fqd+KIrTqYk+3dwmT4mePB0X36pWr//83/9W2rp16rp1q7ydO2t5z54R\n9f1xzLEJx0dEyng4Jr9oPd6wYYNyc3MlSVlZWRo9erTqolb7/O7cuVNjxozR4sWL5Xa71b9/f82f\nP18lJSW64YYbtGzZMr/XsM8vEHwN2afXlp0t15w5cmZmyrF+vUrPPluePn3kHjpUvpSUII8cAIDA\nCPg+v/fdd58yMzN16NAhXXDBBZo2bZomTZqkkSNHSpKmTJlS/9ECqJdAdHpteXmK2bFDxRMmqLR3\nbykhIUijBQAgcnCHN/hZtWpV+Z8XEFlqs9J7dH4x27fL8cknco8aJdHNNwLXn7nIzmzkZy7u8AZE\noVqv9Lrdarp+veI/+EDO5ctly82V59JL5R46VEpMDP3AAQCIMKz8AhGsrp3epMGDZSsslOcPf5Cn\nT5/f9uKNqfemLgAARDxWfoEoUO1Kr9crHT4sNWrk97qCefMklyvEowUAwBwsCcHPsdu+IHSqug1x\nk6J8uebPV8LNNyu5QwfFvvx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"text": [ - "" + "" ] } ], @@ -1285,12 +1285,13 @@ " self.y = -0.5*9.8*t**2 + self.v0_y*t + self.y0\n", " \n", " self.x += randn() * self.noise_scale\n", - " self.y += randn() * self.noise_scale" + " self.y += randn() * self.noise_scale\n", + " return (self.x, self.y)" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 43 + "prompt_number": 27 }, { "cell_type": "markdown", @@ -1324,11 +1325,11 @@ "output_type": "display_data", "png": 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DcyWWqcUijqgXyqxIzP+rryyuuiqNa65J4+KL05k/PzaXiiMx+3ii/M0KR/5f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\nfv36Yds2a9asoaCggKysLPLy8sjNzWX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"text": [ - "" + "" ] } ], - "prompt_number": 46 + "prompt_number": 28 }, { "cell_type": "markdown", @@ -1378,13 +1379,13 @@ "cell_type": "code", "collapsed": false, "input": [ - "def ball_filter(dt):\n", + "def ball_filter(dt,R=1., Q = 0.1):\n", " f1 = KalmanFilter(dim=5)\n", - " g = 9.8\n", + " g = -9.8\n", "\n", " f1.F = np.mat ([[1., dt, 0, 0, 0],\n", " [0, 1., 0, 0, 0],\n", - " [0, 0, 1., dt, -dt*dt*g],\n", + " [0, 0, 1., dt, dt*dt*g],\n", " [0, 0, 0, 1., dt],\n", " [0, 0, 0, 0, 1.]])\n", "\n", @@ -1395,10 +1396,11 @@ " [0,0,0,0,0]])\n", "\n", "\n", - " f1.R = np.eye(5) * 1.\n", + " f1.R = np.mat(np.eye(5)) * R \n", + " \n", " f1.Q = np.zeros((5,5))\n", - " f1.Q[4,4] = 0.1\n", - " f1.x = np.mat([0, 21.2 , 0, 20.7, -9.8]).T\n", + " f1.Q[4,4] = Q\n", + " f1.x = np.mat([0, 0 , 0, 0, 0]).T\n", " f1.P = np.eye(5) * 5.\n", " f1.B = 0.\n", " f1.u = 0\n", @@ -1408,277 +1410,304 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 170 + "prompt_number": 29 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_ball_filter (traj):\n", + " xs, ys = [],[]\n", + " pxs, pys = [],[]\n", + " \n", + " for z in zs:\n", + " m = np.mat([z[0], 0, z[1], 0, 0]).T\n", + "\n", + " f1.predict ()\n", + " f1.update (m)\n", + "\n", + " xs.append (f1.x[0,0])\n", + " ys.append (f1.x[2,0])\n", + " pxs.append (z[0])\n", + " pys.append(z[1])\n", + " \n", + " if z[1] < 0:\n", + " break;\n", + "\n", + " p1, = plt.plot (xs, ys, 'r--')\n", + " p2, = plt.plot (pxs, pys)\n", + " plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", + " plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "dt = 0.1\n", - "f1 = ball_filter(dt)\n", - "# initialize storage and other variables for the run\n", - "count = 30\n", - "xs, ys = [],[]\n", - "pxs, pys = [],[]\n", + "f1 = ball_filter(dt,R=0.1, Q=0.1)\n", "\n", - "traj = BallTrajectory2D (30., angle_degrees=45., noise_scale=0.3)\n", - "traj.update(0)\n", - "x,y= (traj.x,traj.y)\n", - "traj.update(dt)\n", - "print (f1.x)\n", - "print (traj.x - x, traj.y - y)\n", - "log = True\n", - "#print (f1.F*f1.x)\n", - "for t in np.arange(dt,5,dt):\n", - " traj.update(t)\n", - " z = np.mat([traj.x, 0, traj.y, 0,0]).T\n", - " if log: print (traj.x, traj.y)\n", + "traj = BallTrajectory2D (20., angle_degrees=45., noise_scale=0.0)\n", + "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", "\n", - " f1.predict ()\n", - " if log: print (f1.x.T)\n", - " \n", - " #f1.x[4]=-9.8\n", - " \n", - " f1.update (z)\n", - " if log: print (f1.x.T)\n", - "\n", - "\n", - " xs.append (f1.x[0,0])\n", - " ys.append (f1.x[2,0])\n", - " pxs.append (traj.x)\n", - " pys.append(traj.y)\n", - "\n", - "p1, = plt.plot (xs, ys, 'r--')\n", - "p2, = plt.plot (pxs, pys)\n", - "plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", - "plt.show()" + "plot_ball_filter (zs)" ], "language": "python", "metadata": {}, "outputs": [ { - "output_type": "stream", - "stream": "stdout", + "metadata": {}, + "output_type": "display_data", + "png": 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PpuOdgO44uW0fhMxMOLVqBc3atYDRKHeZRGRhOANMVJmKiqC4fh3GoKD7Pp1R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\n3RnYv/O23OWQGeMMsIXQfP011Fu2wGA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{}, + "source": [ + "Here, we can see that the filter tracks the trajectory quite closely, but not perfectly. Let's look at the effect of a slower and faster initial velocity." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dt = 0.1\n", + "f1 = ball_filter(dt,R=.1, Q=.1)\n", + "traj = BallTrajectory2D (10., angle_degrees=60., noise_scale=0.0)\n", + "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", + "plot_ball_filter (zs)\n", + "\n", + "f1 = ball_filter(dt, R=0.1, Q=0.1)\n", + "traj = BallTrajectory2D (60., angle_degrees=60., noise_scale=0.0)\n", + "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", + "plot_ball_filter (zs)" + ], + "language": "python", + "metadata": {}, + "outputs": [ { - "output_type": "stream", - "stream": "stdout", + "metadata": {}, + "output_type": "display_data", + "png": 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Ljx4QAwJuHSuK8OvcGb733gvtpElQff89hAsXXB+zG/H9gqQwL8he1brz++uvvyIyMhIN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\nlRxja9wYJd98A9nFiy6OjuoqFr+uJIr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xbVwGl+IkIqvBBplqxdSzWLKcHNhPmACHCRNQ8tZb0I4efdfHx10rwLL9SZjf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\ng5xOp5YvX66TJ09q1KhRio+Ppz8DxMXFacyYMVq8eLF8Pp8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cS9E5IlR0LCLSEa5bmBjuRj2YSq3BR4dTcSSnCqsmdIPf4F46fwx2Lxb7F8uY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\noN8rGTdENce+0pcfHTZdStSJqCb5ktevf//sop6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"text": [ - "" + "" ] } ], - "prompt_number": 177 + "prompt_number": 43 }, { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "prompt_number": 46 + "source": [ + "Can you explain what is happening here?\n", + "\n", + "When the initial velocity is low, the change in velocity per time period is large compared to the velocity. In the physical world the ball's velocity is changing continuously, but we are imposing a step function on it because we are stepping by $0.1s$. This means our model of the ball does not exactly match the true behavior of the ball, and so the Kalman filter will not exactly predict the ball's behavior. A slow initial velcocity exaberates that \n", + "\n", + "**author's note** complete this" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So we seem to be doing a good job of tracking the ball. What happens if we inject noise?" + ] }, { "cell_type": "code", "collapsed": false, "input": [ - "%run?" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 166 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "math.cos(math.pi/2.)" + "dt = 0.1\n", + "f1 = ball_filter(dt, R=.16, Q=0.0)\n", + "\n", + "traj = BallTrajectory2D (40., angle_degrees=45., noise_scale=0.4)\n", + "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", + "plot_ball_filter (zs)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, - "output_type": "pyout", - "prompt_number": 21, + "output_type": "display_data", + "png": 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O9dcPYsTBX7midW3uOa8eIQF2Xli5D8Pw3A9TfTEnX6WszFFOnqcGWcTNbPv3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\n/P0cDrX87Gdq/cY3JEmjh2Ro4QSPnthdLb8/ohu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"text": [ - "6.123233995736766e-17" + "" ] } ], - "prompt_number": 21 + "prompt_number": 44 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can see that the filter follows an almost perfect parabola despite the noise in the signal. Because I know the noise characteristic of my filter, $\\sigma=0.4$, I was able to specify the variance as $\\mathbf{R} = \\sigma^2=0.16$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's make this more realistic. We don't have much call to track balls thrown on airless planets. On Earth, balls are subject to the effects of the atmosphere. \n", + "\n", + "blah blah\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import baseball\n", + "dt = 0.01\n", + "f1 = ball_filter(dt, R=1.16, Q=5.5)\n", + "\n", + "x,y = baseball.compute_trajectory(v_0_mph = 90., theta=65., dt=dt)\n", + "zs = zip (x,y)\n", + "plot_ball_filter (zs)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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pjK/6x49eGWfRHW3P+TG/nL21Wq1YLBasVitOp5PDhw9z9913YzaX/QPqdrtPFsnZ2dmM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\nrfXYrFJIktq3V82LL0pxcXYZggyT3Al4Z3uFln9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+ "text": [ + "" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def ball_filter6(dt,R=1., Q = 0.1):\n", + " f1 = KalmanFilter(dim=6)\n", + " g = -9.8\n", + " g=1\n", + "\n", + " f1.F = np.mat ([[1., dt, dt**2, 0, 0, 0],\n", + " [0, 1., dt, 0, 0, 0],\n", + " [0, 0, 1., 0, 0, 0],\n", + " [0, 0, 0., 1., dt, dt*dt*g],\n", + " [0, 0, 0, 0, 1., dt],\n", + " [0, 0, 0, 0, 0., 1.]])\n", + "\n", + " f1.H = np.mat([[1,0,0,0,0,0],\n", + " [0,0,0,0,0,0],\n", + " [0,0,0,0,0,0],\n", + " [0,0,0,1,0,0],\n", + " [0,0,0,0,0,0],\n", + " [0,0,0,0,0,0]])\n", + "\n", + "\n", + " f1.R = np.mat(np.eye(6)) * R \n", + " \n", + " f1.Q = np.zeros((6,6))\n", + " f1.Q[4,4] = Q\n", + " f1.x = np.mat([0, 0 , 0, 0, 0, 0]).T\n", + " f1.P = np.eye(6) * 5.\n", + " f1.B = 0.\n", + " f1.u = 0\n", + " \n", + " return f1" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 67 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_ball_filter6 (zs):\n", + " xs, ys = [],[]\n", + " pxs, pys = [],[]\n", + " \n", + " for i,z in enumerate(zs):\n", + " m = np.mat([z[0], 0, 0, z[1], 0, 0]).T\n", + "\n", + " f1.predict ()\n", + " f1.update (m)\n", + "\n", + " xs.append (f1.x[0,0])\n", + " ys.append (f1.x[3,0])\n", + " pxs.append (z[0])\n", + " pys.append(z[1])\n", + " \n", + " if i > 0 and z[1] < 0:\n", + " break;\n", + "\n", + " p1, = plt.plot (xs, ys, 'r--')\n", + " p2, = plt.plot (pxs, pys)\n", + " plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", + " plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 85 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dt = 0.1\n", + "noise = 0.3\n", + "f1 = ball_filter6(dt, R=.16, Q=0.1)\n", + "\n", + "x,y = baseball.compute_trajectory(v_0_mph = 90., theta=65., dt=dt)\n", + "zs = zip (x,y)\n", + "znoise = [(i+randn()*noise,j+randn()*noise) for (i,j) in zs]\n", + "plot_ball_filter6 (znoise)\n", + "print (zs[0:5])\n", + "print (znoise[0:5])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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eEQelS0KLNDSGgfPPP7Mvrj1zN6ezNa2QIe1CGNgqRA2xiA1yOnToxJFk95NH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\n72vk3o8049+/p/AIu+mSuhyzZuaQvVnkbxb5m0P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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[(0.0, 0.0), (1.700193266982834, 3.646076227248443), (3.363396716383785, 7.114827534704153), (4.989282707845675, 10.407750130907692), (6.577522827472383, 13.526428179417952)]\n", + "[(0.0077428794280200615, -0.24993790836595048), (1.6319949358597867, 3.906624591863025), (2.927767750429539, 7.282837525906626), (4.889897158515106, 10.321582956313172), (6.55031695691016, 13.756792084374545)]\n" + ] + } + ], + "prompt_number": 88 } ], "metadata": {} diff --git a/baseball.py b/baseball.py new file mode 100644 index 0000000..2c86b45 --- /dev/null +++ b/baseball.py @@ -0,0 +1,83 @@ +# -*- coding: utf-8 -*- +""" +Spyder Editor + +This temporary script file is located here: +/home/rlabbe/.spyder2/.temp.py +""" + + +""" + +Computes the trajectory of a stitched baseball with air drag. +Takes altitude into account (higher altitude means further travel) and the +stitching on the baseball influencing drag. + +This is based on the book Computational Physics by N. Giordano. + +The takeaway point is that the drag coefficient on a stitched baseball is +LOWER the higher its velocity, which is somewhat counterintuitive. +""" + + + +import math +import matplotlib.pyplot as plt + +def a_drag (vel, altitude): + """ returns the drag coefficient of a baseball at a given velocity (m/s) + and altitude (m). + """ + + v_d = 35 + delta = 5 + y_0 = 1.0e4 + + val = 0.0039 + 0.0058 / (1 + math.exp((vel - v_d)/delta)) + val *= math.exp(-altitude / y_0) + + return val + + + +def compute_trajectory(v_0_mph, theta, v_wind_mph=0, alt_ft = 0.0, dt = 0.01): + ### comput + theta = math.radians(theta) + + v_0 = v_0_mph * 0.447 # mph to m/s + v_x = v_0 * math.cos(theta) + v_y = v_0 * math.sin(theta) + + v_wind = v_wind_mph * 0.447 # mph to m/s + altitude = alt_ft / 3.28 # to m/s + + ground_level = altitude + + x = [0.0] + y = [altitude] + + i = 0 + while y[i] >= ground_level: + g = 9.8 + + v = math.sqrt((v_x - v_wind) **2+ v_y**2) + + x.append(x[i] + v_x * dt) + y.append(y[i] + v_y * dt) + + v_x = v_x - a_drag(v, altitude) * v * (v_x - v_wind) * dt + v_y = v_y - a_drag(v, altitude) * v * v_y * dt - g * dt + i += 1 + + return (x,y) + +if __name__ == "__main__": + x,y = compute_trajectory(v_0_mph = 110., theta=35., v_wind_mph = 0., alt_ft=5000.) + + plt.plot (x, y) + plt.show() + + + + + \ No newline at end of file