From 58d91c2de350368363a5398fcc1e9cc24558d91c Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 10 Jan 2016 08:58:37 -0800 Subject: [PATCH] Copy and general edits. Trimming the flab out of the language. Added a few examples and such to clarify concepts. --- 10-Unscented-Kalman-Filter.ipynb | 801 +++++++++++-------------------- 1 file changed, 283 insertions(+), 518 deletions(-) diff --git a/10-Unscented-Kalman-Filter.ipynb b/10-Unscented-Kalman-Filter.ipynb index c7098b5..77f381e 100644 --- a/10-Unscented-Kalman-Filter.ipynb +++ b/10-Unscented-Kalman-Filter.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -262,7 +262,7 @@ "" ] }, - "execution_count": 3, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -290,7 +290,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "collapsed": false, "scrolled": true @@ -298,9 +298,9 @@ "outputs": [ { "data": { - "image/png": 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Yf/ALAEC7Vp0xcchMtHDz0ntWIiKi+jCYpdITEhLkilEvkiQhtyQTKTk3EZd2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\niMiCWGATEREREVkQC2wiIiIiIgv6/36FgdS2aAzBAAAAAElFTkSuQmCC\n", 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M3DRVmyCIGNp9Qp1+BLo2ONg648V+0/D+2G/RzKetWt+lW+ex/sDXkHFlTSIiIqoGFtj0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\n1yMTjL9E1XKRGSKyA4LYiE7SRUVFePDgQYPH+Pr6Yu7cudi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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -332,7 +332,7 @@ "\n", "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a *Monte Carlo* approach, and it used by some Kalman filter designs, such as the Ensemble filter and particle filter. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough sigma points we will build an accurate output distribution.\n", "\n", - "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. Ensemble filters and particle filters use clever techniques to significantly reduce this dimensionality, but the computational burdens are still very large. The unscented Kalman filter uses sigma points but drastically reduces the amount of computation by using a deterministic method to choose the points." + "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. The number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. Ensemble filters and particle filters use clever techniques to significantly reduce this dimensionality, but the computational burdens are still very large. The unscented Kalman filter uses sigma points but drastically reduces the amount of computation by using a deterministic method to choose the points." ] }, { @@ -351,7 +351,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "collapsed": false, "scrolled": false @@ -361,7 +361,7 @@ "data": { "image/png": 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39GnIjh8+js1hI+gL3vYopclkwuFykOXJYuHH9CnKevaWfmnQL3gboA1gxpQZ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\nuz2DF15I5tq1s+Tm5krwFRHJarViCLT+Z/f4oeOPFXwB1KCK1+OlvLS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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -399,7 +399,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true @@ -409,14 +409,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Difference in mean x=-0.011, y=42.812\n" + "Difference in mean x=-0.212, y=42.797\n" ] }, { "data": { - "image/png": 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IMmJS7IZuJQB8bbfbFcGyeq7I98v/M+3I6kaPxwO3220iTxS5M2UnWxzJMcdi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jTu3VvV2Ec/8Qn83f/9v7j11ltx0UUXIRgMFvWytPc+1hif7+q062VZLRjRKWVLUe2Y/FtWLpbr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\nnfOhQ4ewb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hIBAIwO12K3NYEkXZuoljkRWYbrdbCfq9Xq/Sskl/M6Y9CUlUC50zrmMtTrDq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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -474,7 +474,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 6, "metadata": { "collapsed": false, "scrolled": false @@ -484,7 +484,7 @@ "data": { "image/png": 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amgqATqezcyaiPmtM88RsNhMfX87EiU6AgpY+2Twc/XeatSi4OkLJEyP+h76d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\nB6lknojakHkibqc+zZGcC6fYnbGdtCO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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -499,36 +499,33 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So we can take those three points, pass them through a nonlinear function f(x), and compute a new mean and variance. We can compute the mean as the average of the 3 points, but that is not very general. For example, for a very nonlinear problem we might want to weight the center point much higher than the outside points, or we might want to weight the outside points higher if the distribution is not Gaussian. A more general approach is to compute the mean as $\\mu = \\sum_i w_if(\\mathcal{X}_i)$.\n", + "We can pass these points through a nonlinear function f(x) and compute the resulting mean and variance. The mean can be computed as the average of the 3 points, but that is not very general. For example, for a very nonlinear problem we might want to weight the center point much higher than the outside points, or we might want to weight the outside points higher if the distribution is not Gaussian. \n", "\n", + "A more general approach is to compute the weighted mean $\\mu = \\sum_i w_i\\, f(\\mathcal{X}_i)$, where the calligraphic $\\mathcal{X}$ are the sigma points. We need the sums of the weights to equal one. Given that requirement, our task is to select $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the input Gaussian. \n", "\n", - "For this to work for the identity function we want the sums of the weights for the mean to equal one. We can always come up with counterexamples, but in general if the sum is greater or less than one the sampling will not yield the correct output. Given that, we then have to select *sigma points* $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the input Gaussian. \n", - "\n", - "It is possible to use different weights for the mean ($w^m$) and for the variance ($w^c$). So we can write\n", + "If we weight the means it also makes sense to weight the covariances. It is possible to use different weights for the mean ($w^m$) and for the covariance ($w^c$). I use superscripts to allow space for indexes in the following equations. We can write\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{Constraints:}\\\\\n", - "1 &= \\sum_i{w_i^{m}} \\\\\n", - "1 &= \\sum_i{w_i^{c}} \\\\\n", + "1 &= \\sum_i{w_i^m} \\\\\n", + "1 &= \\sum_i{w_i^c} \\\\\n", "\\mu &= \\sum_i w_i^mf(\\mathcal{X}_i) \\\\\n", "\\Sigma &= \\sum_i w_i^c{(f(\\mathcal{X})_i-\\mu)(f(\\mathcal{X})_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", - "The first two equations are the constraint that the weights must sum to one. The third equation is how you compute a weight mean. The forth equation may be less familiar, but recall that the equation for a covariance is:\n", + "The first two equations are the constraint that the weights must sum to one. The third equation is how you compute a weight mean. The forth equation may be less familiar, but recall that the equation for the covariance of two random variables is:\n", "\n", "$$COV(x,y) = \\frac{\\sum(x-\\overline x)(y-\\bar{y})}{n}$$\n", "\n", - "and you should see where it came from.\n", - "\n", - "These constraints do not limit us to a unique answer. For example, if you choose a smaller weight for the point at the mean for the input, you could compensate by choosing larger weights for the rest of the $\\mathcal{X}$, and vice versa. We can use different weights for the mean and variances, or the same weights. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n", + "These constraints do not form a unique solution. For example, if you make $w^m_0$ smaller you can compensate by making $w^m_1$ and $w^m_2$ larger. You can use different weights for the mean and covariances, or the same weights. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n", "\n", "We want an algorithm that satisfies the constraints, preferably with only 3 points per dimension. Before we go on I want to make sure the idea is clear. Below are three different examples for the same covariance ellipse with different sigma points. The size of the sigma points is proportional to the weight given to each." ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "metadata": { "collapsed": false, "scrolled": false @@ -538,7 +535,7 @@ "data": { "image/png": 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No9T5irvlsjs6CRcLzjZKL9lFq5kSc8slVldUjkSHpM5XbMtW2YMFB/CLC2kW\nl9oYLY8sDhXbttl3rHbjqGk6P5xJsrAAsWAEn0sWh4q757Tb0doK1XobzWKzJhL87pJmS+P12RTz\nczDWF+0cHyjENrgdjk72ymJ34el8hauJAstLitw0invituj07eX4OvHlFs2qS2YaxbYpioLD5qDR\ntN64I8HvLjk/v0ZiSUPRvAzKpuLiHrxR9mCdi1Bb0zs3jQudcgeP09ntJgkTcjo2F+5Yp+9kizWm\n4znicYUjg0OoctMo7oFVZxwl+N0Fa7kKc8tFVlZUjkRjkrkS98Rpd9BsKlTrLXTdGke1Xo6vE19q\nodXdUu4g7pnVdkrRdYPXZ5MsLMJgoF/KHcQ925xxtNKNI0jwu2OapnN2rpO5Gg5FcDskcyXujaoo\n2G02Wi1otNrdbs6ey5frXInnSCSk3EHsjMvuoNXqnKppBTPLWRIrTaolJyN9kW43R5iY026n2bTG\nmHMtCX53aDqRYWmlRbvmYigkmSuxMzZFRdPp+S2bdN3g9Zkk8ThE/X2yIb/YEZuqomm932+gc5jF\n5XiGxUU4Eo1JuYPYEZtqs0zfuZYEvztQrDS4ksixuAiHJXMldoFNVdHavX8hml/NkVhtUC46JHMl\ndkxVVdoWGcDPzqVIJAyCrpDsIy92xDAMVEVB06HV7v2+cy17txtgZmfnUsTjBhFfH3631FyJnbNC\nBqvebHMpnmFhAQ4NxGRfUrFjNlVFt8CMyXK6yOJKlcy6jfvHot1ujjAhwzAoFAosLi6STCaptBoo\noTZHRiZ45Jh1kngS/N6j1UyJpWSNfNbOgxMD3W6O6BFWGMQvx9dZXtbx2gOEvb5uN0f0AFVRwFDQ\nNANN07HZeu+GStcNLsXXWYx3ttN0yAmIYpsMw+DSpUv8/u//PrOzM50HHXYIajz7zBL/71P/N//g\nH/wDPJ7eP2So964Q+0DXDS4trpNIwGh/RDJXYteoSif47dXdHoqVBnMrBZJJhfGINW8a2+02CwsL\nnDt3jsuXL1MoFDCM3vz33k+qonT6To9+lvOrOVaSLfSGi4FAsNvNESZjGAbT09P85m/+5huBb+cJ\nQGV9PcOTTz7Js88+i673bvJlk2R+78FiKs9yqkmz5iQ6IHv6il2kdK5FvTl8w8XFNCvLEPGFLbcz\nimEYxONxvvWtb/H888/TbDYAOHbsGB/72Md58MEHcco+x/dMURQMNsbyHtNsaVxZypJIwEQkapmp\nabF76vVMuWi4AAAgAElEQVQaTz/9NNVq5SbPdn6fDMPgX/2rf8UjjzzCsWPH9reB+0xSltvUamtM\nJzIk4jAuFyGxy1RFwTB6M/ObzldIJCtk1lVLLnJbWlriqaee4tln/3or8AW4evUqv/mbv8lLL71o\niYzLXlEUBaNHM79XlzIsr2o4FZ+UCol7Eo8nePHFF298wjDoBL+dWGZ9fZ2zZ8/2/GyUBL/bNLOc\nZWVVw2Z46PP5u90c0XMUdKP3BnDDMLi4kCaxBEOhiOXqFXVd55VXXiGRiN/iFQa/+7u/RzKZ3Nd2\n9RKFTua3124cq/UWsyt5VpaxbKmQ2LlsNsut5xQVuCaRd/ny5X1pUzdJ8LsNtUaLq0s5lpZhIjLY\n7eYIYRrL6yWWUw0qRQexULjbzdl3mUyG//k//+dtX1MqFYnHbxUcC6u6tJhmedkg6A7KSW7inm0n\nk2uFGW0JfrfhcnydlRWDgDMgW5uJPaHrOjYV7D20Wl3TdC7HOwtEx/oHLLlAtF6vk8tl7/i6crm8\nD63pTVoP9p18uc7CaolUSmGsT7K+4t5Fo1FU9SYzbooCaGC8UXJ1+vTp/WtYl/TOVWKPFSsN5leK\npFIK4/2yv6LYG5quY7P11gA+n8yzvNpCb7qI+APdbk5XOJ1OAnexQt/rlUML7pVu9F7fuTC/xvIy\nDAb6cDkc3W6OMLGJiQkee+yxG59QFEDfCn6Hh4d56KGHej772ztXiT3WmXqCAV9YLkJiz2g9NoC3\n2hpXEhkSS9ZeIBqNRvnJn/zJ277G6/UxMTGxTy3qLZqug2JgUxVUtTd+x1LZMstrNfI5G8Ph/m43\nR5ic0+nkwx/+MMHgdTtUXZP5tdvtfOELX+Dw4cPdaOK+6o0Rdo8VynWW1ipkMirDFlylfiu6rlOp\nVKhUKrJKfZf0WuZ3IZknuabjUryELLxKXVVVzpw5w8DArWeNfv7nf56RkZF9bFXv0HUdew/1G+gs\nrl5ehqFQP3aLLRAVu09RFKampvi1X/s13vrWM2zu7tD5Q2Nq8ghf+9rX+MAHPmCJJIXs83sXZldy\nJJMQ9Ycst0r9ZjRNY3Z2ltdff50XXngBgHe/+908/PDDHD16FJt8RvdsM/h19MAgrusG86t5kqsw\nIZkrDh8+zGc+8xmefvppvv/976PrGgCxWIxPfOITPProo6gWrIfeDZqho/ZQ8Jst1lhJ1ygWbByZ\nsN4CUbE3FEXh6NGj/Lt/9+9YXFwklUqRr1fxDLR48h8e4/946ylLBL4gwe8dVest4qkS6bTC/aN9\n3W5O1+m6zg9+8Cqf//zv0Go1tx5fWJjny1/+Mr/yK7/CW9/6VgmA75G+Efz2wvGsibUCqXQbRXdb\nOuu7SVEUJicn+dSnPsVHPvJhisUSdrud0dFRIpGIZQadvdBri91mV7IkkzAYDFtygajYO4qi4PV6\nOXXqFKdOnWIll0F3rzMUs9Y1SHrVHcyuZEmlDMLegNT6AvPz8/zO7zz1psB3U7vd4qmnnmJ+fr4L\nLesNmt7JYJk982sYBrMrOVZWkXrFayiKgsvl4tix4zz66KM89NBDDAwMWGrQ2Qu9VC5UrjVJrJXJ\nZBRiQcn6ir21Oeb0Qt/ZDmv9tNvUbGkspoqkUjKAQyeguXz58ptOp7peq9Xk4sWLUgN8DwzDwEDH\nblNMn/lNZsuk1pu06g765TAYsce2yoXs5p9xmlnOkkpCvy+Ewy6Ts2JvtXvoxnE7rPXTbtP8ao5U\nSsfn8ON1urrdnK7bPKXqTl555ZWePxpxL/TSRWhmOcvqamexjmQ1xV5r6xo2u/n7Tr3ZJp4qsram\nMByWMjux9zRdw94Ds43bZa2fdhs0TWduNc9qUrK+17LfRSbibl4jbtRoNXG6wOM09+e3Xqiyul6n\nVLQxcBd72wqxU41WC5cLvG5zl6bNreRIpQyCbj9uh7PbzREWsNl3PC5z953tkuD3FuJrBdbSGg48\nBDyebjfnQFBVlXe96113fN273/1uWbV+DxqtFm4X+DzmHvRmlrMkVyEW6pPFOmJfbAW/Jh7AW22t\nszVgsjNjIsR+qLdauNzgM/mN43bJyHQTm4t1VmWxzpsoisKxY8fo67v1ZxIKhTl27JhMdd+DeruF\n2+QXoWKlwfJahWxWZVAW64h90mhv3DiauO8spgqk1nTcNi9+t7vbzREW0NY0UDTcThWXyWcct0uC\n35tYy1VIZ1q0m07CskXTm4yOjvKrv/qrRCI3njPf3x/h05/+NOPj411omfnVW01cLvC5zZv5XUjm\nWVuDAdkTW+yjrb5j0lkTwzBYTOZJpmBIEi5in9Q3ZkzMfNN4r6wV6t+l+FqBdBqigZBkMK+jKAon\nTpzgc5/7HAsLC1y4cAHDMDh9+jSTk5MMDw/LZ3aPGhvTT2atW9Q0neX1Eul1ODEYuvMXCLELNF1H\nNzTcLgWXw5w3XJlijfVci3bDQcjj7XZzhEU02uYec3ZCgt/rNFsaK5kK2azCA2OyWOdmFEVhZGSE\n4eFh3vGOd2w9JkHvzmzV/Jr0QpTMlslkNRyKG69LdkfpNsMwKBQKZLNZFEUhEokQCAR6rp82Whvl\nQh6naX+2xFqB9XUYCARN+zMI82m0mhtjjjlnTHZCgt/rLKWLZDMGAZcfp+xacFsS8O4eTddpG23c\nLgW3SWuvEuni1oyJ6K5iscjZs6/zF3/xNHNzswCcOHGSn/qpn+KBBx7A5+udcq7NkgezLnZrazrL\n62XW1+G+Eek7Yv802i38IfMmXHZCan6vk9goeZAtmsR+2sz6elwOU95Q1BotVtcrFPIKEX+g282x\ntEqlwrPPPstTTz21FfgCTE9f5rd+63N861vfol6vd7GFu8vsq9VX1ktkMjoeh1dOERX7qt4jWwTe\nC3OmmPZIoVwnnWtQq9oIR+VUqv1gGAbVapVEIkG5XMblcjE6OkpfX58pg8B79cZiN3NehJbSRTJZ\nCHn92GWhW1fNzs7y5S//+S2f/+M//mNOnjzJqVOn9rFVe6fRbuILmnexW3yj5EFmTMR+q7eaGzeO\n5uw7OyHB7zXiawXS6xDxB1EtFHh1i2EYTE9P86UvfYkf/vC1rcfHxyf42Z/9WR566CGcTmt0ymqz\ngdcLAa/5amUNwyCeKrCehrGgDODdpGkaL7300h1eZXDu3DlOnDjRE/txVxoNol4ImDD4LdeapDI1\nSiWVqQlJuIj902q30Wnj86h4XNYLBa33E9+Crhssr5dYT8NxWal+W4ZhkMvlSKfTNJtNABwOB4OD\ng9vK2F69epXf+I3foFIpv+nxRCLOf/gP/4FPf/rTvO1tb7NEBrhcrzEUhf6g+Q5UyRZrZPItmg07\nQVmpfludRWh5isUirVYbVVVxuVzEYjFsu5Ax13Wd6enpO77u6tWrPXEEuabr1FsNfD6FsN98e+Mm\n1gqsZ6DfF5ADYcS+Kjfq+H0Q9rstMcZeT4LfDclsmfWMhl1Wqt+SpmksLS0xM3OVZ575SxKJ+Jue\nHxsb56Mf/SjHjh1jbGzstoN5q9Xi+eefvyHw3WQYOn/wB7/P5OQk0Wh0V3+Og8YwDCqNOj4/5hzA\nr1noZsWL6N3QNI3l5SVmZmb5y7/8SxYXF7aec7s9fPCDH+TMmTNMTEzg9/vv+XNUVZVw+M6Hi0Qi\nvbGXbLXRwOMxCPlc2GzmCh4NwyCxVmQ9DUf6JeEi9le5XsPvh76A+RIuu0GC3w1L6SLrGVnodiuF\nQoHvfe97fPGLX6Rer930NUtLCf7Tf/p/cLnc/MzP/AyPP/74LQfilZUVvvvd7972e6ZSKRKJRM8H\nv7VWE7tTJ+hzmG6nB03TWU6XyGTg1LD0nZtZX1/nO9/5Dk8//RfUajf2nXq9xjPPPM0zzzzNfffd\nzyc+8QlOnDhxTwGwqqo88cQTvPji39/2dWfOvK0nSh7KDfMO4OuFKplcG0NzEvCYr/3C3MqNOiMx\n6DNhwmU3mP/qtws0TWctXyGf70w/iTfL5XJ8+ctf5g//8A9uGfheq9Go80d/9If8+Z//Odls9qav\nqdfrtNutO75XL61Kv5VKvd4ZwE14EcoUa+SLOg7VjdthvprLvZZKJfmjP/pD/uzP/vtNA9/rXbhw\nnl//9V/n7Nmz91SWoCgKU1NTnDhx8pavectbHuXw4cM9kaUvb/adgPn6TjJbJpdDdkcR+84wDCr1\nOj6fOWcbd4MEv0C6UKVQMHDb3LK373VqtSrPP/88X/vas9v+2uee+zrf/OY3qVarNzzn8XhwOu9c\nXuL19n4NqZmzV8lsmXweOQb8JvL5HF/5ylf527/92219XbVa4bd/+7e5cuXKPQXAg4OD/Nt/+2/5\nkR95D4ryxiVeVW28733v55//839OJBLZ9vseRGbuO6lcZaPvyEI3sb9qzSZOV2e20WWy2cbdYs2f\n+jqpzQHcJxeh683PL/ClL33xnr/+z//8f/DQQw9x3333venxkZERPvCBD/Dss399y68dGxtnYmLi\nnr+3WZTrdQZ95sxepXJl8jmYGpC+cy3DMLh8eZr/9b++dU9fX61W+JM/+RN+9Vd/lUBge5lBRVEY\nGxvjX//rf81P/MRPsLa2hqJALDbExMQErh5Z09BotUBp4/fZ8Jtsp4dipUG+2KLdtOPrkX+Pvabr\nOktLS8Tjcer1On6/n4mJCYaGhnqihGc/mfmmcbdYPvg1DIO1fIVcHo4OSPbqWpqm8corr+z4fV5+\n+WVOnjz5pgVwdrud9773vfzd3/0d2Wzmhq+x2x38wi/8An19fTv+/gdZW9NotBv4/Qohn7mC384A\n3kZr2/HeRRbfSqrVKt/4xjd29B7nz58jHo/fcON4NxRFwePxcOLECU6cOLGjdhxU5YZ5y4VSuU7J\nQ9jn64nyk71WqVR44YUX+OM//qM3lQ8FgyH+5b/8l5w5cwaHHBBy18r1Ov6IORMuu8Xyt0vFSoNc\nsY3etuNzWfcX4WaWl5f4+te/tuP3ee6551haWrrh8cnJST772c/yvve9H5vtjfuwhx9+hF//9V/n\nwQcf7PmBodKo492ou1JVc/2s15Y89Pq/03bF43Fee+0HO36fl19+GU3TdqFFvadSr+EzafYqlauQ\nL0jJw93QdZ2XX36Z//pf/8sNdfPFYoGnnnqK8+fP98TWffvF6js9gGR+OwN4Ti5CN7O0tHxXi3Tu\npF6vkUgkOHTo0Jse31yc88lPfpIPfehDVCqVrRPevF6vJQKqUr1GMGDe7FU+DzHpO29iGAYzMzO7\n8l7PPfcc73//+xkZGdmV9+slxXqNQyPmy141mm3W8zUqJYVgf++vadipdDrNf/tv/+2Wz+u6xle+\n8hWOHj267RIhK2q127SMJj6fQtCEhyrtFssHv5uLDoZ8UvJwvZstVLtXtwuiHQ4Hk5OTu/a9zCRf\nKXNoCAb7zPX71xnA65TLCsciMoBfyzAMUqnUrrxXvV6j0Wjsynv1kma7TUOrEwqqRILm+v1by3ey\nvn63Vw62uAsrKys3LY271oUL51ldXZXg9y7kqxVCQRgM+0w327ibLN3z6s02mUKdakWVk6luQtf1\nXXsvTdNkWuo6jVaLpt4w5QCeylUoFCHo9skAfh3DMHY1YN3Nftgr8tUy4RAM9nlNN4DLLg/b02rd\neUtMgHa7vcct6Q35aplwGGImS7jsNkuPWqlsmUIBAha7A9d1/a6C0d1cQOB0Oi1RxrAd+WqFUNis\nA/hGuZDMmNxAURRCod07sUsW8twoX6lsDODmCiB13WAtV6Eg2wPetWAwCNz++ujxePD7zfW70A26\nYVCsVTt9p9/an5elyx4yxRqFAoQschEql8ssLCxw8eJFcrkcIyMjnDhxgkOHDt10+6P+/t07AnU3\n36tX5KtlBkZgyGQXIcMwyBRrFIswNmyNvrMdiqLcUN9+rw4dOkwwKFO519J0nWK9wmTIfOVC+XKd\nYknHobpwyU3NXTl0aIIzZ87w8ssv3fI1H/rQP2R0dHQfW2VOxVoVj08nEnKb7jTR3Wbpnz5XqlEu\nw9BA7694TKfTfPWrX+Wb33zz9kuqauPnfu7n+NEf/VF812XxDh06xOTkFHNzszv63ocPH+Hw4d0J\nBnqFpuuU61WOhjq1V2ZSqbcoVzQw7DKA34SiKBw5cgSv10e1WtnRe330ox8lFLr5EeFWVaxV8fkM\nBsLmG8Dz5TrlMvjd5lqk101ut4ePfexjzM7O3rT298iRSZ544ok3baUpbi5fkZKHTdaZ679Oo9mm\nWGnRbKh4nObaIH27NE3j29/+9g2BL3RWyv7hH/4Br7/++g1lEKFQiA9/+MM7/v4f+chHZAC/TrFW\nxec3GAh7THfCzuZNo9/VWzeNm7W6xWKRZrO5oxr1kZERfvInf3JH7fF4PExNTUq50HXy1Qp9feYr\neYDe7Tt7aXNXoH//7/89H//4z+DfOA66vz/CP/tnv8Av/dIvMTY21uVWmsNW3zHZbONeMNeou4ty\n5TrlSucOvNcHl6WlJZ555pnbvuYrX/kKp0+fJhx+I0hVFIWjR4/S19dPLpe9p+8dCoU5evRoz3/G\n22XmRQe5Um9lrwzDIJ1OMzMzw/PPP8/6+jpDQ0O8733v4+jRowwMDGz7PVVV5dFHH+WZZ56h0ajf\nU7t+6qeeZHRUBvXr5atlhg+btO9sjDvD0d7oO/tFURQmJyc5fPgwTzzxOM1mC7fbTSQSkdPd7lK1\n0UCxtwgH7IR81t3ibJNlf2vemH7q/TvwZDJJvX77/Xrn5mZJp9dueHx0dJRf/uVfxn0Pn5PT6eJX\nfuVX5K78OoZhmHbBDvRe9mp1dZX//J//M5///G/z2ms/IJGI8/LLL/Fbv/U5vvCFL5BKJe/pfY8e\nPcov//Ivoarbn4597LHHeO973ytTudepNOqo9jbhoJ2QyfbGrm/MNrabKh5Hb8827hVVVYnFhhgf\nHycajUrguw35apm+jYSLJKMsHPxuDuBWONXtbqdvNe3GLZUUReHUqVN89rOfJRAI3vX39PsDfPaz\nn+X06dPS0a5TaTSwOdr0hRwETXYH3tZ0CpUmtZqC9yaLJM2m3W7z/PPP8/rrP7zp83//9/8ff/M3\nL9zTdmOqqvLII2/hM5/5NK5tXGfe//4P8IlP/Ow9ZZx7Xa5SNnXJQ6UMPpdHroli3+U2632l5AGw\naNmDYRjkSnUqFfCHez/47UwN2dD1Wx+TOjAQveWODKqqcv/99/Mbv/EbvPjiizz77LO3XMjj9fr4\n8R//cd7+9rczNTUlF/mbWC8ViERg2IQXoc6MiYHb4e6J7QGXlpb4+te/ftvXPPPMM7zzne+8pxkM\nu93Oo4++lc997nP84Ac/4K/+6q+oVMo3fe1b3vIoP/ZjP8bJkycIh/u2/b16nWEYZMpFjo7AcMR8\nfafXyoWEedSaTZpGnb6wSjRkrj3l94olg99StUm5qmNXHDjsvf8RTExM8Pjjj/Od73z7lq/5R//o\nHxGNRm/5/Gb97+TkJO95z3uYm5vj5ZdfJpPJYBgGkUiEM2fOMDU1xejoqExH3YJuGGQrJe6bhPHB\n3dsLdr/kSrXOTWOPzJhks1mazdsfSFGplMnlcvdcvqOqKsePH+fo0aM89thjzM/PE4/HyefzeDwe\notEoR48eZWJiwjLHet+LUr2GzdEi0mdnwIQD+NbuQr7eKBcS5rFeKjAQgdGBADabjM1g0eC312oW\n78TpdPLRj36URCLO1atXb3j+iSfey5kzZ+5q0FVVlfHxccbGxnjssce2poNVVUVVVRm47yBXKeP1\nawz2uU1X8gBv1MqHe6RW/m5/X3fj91pVVcbGxhgdHcUwDAzDQFGUrf/E7aVLBQYGOjeNZvu8dN0g\nX25QqYCvvzduHIU5GIbBeqnIyQlzJlz2iiWD380B3Ar1vtAZuMfHx/mlX/plrly5wje+8Q3y+TwT\nExP86I/+nxw9eoy+vu1NsyqKgs1mkwU525QuFoiOwPjg3ddPHySbfWdsqDf6TiwWIxAIUioVb/ma\naHSQWCy2a99Tgt3t03SdfLXMxDEYj5qv75RrTSpVHbvqxCHXTLGP8tUKLk+baJ+T/mBvJC12gyWD\n33KtSb0G/X7rrLhVFIWhoSFisRhvf/vbaTQauN1uHA6HDMT7pNFqUWlVOBlRGDPhAN7WdCr1Nq2W\ngsveG4dbDA0N8dM//dP8/u9/4Zav+fjHPy6Lz7osWy4RDOoM9Xvxecx33S7XmtRq4O3xPeXFwbNe\nKhIdlKzv9SxZ/FFttGg0wG3B7WYURcHlchEMBnE6nRL47qNMuUh/P4xE/Djs5sv+VOstmg1w2Xvn\nhklVVd797nfzkY985CbPKnz84z9z1yVBYu+kSwWiUfPOmGyOOb1y0yjMoaVpFOtlIiZNuOwly2V+\nNU2nupG9clpgsZs4ONKlIlPHzXsHXqk3qdd776axv7+ff/yP/wlvf/s7uHjxIuvraWKxIU6dOsWh\nQ4fweGSqsJtqzSYNrUZ/n8pwJNDt5tyTSq1JvQHeHus74mDLlIqE+wyG+n2mOwp8r1nu06g2WjSa\n4Oyh7FU3GIZBsVgkk+mctR6JRAgGg/KZ3kKpVkO1NxnosxMNm2+lOnQyv40GuBy9l73y+XycPn2a\nkydPYhiGLN48QNZLBSIDMBYNYDfpSvVKvUWjDv2+3us74uBaLxWYmISJmDkTLnvJcsHv5kXI3YMD\n+H4pl8ucPXuWr371q8zOzgAwNXWUJ598kgcffJBAwJzZmb1k5pXqmyr11kbmt3f7jmzRd7AYhsF6\nucjJcfPOmMA1ZQ/h3u074mCpNOpoSoNIv82Uh8LsNctd6beyV1J7dU9qtSrPPfccn//8b28FvgCz\nszP8zu98nq9//etUq9UutvDgaWkauUqxE/yauO6qUu9M3fZa2YM4uLKVMi5PmwETr1TXdYNKrUWz\nqeCUcUfsk1QhTzQKY9EgqmrOhMteslzw26t1i/tlbm6eP/uz/37L57/0pS8yNze3jy06+FKFHP0D\nBmODflOuVN8kN45iv63mswwPweSIeU+8qzZaNJvgtNtRTTrrI8yl2W6TrxWJxRSODIW73ZwDyYLB\nb2fqthfrFvearuu89tprd3zdq6++unX4hdVpus5aMc/wEBwdvfnx0Wag6wbVRptmU/qO2B/FWhVd\nqROL2sw9Y7Kx2M1lN++NrzCXZCHHwIDBuMkTLnvJcsFvLy/a2WuGYdz0hLjrXb16FcMw9qFFB1+6\nWCAQ0hiOekw7bQtQa7RoNAwcqkOyV2JfrOSyDA93sr5mPpJV1pmI/dTWNNZLeWJDMGXihMteM+8V\n5R41Wm1aLXDaLLfWb1f099+5M233tLhepRsGyUKO4WFzZ30BGi1ta+pWiL1WbTSoaRUGB1UOm3za\ndmvMkb4j9sFaMU+oT2c06iXs742TOPeCpYJfwzBoazqaBjZZ1b1tqqryrne9846ve+yxx2TVPJ1T\nqVyeFkMDTmJ9vm43Z0famo6mS78R+2M1n2UoBkeGQqY8EOZam2OOXBPFXtMNg1Qhz0gPJFz2mqV6\no6YbW4GvWbeb6iZFUThyZJKHHnr4lq+57777mZyclM8XSOazDI/A1Ei/6T+PVluTm8ZdpOs6mqah\naZqUCF2n0WpRqJeIxRRTL3Tb1NZ02tJ3xD5YLxXwBdrEIi6iYXMnXPaapeZh5A585yKRCP/iX/wL\nnn76ab773e+i6xoAqmrj8ccf58knn2RgYKDLrey+fLUC9gZDUXtPHCup6Qa6DOA71mg0mJ+f59y5\nc1y+fIlgMMg73vFOJicnGRgYMP1N0m5IFnJEowYTsSAel/nrZFttjXqthaqVcBkKfr9fxiCx6wzD\nYDWf48hRyfreDesFvzrYFLnw3CtFURgbG+OTn/wkH/zgB0mlkgDEYjEmJg7hcrm63MKDYXUj6zs5\n3NcTeyxuZX6l79yzWq3G9773PX7v934Pw3hjN5Rvf/vbnDhxkn/zb/4N4+Pjlg6AW5rGernAg5Od\nGRMzMwyDRCLBd7/3t/zpl15nfS6H2+bgiSee4MEHH2RychK71AGLXZKrlHG4mgwNOBgZkIOm7sRS\nPU+mbnePy+Xi2LFjHDt2rNtNOXBKtRpNvcpgVO2ZYyVl1mRnDMPg4sWL/O7v/tebPj89fZk//dM/\n5Rd/8Rfx+aw7XZnMZ+mP6IxGfQR95r2RNgyDS5cu8clPfpIXzi6C/S1QMKCt8ad/+ieoqo1f/MVf\n5F3vehcO2QVC7JBhGKzks4xOdHZHsfIN9N2y1EjW1nS0tgS/Ym/FM2uMjcHUSJ/pF+tskoWiO1Ov\n1/j6179+29e89NKLLC4u7lOLDp5Gq8VaKcfoCBwfj3S7OTuytrbGpz71KV544QVQVMAG19R267rG\nf/yP/5Hz589LzbfYsUy5hOqoMxyzM2HiY8D3k6VGsramo8uKdbGHMuUShr3OyJC9p/ZYlOB3ZzKZ\nLK+++uodX5dMJvehNQfTci5DLGZweDhAX8C8e2IDnDt3jv/9v/93539uEvwCGIbOX//1X1Or1fa/\ngaJn6IbBUnad8XE4OTFg6j2x95OlPqXNVbcydSv2QucilGZiHE6MR7D30EVoK/iVmt89ZdUsYLXR\nIF8rMDqqcHLC3AtmdV3nueeee+MBRQXUG4Jf6JyGuby8tH+NEz0nmc/hC7QYjbl6YnH1frHUSKbp\nBoYOqgzgYg+sFfK4vS1GYs6eqfXdpOkGhiE3jveqr6+Phx566I6vGxoa2ofWHDzxTJrRMZgaCZv+\nOFZd17ly5cobD2wFvzd7tUG1KplfcW9amkaykGV8HE4fjkqt7zZYaiRTFYXO74Y1syti77Q1jZV8\nhokJOH2o9y5CqqqAYt3M5E55vV5+/Mf/4W1f88gjb+HQoUP71KKDo1Ct0DAqjA7bODZm7lpf6OyI\nE4vF3njgDn3G6TR3sC+6ZzWXoT+iMT7kk319t8lawa/aCX51GcDFLlvJZ+nr1xiLeYn1+7vdnF2n\nALSGmawAAB93SURBVKoEv/dMURTuu+9+fv7n/9lNn5+cnOLnfu7nLLfTg2EYJDKdUqFjY/04HeZf\nIKqqKj/xEz9xzSMGoMNNbognJ6cYHh7et7aJ3lFvNVmv5Bkd6yRcxPZYaqszhc71RwZwsZsarRbp\nUo4HHuhMPfWircxvtxtiYl6vlw984AMcO3aMV199lQsXLhAMBnn88ceZnJwkFov13IzBnayXi6iu\nBiNDDo4MhbvdnF2hKAoPPfQQU1NTzM7Objx6857z5JNPEgr1VomU2B9L2XWGhgwmR0Km3hawWywV\n/G5mfiX2FbtpKbdObMjgyEiQsN/d7ebsCVVRJPO7C9xuN6dPn+bkyZPouo6iKKgWPW5d03WWsusc\nO957q9QPHTrEF7/4RT7ykY+wWjdAMTrZl2u6zz/5Jz/NQw89ZMl/e7Ez5XqNUrPE1LD5F4h2i6WC\nX5uqotpAv+Z0JSF2olyvUawXefhkb1+EbDYVVQVNk76zG1RVtfziwWQhRyDYZjTmZrTHTqRSFIW3\nve1tfPOb3+S/fOkbfPF/XKKSqwNw5swZfuzHfoxTp07h9/deiZTYW4ZhEM+kGRuD4+P9uJ2WCuN2\njaU+NbtNxaZ2Mg5C7JRuGCykU0xMwLGxPrzu3j2pyW5TsdlAb0nfETtXazZJFTPcfz/c16Or1BVF\n4cEHH+SntQDBcIoBRx9+t4dodOD/b+9OfuPKrseOf2ue53kkq4rFWZK7ZVvdzq9/Wfj/cOBF1gay\n98Ib/wUGvE4QBAiC/AJkF2flXYzYv8DtbrVmcWZVsVjz/N6rl0WRbLVas0QWWe98AIJUN9U4ovq+\ne+65592L0+layD+zuHwn3TbYhuTSVlYW6Cz5q2a85NcyO4pGiI9VaTWxusbk0jZWF+At9TexWma7\nJrJwFJ/CTr1KOq1TygaIBNzzDudS2a0WYrEQGV8Ov2ux/6zick1UlcNmnfUN2C7EF+os+atmqJ/c\nefKrygQuPtJYUah0Tiksw+1SYqH6FV9Fxo74VE66babmAbmsxRBvqdusFiyycBSfwN5pjVhcYznt\nJRVZrFahq7bYM/ZLbFbz2UNIm3co4obbqVdJpqYUM35DnK9os5ixytgRH0nRNA4aJywvzypXi3C0\n2dtYLWYsVlBl7IiP0Oz36Ktdcjkzt4rxeYdz4xks+bXgdJjBPEXR5EEkPsxJt41Cn3zWwtaCHm32\nMpfDhsMxq3gL8aF261UiMY3ljMcwV7G6nTJ2xMdRNY2depXCMmwuRXE5Fvf9kqtiqOQXwC2TuPgI\nE1XloHFCsQjbhRgOg7xp63HacDhhJONGfKBmv8dA7bKUN3O7mHj7b1gQF3OOKmNHfJj9xgnBsMpS\nxkUhtRjnYc+b4ZJfj8uO0wFjZTLvUMQNtFuvEktoLKc95OLGOZzeYbfitJvBpKHKrol4T8p55aoA\nW8vRhT4Z5WUep+1szpHkV7y/9qBPe9RmecnEnZLxLsK5LIZLfmUVLj7UabfDWO+Rz5q5s5KcdzhX\n7mL7VsaOeE979RqRqMpyxs3ygtzk9q6k7UF8KG065fnJbNG4sRTB55ab3D4VwyW/HqcNp1MmcPF+\nxorCXqNGoQC3inFDHizukUlcfIDTboee2iGfNxuycuW0W3E6TGi6Kic+iPeyU68SCCnk00450/cT\nM1zye74Kl95F8a6mus7T2jGptEYx6yWfME67w4vcDun7Fe9npEzYPa1SXoFbxRgel33eIV05k8mE\n22nDbpeFo3h3J902A7VDoWDms3LScIvGy2a85FdeeBPv6aBRx+ocUliy8VnZeO0O56TtQbyPqa7z\npHJEJjdlJeczXLvDi9wO2XEU724wGbPfqLGyAj9ZiUu7wyUwXPI7O7LJhDJVmOr6vMMR11yz36Mx\naFAqmfi8nMJmXfxzSV/H45SXRcW726vXcHrHFHI2bpeMc7rDq7jP2+2k6CLeQptOeVo9JpefUs77\nDfVi9VUyXPJrNpvwue24XNAfjeYdjrjGxorC85MKKyuwXYwS9rvmHdJc+dx23G7oj8fosnAUb9Do\ndWlPWpRKJn66ljb0ohHA73bgckN/LHOOeLPdeg23f0whZ+eWgY4EvGqGS34Bwj4Xfh90R8N5hyKu\nqfM+32Rao5j1UEqH5h3S3LkcNvxeG1a7xnAi1V/xaiNlwk69wkpp1ucb8DrnHdLchf0ufF7ojAbz\nDkVcY/Vuh57SplgwcXc1jdViyBTtShjyJxvxu/B6oSsPIvEah406FseQ4pKVz8opedngjCwcxZtM\ndZ0n1WMy2SkreR+FlCwaAbwuOz6vBcyqtD6IVxpOJuw1qpTL8JOVBH6P9PleJkMmv2G/C58PeqOR\nbN+KH2kN+tTP+nzvrqax24y9ZfuiyNnYkYWjeJX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OOvztYYWdHZ1u204xlpTLMJgdtn/c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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -554,9 +551,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The points do not lie along the major and minor axis of the ellipse; nothing in the constraints above require me to do that. Furthermore, in each case I show the points evenly spaced; again, the constraints above do not require that. \n", + "The points do not lie along the major and minor axis of the ellipse; nothing in the constraints require me to do that. Furthermore, I show the points evenly spaced; again, the constraints do not require that. \n", "\n", - "We can see that the arrangement and spacing of the sigma points will affect how we sample our distribution. Points that are close together will sample local effects, and thus probably work better for very nonlinear problems. Points that are far apart, or far off the axis of the ellipse will sample non-local effects and non Gaussian behavior. However, by varying the weights used for each point we can mitigate this. If the points are far from the mean but weighted very slightly we will incorporate some of the knowledge about the distribution without allowing the nonlinearity of the problem to create a bad estimate. " + "The arrangement and weighting of the sigma points affect how we sample the distribution. Points that are close together will sample local effects, and thus probably work better for very nonlinear problems. Points that are far apart, or far off the axis of the ellipse will sample non-local effects and non Gaussian behavior. However, by varying the weights used for each point we can mitigate this. If the points are far from the mean but weighted very slightly we will incorporate some of the knowledge about the distribution without allowing the nonlinearity of the problem to create a bad estimate. " ] }, { @@ -570,18 +567,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For the moment assume an algorithm exists for selecting the sigma points and weights. How are the sigma points used to implement a filter?\n", + "For the moment, assume an algorithm for selecting the sigma points and weights exists. How are the sigma points used to implement a filter?\n", "\n", - "The *unscented transform* is the core of the algorithm yet it is remarkably simple. We pass the sigma points through a (usually nonlinear) function yielding a transformed set of points.\n", + "The *unscented transform* is the core of the algorithm yet it is remarkably simple. We pass the sigma points $\\boldsymbol{\\chi}$ through a (usually nonlinear) function yielding a transformed set of points.\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", - "I use a calligraphic $\\boldsymbol{\\mathcal{Y}}$ to denote that it consists of a set of sigma points. We then compute a new mean and covariance of the transformed sigma points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " + "We then compute a new mean and covariance of the transformed points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -590,7 +587,7 @@ "data": { "image/png": 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nx54MlmVx4cKFse4MtypneOqpp9izZ89YOcOd6B4K4Y8NkZc9c2bDp5t02kJX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\nN0oTKRoz6Os3mZc/h/vml8nGFkJkmIR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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -605,7 +602,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The mean and covariance of the transformed sigma points are computed as:\n", + "The mean and covariance of the sigma points are computed as:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w^m_i\\boldsymbol{\\mathcal{Y}}_i \\\\\n", @@ -629,28 +626,22 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 9, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Difference in mean x=-0.097, y=0.549\n" + "ename": "NameError", + "evalue": "name 'f' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 24\u001b[0m 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\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m30\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m30\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mylim\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m90\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 28\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m121\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'f' is not defined" ] - }, - { - "data": { - "image/png": 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+PZVfz9LTr5+ePaeTO5KybMZrAwMDA4P9H4YYNRByZaHVFXzIS1+PXjPIiVRJ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ @@ -705,18 +696,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can present the entire Unscented Kalman filter algorithm. Assume that there is a process model $\\mathbf{\\overline x} = f(\\mathbf x, \\Delta t)$ that performs the state transition for our filter - it predicts the next state given the current state. It is the analogue of the $\\mathbf F$ matrix of the Kalman filter. Also assume there is a measurement function $\\mathbf z = h(\\mathbf{\\overline x})$. It takes the prior and computes a measurement for it. It is the analogue of the $\\mathbf H$ matrix used by the Kalman filter.\n", - "\n", - "The algorithm is straightforward. $f()$ is nonlinear, so we will compute a set of sigma points $\\mathcal{X}$ and weights $W^m, W^c$ from $\\mathbf x$ and $\\mathbf P$. We then pass those sigma points through the unscented transform to find the prior:\n", - "\n", - "$$\\begin{aligned}\n", - "\\mathcal{X}, W^m, W^c &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\ \\\\\n", - "\\boldsymbol{\\mathcal{Y}} &= f(\\boldsymbol{\\chi}) \\\\\n", - "\\mathbf{\\overline x}, \\mathbf{\\overline P} &= \n", - "UT(\\mathcal{Y}, \\boldsymbol{\\bar \\mu}, w_{m,c}, \\mathbf Q)\n", - "\\end{aligned}$$\n", - "\n", - "Now we incorporate the measurement. We need to compute the residual: the difference between the predicted measurement and the actual measurement. In the linear Kalman filter the computation is $\\mathbf y = \\mathbf z - \\mathbf{H\\bar x}$. In the UKF we perform all of our computations on sigma points, not the state. " + "We can now present the UKF algorithm. " ] }, { @@ -737,7 +717,7 @@ "\\mathcal{X} &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\\n", "W^m, W^c &= \\text{weight-function}(\\mathtt{n, parameters})\\end{aligned}$$\n", "\n", - "We pass each sigma point through $f(\\mathbf x, \\Delta t)$. This projects the sigma points forward in time according to the process model, forming the new *prior*.\n", + "We pass each sigma point through $f(\\mathbf x, \\Delta t)$. This projects the sigma points forward in time according to the process model, forming the new *prior*, which is a set of sigma points we name $\\boldsymbol{\\mathcal Y}$:\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi}, \\Delta t)$$" ] @@ -759,7 +739,7 @@ "\\end{aligned}\n", "$$\n", "\n", - "This table compares the Kalman filter with the Unscented Kalman Filter equations." + "This table compares the linear Kalman filter with the Unscented Kalman Filter equations." ] }, { @@ -788,11 +768,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can perform the update step of the filter. Recall that Kalman filters perform the update state in measurement space. So, the first thing we do is convert the sigma points from the predict step into measurements using a measurement function $h(x)$ that you define.\n", + "Now we can perform the update step of the filter. Recall that Kalman filters perform the update state in measurement space. Thus we must convert the sigma points of the prior into measurements using a measurement function $h(x)$ that you define.\n", "\n", "$$\\boldsymbol{\\mathcal{Z}} = h(\\boldsymbol{\\mathcal{Y}})$$\n", "\n", - "Now we can compute the mean and covariance of these points using the unscented transform.\n", + "Now we can compute the mean and covariance of these points using the unscented transform. The $z$ subscript denotes that these are the mean and covariance of the measurement sigmas.\n", "\n", "$$\\begin{aligned}\n", "\\boldsymbol\\mu_z, \\mathbf P_z &= \n", @@ -802,8 +782,6 @@ "\\end{aligned}\n", "$$\n", "\n", - "The $z$ subscript denotes that these are the mean and covariance for the measurements.\n", - "\n", "All that is left is to compute the residual and Kalman gain. The residual of the measurement $\\mathbf z$ is trivial to compute:\n", "\n", "$$\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z$$\n", @@ -816,7 +794,7 @@ "\n", "$$\\mathbf{K} = \\mathbf P_{xz} \\mathbf P_z^{-1}$$\n", "\n", - "If you think of the inverse as a *kind of* matrix division, you can see that the Kalman gain is a simple ratio which computes:\n", + "If you think of the inverse as a *kind of* matrix reciprocal, you can see that the Kalman gain is a simple ratio which computes:\n", "\n", "$$\\mathbf{K} \\approx \\frac{\\mathbf P_{xz}}{\\mathbf P_z^{-1}} \n", "\\approx \\frac{\\text{belief in state}}{\\text{belief in measurement}}$$\n", @@ -829,7 +807,7 @@ "\n", "$$ \\mathbf P = \\mathbf{\\overline P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\n", "\n", - "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. We convert the mean and covariance into measurement space, add the measurement error into the measurement covariance, compute the residual and kalman gain, compute the new state estimate as the old estimate plus the residual times the Kalman gain, and adjust the covariance for the information provided by the measurement. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same Bayesian algorithm we have been implementing throughout the book. \n", + "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same Bayesian algorithm we have been implementing throughout the book. \n", "\n", "This table comparing the Kalman filter equations with the UKF equations should help clarify the relationship between the filters." ] @@ -871,36 +849,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There are several published ways for selecting the sigma points for the unscented Kalman filter. Since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1] because it performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", + "There are many algorithms published for selecting the sigma points for the UKF. Since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1]. It performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", "\n", - "Van der Merwe's formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. Before we work through the equations, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and size the points based on the weights assigned to them." + "Van der Merwe's formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. Before we work through the equations, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and scale the points based on the mean weights." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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cHOXgKw/P9/GVj4/XT7I1+ok2ev//NZ2QESKshQgZJpGQQTRskIyaJCImmqZt97cpxDIS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\nqaegqiouueQSfPOb38TOnTtnP79582ZccMEFuP/++0/4f/l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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "3.91\n" - ] - } - ], + "outputs": [], "source": [ "ukf_internal.plot_sigma_points()" ] @@ -909,7 +869,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that the sigma points lie between the first and second deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weighs the mean (center point) higher than the smaller $\\alpha$, and weighs the rest of the sigma points less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable." + "We can see that the sigma points lie between the first and second standard deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weights the mean (center point) higher than the smaller $\\alpha$, and weights the rest less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable." ] }, { @@ -924,7 +884,7 @@ "\n", "$$ \\mathcal{X}_0 = \\mu$$\n", "\n", - "For notational convenience we define $\\lambda = \\alpha^2(n+\\kappa)-n$, where $n$ is the dimension of $\\mathbf x$. Then the remaining sigma points are computed as\n", + "For notational convenience we define $\\lambda = \\alpha^2(n+\\kappa)-n$, where $n$ is the dimension of $\\mathbf x$. The remaining sigma points are computed as\n", "\n", "$$ \n", "\\boldsymbol{\\chi}_i = \\begin{cases}\n", @@ -932,7 +892,7 @@ "\\mu - (\\sqrt{(n+\\lambda)\\Sigma})_{i-n} &\\text{for i=(n+1) .. 2n}\\end{cases}\n", "$$\n", "\n", - "In other words, we scale the covariance matrix by a constant, take the square root of it, and then to ensure symmetry both add and subtract if from the mean. We will discuss how you take the square root of a matrix later.\n", + "In other words, we scale the covariance matrix by a constant, take the square root of it, and ensure symmetry by both adding and subtracting it from the mean. We will discuss how you take the square root of a matrix later.\n", "\n", "### Weight Computation\n", "\n", @@ -948,7 +908,7 @@ "\n", "$$W^m_i = W^c_i = \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n$$\n", "\n", - "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to 1 standard deviation. However, there is an $n$ term in there - the more dimensions there are the more the points will be spread out and weighed less.\n", + "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to $\\pm 1\\sigma$ times some scaling factor. There is an $n$ term in the denominator, so with more dimensions the points will be spread out and weighed less.\n", "\n", "### Reasonable Choices for the Parameters\n", "\n", @@ -966,11 +926,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Lets launch into solving some problems so you can gain confidence in how easy the UKF actually is. We will use FilterPy's UKF implementation. Later we will implement the UKF ourselves.\n", + "Lets solve some problems so you can gain confidence in how easy the UKF is to use. We will start by using FilterPy's UKF implementation. Later we will implement the UKF ourselves.\n", "\n", - "Let's start by solving a problem you already know how to do. Although the UKF was designed for nonlinear problems, it obtains the same result as the linear Kalman filter for linear problems. We will write a filter for the problem of tracking using a constant velocity model in 2D. This will allows us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", + "Let's start by solving a problem you already know how to do. Although the UKF was designed for nonlinear problems, it obtains the same result as the linear Kalman filter for linear problems. We will write a filter to track an object in 2D using a constant velocity model. This will allows us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", "\n", - "To design a linear Kalman filter you need to design the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times already so let me present a design to you without a lot of comment. We want a constant velocity model, so we define $\\bf{x}$ to be\n", + "Designing a Kalman filter requires you to specify the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times already so I will give you the matrices without a lot of discussion. We want a constant velocity model, so we define $\\bf{x}$ to be\n", "\n", "$$ \\mathbf x = \\begin{bmatrix}x & \\dot x & y & \\dot y \\end{bmatrix}^\\mathsf{T}$$\n", "\n", @@ -987,43 +947,32 @@ "$$x_k = x_{k-1} + \\dot x_{k-1}\\Delta t \\\\\n", " y_k = y_{k-1} + \\dot y_{k-1}\\Delta t$$\n", "\n", - "Our sensors provide position measurements but not velocity, so the measurement function is\n", + "Our sensors provide position but not velocity, so the measurement function is\n", "\n", "$$\\mathbf H = \\begin{bmatrix}1&0&0&0 \\\\ 0&0&1&0\n", "\\end{bmatrix}$$\n", "\n", - "Let's say our sensor gives positions in meters with an error of $\\sigma=0.3$ meters in both the *x* and *y* coordinates. This gives us a measurement noise matrix of \n", + "The sensor readings are in meters with an error of $\\sigma=0.3$ meters in both *x* and *y*. This gives us a measurement noise matrix of \n", "\n", "$$\\mathbf R = \\begin{bmatrix}0.3^2 &0\\\\0 & 0.3^2\\end{bmatrix}$$\n", "\n", - "Finally, let's assume that the process noise can be represented by the discrete white noise model - that is, that over each time period the acceleration is constant. We can use `FilterPy`'s `Q_discrete_white_noise()` method to create this matrix for us, but for review the matrix is\n", + "Finally, let's assume that the process noise can be represented by the discrete white noise model - that is, that over each time period the acceleration is constant. We can use `FilterPy`'s `Q_discrete_white_noise()` to create this matrix for us, but for review the matrix is\n", "\n", "$$\\mathbf Q = \\begin{bmatrix}\n", "\\frac{1}{4}\\Delta t^4 & \\frac{1}{2}\\Delta t^3 \\\\\n", "\\frac{1}{2}\\Delta t^3 & \\Delta t^2\\end{bmatrix} \\sigma^2$$\n", "\n", - "Our implementation might look like this:" + "My implementation of this filter is:" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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UjYd1Rx08Puek7RVpKpQuug3ZOgvkaSrI01RIS0mHWMSL3YmIaGHjaSoiirig\nEESj9QI+vvgOzjedxujYyJTtE+OTsDz/FtxYdDvyjSUM6URERF+DwZ2IIqbb34VPat/FJzXvoNvv\nmrSdRBIHkyYP2bpC5OgXoSS7FAnxiTNYKRERUexhcCeib2RoZBDnG6vwp9r30Gi9AAHCVW0y0jXI\n0RUiW1+IbF0BDKocbrtIRER0jRjcieiajYwNo6mzBp/WvjfpUpiUxDSULboNq4rvgEmTOwtVEhER\nzS8M7kQ0qcHhfji6rXB2W+Ho7gg9d/tdX3tmXSQSo9C0FDeV3IkluSsRH5cwC1UTERHNTwzuRAuQ\nIAgYGOqFf6AHvQM98Pd7L//Zi94BH3p63XB6O+Hr7w5rPL0yCyuLvoOywjWQpWVEuXoiIqKFicGd\naB4LBMbg6rHD7mmDw9MBu6cNdk87PH4XAsGx6x5XJBJDLdOhOKcMK4u+jUxVzlX3ayAiIqLIYnAn\nmieCwQA63W1ottWgxV4Hu6cNLq/tGwV0iSQOWnkmtBlG6DJMl5+NUMszeXEpERHRDGNwJ4pRo2Oj\naHc2oKnzIppstWixX8LQyEDY/ZMTUiBNkUOaqkB6ihzpqQpIk2Whn9VyA5QyLSRiSRQ/BREREYWL\nwZ0oRoyOjaLNWY9G6wU0Wi+gxV6H0cDUNzYCAIVUDX2GCXpVFvRKc+jMeWJ80gxUTURERJHC4E40\nR/UP+tHhakaL/RIaOy+iNYygLkvNQF5mMXINRTBp8qHLMCE5MWWGKiYiIqJoYnAnmgN6B3rQ4WpC\nh6sZHa4mWF1N6O7tmrafWqZHnrEEeYZi5GUWQ5mu5UWiRERE8xSDO9EMCwpB2N3taOy8MH4m3VEP\nX58nrL5quQEWYwnyMhcjP7MECqkqytUSERHRXMHgThRlgiDA5m5FfccXaOy8gCZbLQaGeqftJ5HE\nIVOZDZMmD3mZxcg3LoY8TTkDFRMREdFcxOBOFCW9Az349NL7+KTmHdg97VO2jY9LQKY6ByZ1Hoya\nXGRp8qDLMEEi4V9RIiIiGsdUQBQBQSEYutuoy9uJBusXuNBSjWAw8LXt05JlyM8sQb6xBHmGEuiU\nJm67SERERFNicCe6Rt7eLrQ66mH3tMPltcHptcLl7cTo2OQ7viTEJ6EkuxQW4xLkG0ugVRh5ESkR\nERFdEwZ3oimMjo3C2tWMVnsdWuyX0OKoC/tCUgDI1RdhVckduMGyGkkJyVGslIiIiOY7BneiLxkd\nG0GzrRZOi6ZrAAAUoUlEQVSX2s+hyVYDq6sZY4HRsPqmJcugURigVRihzchESc6N0Coyo1wxERER\nLRQRD+4VFRV4/fXXUVdXh8TERNx0002oqKhASUnJhHZ79uzB0aNH4fV6sWrVKlRWVqK4uDjS5RBN\nSRAEOLqtuNT2GS61n0Nj54Upl7wA48tesrUWGDV50GYYx4O6woDU5PQZqpqIiIgWoogH9w8++ACb\nNm1CWVkZBEHArl27cOedd6K2thZyuRwAcPDgQRw6dAjHjh1DQUEB9u7di/LyctTX1yM1NTXSJRGF\nDA4PXL7RUSPanA1osU+/9EUt0yNbX4hsfSFy9IXQK828kJSIiIhmXMSD+9tvvz3h55deegkymQwf\nffQRvv/97wMAnnnmGezYsQN33303AODYsWPQaDR4+eWX8dBDD0W6JFqAhkYG0e13wdvbBbfPgXZn\nI9qdjXB5OyFAmLKvRm7AIvNyFJiWIUdfCGmKfIaqJiIiIppc1Ne4+/1+BINBKBQKAEBLSwscDgfK\ny8tDbZKSkrBmzRpUVVUxuFPYRkaH4ejugN3TjnOtn8I/2I136n8Hr78LA8N9YY+TnJCCgqxlWJS1\nHIvMy6FM10axaiIiIqLrE/XgvmXLFqxYsQI333wzAMDhcEAkEkGrnRiOtFotbDbblGNVV1dHrU6a\n2wRBgKfPhk5vEzz9DvQMuNA31HPN44gggjxFDWWaASqpHso0AxSpWohFYmAYaKnvQAs6ovAJaK7g\n9wiFg/OEwsF5QlOxWCwRHzOqwf2JJ55AVVUVPvroI+5ZTddseHQQtp4mdHqbYOtpwtDoQNh9xSIJ\nUhPTkZooQ1qiDPJUDVRpBmSk6hAniY9i1URERETREbXgvm3bNvz7v/873nvvPZjN5tBxnU4HQRDg\ndDphNBpDx51OJ3Q63ZRjlpWVRatcmgMGh/vR4WpCi/0SalrPotVRD0EITtpeJBJDLdNBp8wChuMg\nS1GhbPlNyEjXQJoiHz+LTnTZlTNj/B6hqXCeUDg4TygcPp8v4mNGJbhv2bIF//Ef/4H33nvvql8T\n5OTkQKfT4cSJEygtLQUADA0N4dSpU3j66aejUQ7NQYPDA7B72tDmbEC7sxEdzka4eqZeKiVNlqEo\newUKTEuRqcqGRpGJ+LgEAH/+Es3RL4p67URERESzIeLB/bHHHsO//du/4c0334RMJoPT6QQApKWl\nhbZ63Lp1KyoqKlBYWAiLxYJ9+/ZBKpViw4YNkS6HZtmXLyB1dLfD7hn/s7e3a9q+IoiQpbOgOLsU\nJdmlMGpyeRadiIiIFqyIB/cjR45AJBLhjjvumHD8qaeewu7duwEA27dvx9DQEDZt2hS6AdPx48e5\nh3uMGxkbRmdXC9ocDeNn0h0NcPsc026/eIVYJIZeZUaWJh/5xhIsyroB0hRZlKsmIiIiig0RD+7B\n4ORrkr9s9+7doSBPsScoBOHstoZCepuzHjZ3G4LBQFj9xWIJtIpMmDR5yNLmw6TJR6Y6GwlxiVGu\nnIiIiCg2RX07SJo//P09qOs4h9q2z1DXfh69A9Nvx3jlAlK9Mgs6ZRb0lx9quZ67uxARERFdAwZ3\nmpQgCLB2NeOz+o9Q2/4ZOrtapu2jUWTCrLXArLPArLXAoMoOXUBKRERERNePwZ2u4vY5cKbuA1Rf\n+gBOr3XSdqlJUuRlFiNLOx7STdo8pCSmzWClRERERAsHg/sCFwwG4O11w+nthKO7HecbP0aL/dLX\nthWLJcjRL0JR1nIsMt/AXV6IiIiIZhCD+wIxOjYKl7cTNk8bnN1WuLyd448eG8YCo5P2S4hPwtK8\nVViefwssxiVITkyZwaqJiIiI6AoG93kmGAzA7XPA7mmHzdMOu6cNdk87urw2BKe4C+mXiUViFJlX\noGzRGizOXYnE+KQoV01ERERE02Fwnwe6euy41PYZatvPoaHjcwyPDl1Tf2myDBpFJjSXt2dcln8z\n908nIiIimmMY3GPQ8MggGqwXUNv2GS61fYYunz2sfkqZFnqlGboME7SKTGgzjNAoDLyglIiIiCgG\nMLjHgEBgDG3OBtS1n0d9x+docdRNeaOj9BQF9Kos6JVm6JVZMCjN0GUYkZiQPINVExEREVEkMbjP\nIUEhiJ5eD9w+B9w+O9w942vVGzsvTLn8JSEuERbjEiwyL0eReQXUcj1EItEMVk5ERERE0cbgPku8\nvW40WL9Ah6sJ7h7HeFj3OxAIjIXV36A0oyj7BizKugG5hmLEx/EupERERETzGYP7DPH1d6Oh4ws0\ndl5AQ8eFsNelX6GQqlGYtQyFpqWwGJciPVUepUqJiIiIaC5icI+SoBBEq70O5xpPo6b1DFzezrD6\npSXLoJLp/vyQ65CjXwSVTMflL0REREQLGIN7BAWCATR1XsS5xtP4vOlj+Pu9k7aNlyQgx7AIeZkl\n0GWYQkGdNzgiIiIioq/D4H6NgsEAevrGLyDt6rGPr03vsaPLN75OfWSSi0jjJPHI1hfCYlwCi3Ex\nzNoCrksnIiIiorAxuE9jdGwUrY46NFi/QIP1Atoc9RgLjIbVNy1ZhqV5K7Es/xbkZ5YgPi4hytUS\nERER0XzF4P4V43umN44H9Y7P0WKvw2hgJOz+stQMLMu/Ccvyb0auoRgSsSSK1RIRERHRQrEgg7sg\nCPD3e8f3Sr+8xOXKloz27o5Jl7tcIU2WQSnXQS3TQyXXQyXTQS3XQy3TISVJyotIiYiIiCji5nVw\nHxzuh8vbCVePbfzZO/7c1WPHyNhw2OOoZXpYTIthMS6FxbgY6amKKFZNRERERHS1WQ3uzz//PH71\nq1/BbrejpKQE//zP/4xbb731uscLBgP4rOEjnL5wAvbuDvQO9FzXOBnpmtBFpBbjEiikquuuiYiI\niIgoEmYtuL/22mvYunUrfv3rX2P16tWorKzE2rVrUVtbC6PReE1jBYUgzjVU4e1PXoWz2xpWn5TE\ntNA+6SqZDsp0LVRyHdRyA+Rpyuv5SEREREREUTNrwf3QoUP46U9/ip/+9KcAgMOHD+MPf/gDjhw5\ngv3790/b39ffjXZnIzqcTTjfdBp2T/tVbeIk8VDL9dDIDdAoMqFRXH6WG5CanB7xz0REREREFC2z\nEtxHR0dx5swZ/OxnP5tw/Lvf/S6qqqom7ffHP/072p2NaHc1wdfn+do2iQnJuH35D7Cy+HZkSNUQ\nc1cXIiIiIpoHZiW4u91uBAIBaLXaCce1Wi3eeeedSfv939MvT/panDgeRYaVKDbchMT4ZLQ2WNGK\n8JbN0PxRXV092yXQHMc5QuHgPKFwcJ7QVCwWS8THjNldZeLE8chI00GZqocyTQ+DIg9J8SmzXRYR\nERERUVTMSnBXqVSQSCRwOp0TjjudTuh0ukn73bp0LczafJg0+dBmGHlzIwq5ctajrKxsliuhuYpz\nhMLBeULh4DyhcPh8voiPKY74iGGIj49HaWkpTpw4MeH4iRMnsHr16kn73XP7RqwqvgMGlZmhnYiI\niIgWlFlbKvPEE0/gvvvuw4033ojVq1fjyJEjsNvt2Lhx42yVREREREQ0Z81acL/nnnvQ3d2N/fv3\nw263Y/HixXj77bdhMplmqyQ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "from filterpy.kalman import KalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", @@ -1057,7 +1006,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This should hold no surprises for you. Now let's implement this with a UKF. Again, this is purely for educational purposes; using a UKF for a linear filter confers no benefit. `FilterPy` implements the UKF with the class `UnscentedKalmanFilter`. \n", + "This should hold no surprises for you. Now let's implement a UKF. Again, this is purely for educational purposes; using a UKF for a linear filter confers no benefit. `FilterPy` implements the UKF with the class `UnscentedKalmanFilter`. \n", "\n", "The first thing to do is implement the functions `f(x, dt)` and `h(x)`. `f(x, dt)` implements the state transition function, and `h(x)` implements the measurement function. These correspond to the matrices $\\mathbf F$ and $\\mathbf H$ in the linear filter.\n", "\n", @@ -1066,7 +1015,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false @@ -1091,21 +1040,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next you specify how to compute the sigma points and weights. We gave the Van der Merwe's scaled unscented transform version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement two methods:\n", + "Next you specify how to compute the sigma points and weights. We gave Van der Merwe's version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement two methods:\n", "\n", "```python\n", "def sigma_points(self, x, P)\n", "def weights(self)\n", "```\n", "\n", - "FilterPy provides the class `MerweScaledSigmaPoints`, which implements the Van der Merwe algorithm. It derives from `SigmaPoints` and implements the aforementioned methods." + "FilterPy derives the class `MerweScaledSigmaPoints` from `SigmaPoints` and implements the aforementioned methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "When you create the UKF you will pass in the $f()$ and $h()$ functions and the sigma point object as in this example:\n", + "When you create the UKF you will pass in the $f()$ and $h()$ functions and the sigma point object, as in this example:\n", "\n", "```python\n", "from filterpy.kalman import MerweScaledSigmaPoints\n", @@ -1120,35 +1069,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The rest of the code is the same as for the linear kalman filter. I'll use the same measurements used by the linear Kalman filter, and compute the standard deviation of the difference between the two solutions." + "The rest of the code is the same as for the linear kalman filter. I'll use the same measurements used by it and compute the standard deviation of the difference between the two solutions." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "UKF standard deviation 0.013\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", @@ -1170,55 +1101,44 @@ "uxs = np.array(uxs)\n", "\n", "plt.plot(uxs[:, 0], uxs[:, 2])\n", - "print('UKF standard deviation {:.3f}'.format(np.std(uxs - xs)))" + "print('UKF standard deviation {:.3f} meters'.format(np.std(uxs - xs)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This gave me a standard deviation of 0.013, which is quite small. \n", + "This gave me a standard deviation of 0.013 meters, which is quite small. \n", "\n", - "So far the implementation of the UKF is not *that* different from the linear Kalman filter. Instead of implementing the state function and measurement function as the matrices $\\mathbf F$ and $\\mathbf H$ you supply functions `f()` and `h()`. The rest of the theory and implementation remains the same. Of course the `FilterPy` code for the UKF is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." + "The implementation of the UKF is not *that* different from the linear Kalman filter. Instead of implementing the state transition and measurement functions as the matrices $\\mathbf F$ and $\\mathbf H$ you supply nonlinear functions `f()` and `h()`. The rest of the theory and implementation remains the same. The code implementing `predict()` and `update()` differs, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Tracking a Flying Airplane" + "## Tracking an Airplane" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let's tackle our first nonlinear problem. We will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n", + "Let's tackle our first nonlinear problem. We will write a filter to track an airplane using radar as the sensor. To keep the problem similar to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. Each dimension is independent so we can do this with no loss of generality.\n", "\n", - "Radars work by emitting radio waves or microwaves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. Radars also provide velocity measurements via the Doppler effect, but we will be ignoring this complication.\n", + "Radars work by emitting radio waves or microwaves. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to return it can compute the *slant distance* and bearing to the target. Slant distance is the straight line distance from the radar to the object. Radars also provide velocity measurements via the Doppler effect, but we will be ignoring this complication for the moment.\n", "\n", - "We can compute the (x,y) position of the aircraft from the slant distance and angle, as in the diagram below." + "We compute the (x,y) position of the aircraft from the slant distance and bearing as illustrated by this diagram:" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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+/fqaOXOmLl68qJdeekmSdOzYMXXr1k3169fXsmXLtGvXLs2bN0+S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\nRK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import ekf_internal\n", "ekf_internal.show_radar_chart()" @@ -1228,7 +1148,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We will assume that the aircraft is flying at a constant altitude. This leads us to design a three variable state vector:\n", + "We will assume that the aircraft is flying at a constant altitude. Thus we have a three variable state vector:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}= \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$" ] @@ -1237,18 +1157,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Our state transition function is linear \n", + "The state transition function is linear \n", "\n", "$$\\mathbf{\\overline x} = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}\n", "$$\n", "\n", - "which we can implement very much like the previous problem." + "and can be computed with:" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false @@ -1269,22 +1189,22 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we design the measurement function. As in the linear Kalman filter the measurement function converts the filter's state into a measurement. We need to convert the position and velocity of the aircraft and into the bearing and range from the radar station.\n", + "Next we design the measurement function. As in the linear Kalman filter the measurement function converts the filter's prior into a measurement. We need to convert the position and velocity of the aircraft into the bearing and range from the radar station.\n", "\n", "Range is computed with the Pythagorean theorem:\n", "\n", "$$\\text{range} = \\sqrt{(x_\\text{ac} - x_\\text{radar})^2 + (y_\\text{ac} - y_\\mathtt{radar})^2}$$\n", "\n", - "To compute the bearing we use the arctangent function.\n", + "Bearing is the arctangent of $y/x$:\n", "\n", "$$\\text{bearing} = \\tan^{-1}{\\frac{y_\\mathtt{ac} - y_\\text{radar}}{x_\\text{ac} - x_\\text{radar}}}$$\n", "\n", - "As with the state transition function we need to define a Python function to compute this for the filter. I'll take advantage of the fact that a function can own a variable to store the radar's position. While this isn't necessary for this problem (we could hard code in the value), this gives the function more flexibility without requiring it to use a global variable." + "We need to define a Python function to compute this. I'll take advantage of the fact that a function can own a variable to store the radar's position. While this isn't necessary for this problem (we could hard code the value, or use a global), this gives the function more flexibility." ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false @@ -1305,14 +1225,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between 359° and 1° is 2°, but subtracting two values yields a value of 358°. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", + "There is a nonlinearity that we are not considering, the fact that angles are modular. The residual is the difference between the measurement and the prior projected into measurement space. The angular difference between 359° and 1° is 2°, but 359° - 1° = 358°. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later I will show you how to handle this problem.\n", "\n", - "We need to simulate the Radar station and the movement of the aircraft. By now this should be second nature for you, so I will present the code without much discussion." + "We need to simulate the radar and the aircraft. By now this should be second nature for you, so I offer the code without discussion." ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false @@ -1369,53 +1289,22 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's put it all together. A military grade radar system can achieve 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n", + "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n", "\n", - "The design of $\\mathbf Q$ requires some discussion. The state $\\mathbf x$ contains $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are position (down range distance) and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element of $\\mathbf x$ is altitude, which we are assuming is independent of the down range distance. That leads us to a block design of $\\mathbf Q$ of:\n", + "The design of $\\mathbf Q$ requires some discussion. The state is $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are down range distance and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element is altitude, which we assume is independent of $x$. That results in a block design for $\\mathbf Q$:\n", "\n", - "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & 0 \\\\ 0 & Q_\\mathtt{y}\\end{bmatrix}$$\n", + "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & \\boldsymbol 0 \\\\ \\boldsymbol 0 & Q_\\mathtt{y}\\end{bmatrix}$$\n", "\n", - "I'll start with the aircraft positioned directly over the radar station flying at 100 m/s. A typical radar might update only once every 12 seconds and so we will use that for our update period. " + "I'll start with the aircraft positioned directly over the radar station, flying at 100 m/s. A typical radar might update only once every 12 seconds so we will use that for our epoch period. " ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "image/png": 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6jhSsrXuwru7BurrHT1ejuMqwmvzu7m5s3rwZn3/+OSorKwEASUlJuO222/Dg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\nTx7R1d2JspqT0PU/WXawCTh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67WnToCuhNZuavFJFp9dx9spxjpzdxbEL+5TFCP/O3zOIvu0epXm9Dhw6dAiw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\nICKyQf31V+6AgAAIIeDp6Sl7GlFHgoODAQA1NTUYO3Zsu+U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D6NfqTrm6BJ/9uB5XizIM+pxUKoPC1Qfebv7wcm99uflD6eYHu1t0IepvN18t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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "from filterpy.common import Q_discrete_white_noise\n", "import math\n", @@ -1473,36 +1362,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The previous example produced good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. Here are the results if the aircraft starts climbing after one minute." + "The previous example produced good results, but it assumed the aircraft did not change altitude. Here are the filter results if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Actual altitude: 2561.9\n", - "UKF altitude : 1107.2\n" - ] - }, - { - "data": { - "image/png": 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fP38+WVlZrFq1iq+//pp//etfPPzww6xatUqNSUxMZO3atWRmZpKXl0dVVRVR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\ntQrb6o2bMGECRo4cib59+yrKm6PNtvilU5vL5cuXUV5eDl9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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "from ukf_internal import plot_altitude\n", "\n", @@ -1533,7 +1403,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The filter is completely unable to track the changing altitude. What do we have to change to allow the filter to track the aircraft?\n", + "The filter is unable to track the changing altitude. What do we have to change in our design?\n", "\n", "I hope you answered add climb rate to the state, like so:\n", "\n", @@ -1542,16 +1412,16 @@ "\n", "This requires the following change to the state transition function, which is still linear.\n", "\n", - "$$\\mathbf{\\overline x} = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&\\Delta t \\\\ 0&0&0&1\\end{bmatrix}\n", + "$$\\mathbf{F} = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&\\Delta t \\\\ 0&0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\\\dot x\\\\ y\\\\ \\dot y\\end{bmatrix} \n", "$$\n", "\n", - "The measurement function stays the same, but we will have to alter Q to account for the state dimensionality change." + "The measurement function stays the same, but we must alter $\\mathbf Q$ to account for the dimensionality change of $\\mathbf x$." ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1581,31 +1451,12 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Actual altitude: 2561.9\n", - "UKF altitude : 2432.9\n" - ] - }, - { - "data": { - "image/png": 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tLa0YN3gKYf6PYmdjOjzo2rVrlJSU0KNHj0btTZ06lVOnTqlzDwYMGCArAgnR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\nCA6uWAysW7du5Ofns3fvXv17C4mJiRQWFtK9e/c7tiHkkcdr7HocbZ3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w4cMGdc6fP8+v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\nSUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", @@ -1632,7 +1483,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that a significant amount of noise has been introduced into the altitude, but we are now accurately tracking the altitude change. " + "A significant amount of noise has been introduced into the altitude estimate, but we are now accurately tracking altitude." ] }, { @@ -1646,39 +1497,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's consider an example of sensor fusion. We have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system, where you have to account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", + "Now let's consider an example of sensor fusion. We have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system. A full implementation must account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", "\n", - "The accuracy of the radar system in the last examples allowed us to estimate velocities to within a m/s or so, so we have to degrade that accuracy to be able to easily see the effect of the sensor fusion. Let's change the range error to 500 meters and then compute the standard deviation of the computed velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations.\n", + "The radar's accuracy in the last examples allowed us to estimate velocities to within one m/s or so, I will degrade that accuracy to illustrate the effect of sensor fusion. Let's change the range error to $\\sigma=500$ meters and then compute the standard deviation of the estimated velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations.\n", "\n", - "First, here is the code that computes the standard deviation of the filter without using the Doppler:" + "The standard deviation without using Doppler is:" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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EEzUXf/EIq/b8wL6Tm5izfCpfrHiPU0kx900+hRB1h7qinF1nV5BboJ0kwsrC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\nF/G3v/0NEydOxPHjx2FsbIzi4mLWawe88MILCA0NRXh4OAC22a7y23o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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Velocity std 3.4 m/s\n" - ] - } - ], + "outputs": [], "source": [ "range_std = 500.\n", "bearing_std = math.degrees(0.5)\n", @@ -1706,16 +1539,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To include the doppler we need to add the velocity in $x$ and $y$ into the measurement. The `ACSim` class stores the velocity in the data member `vel`. To perform the Kalman filter update we just need to call `update` with a list containing the bearing, distance, and velocity in $x$ and $y$:\n", + "To include Doppler we need to include the velocity in $x$ and $y$ into the measurement. The `ACSim` class stores velocity in the data member `vel`. To perform the Kalman filter update we just need to call `update` with a list containing the slant distance, bearing, and velocity in $x$ and $y$:\n", "\n", - "$$z = [\\mathtt{slant\\_range}, \\text{bearing}, \\dot x, \\dot y]$$\n", + "$$z = [\\mathtt{slant\\_range},\\, \\text{bearing},\\, \\dot x,\\, \\dot y]$$\n", "\n", - "The measurement contains four values so the measurement function also needs to return four values. The slant range and bearing will be computed as before, but we do not need to compute the velocity in $x$ and $y$ as they are provided in the state estimate." + "The measurement contains four values so the measurement function also needs to return four values. The slant range and bearing will be computed as before, and we do not need to compute the velocity in $x$ and $y$ as they are provided by the state estimate." ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1733,35 +1566,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "With that implemented we can implement and execute our filter." + "Now we can implement our filter." ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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z2Q8jJ1tX2Iyw1/o5+8pmhD0mjg1n24npp/XYG6IvDMOofFmeGbSo11xnQzdv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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Velocity std 1.3 m/s\n" - ] - } - ], + "outputs": [], "source": [ "h_radar.radar_pos = (0, 0)\n", "h_vel.radar_pos = (0, 0)\n", @@ -1799,7 +1614,7 @@ "source": [ "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n", "\n", - "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the *Complementary filter*, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates." + "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to the *Complementary filter*, which blends the high update rate inertial velocity measurements with the accurate but slowly updated position estimates of the GPS to produce high rate and accurate position and velocity estimates. The high rate velocity estimates are integrated between the GPS updates to produce accurate and high rate position estimates." ] }, { @@ -1813,30 +1628,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill in the basics if you are interested. In general these systems are beacons that allow you to extract the range and/or bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the *radial* - the direction from the VOR station on the ground to the aircraft. The pilot uses a chart to find the intersection point of the radials, which identifies the location of the aircraft.\n", + "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS, ships and etcand so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill in the basics if you are interested. These systems emit beacons in the form of radio waves. The sensor extracts the range and/or bearing to the beacon from the signal. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the *radial* - the direction from the VOR station on the ground to the aircraft. The pilot uses a chart to find the intersection point of the radials, which identifies the location of the aircraft.\n", "\n", - "That is a very manual approach with low accuracy. We can use a Kalman filter to produce far more accurate position estimates. The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. The width of the circle is proportional to the amount of sensor noise." + "That is a manual approach with low accuracy. A Kalman filter will produce far more accurate position estimates. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. The width of the perimeters are proportional to the $3\\sigma$ of the sensor noise. The aircraft must be positioned somewhere within the intersection of the two perimeters with a high degee of probability." ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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zx0v/5qnoeE3nLLVh7iIkvfQvloyEIIXe0OV1ueDSxY9EJA8m2ERhwOnyYH9F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\nRqPR5/E+vT1+8skn8fTTT3f7uCAI2LJ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CyWSCVqvtfIdfWFiIqKgozJw58/+3d/8gyYRx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\nIiIishEbbCIiIiIiG/0Agp4YykJl5dAAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "ukf_internal.show_two_sensor_bearing()" ] @@ -1845,12 +1649,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can compute the bearing between a sensor and the target as follows:" + "We compute the bearing between a sensor and the target as:" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1865,12 +1669,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The filter receives a vector of 2 measurements during each update, one for each sensor. We can implement that as:" + "The filter receives the measurement from the two sensors in a vector. The code will accept any iterable container, so I use a Python list for efficiency. We can implement that as:" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1886,12 +1690,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "I will assume a constant velocity model for the aircraft. For a change of pace I compute the new positions directly rather than using matrix math:" + "Assume a constant velocity model for the aircraft. For a change of pace I compute the new positions explicitly rather than using matrix-vector multiplication:" ] }, { "cell_type": "code", - "execution_count": 31, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1907,12 +1711,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Next we need to implement the measurement function, which converts the state $\\mathbf x$ to an array containing the measurement to station A and B. I'm not a fan of global variables, but I put the position of the stations in the global variables `sa_pos` and `sb_pos` just to illustrate this technique of using external data in the $h()$ function:" + "Next we need to implement the measurement function, which converts the prior to an array containing the measurement to both stations. I'm not a fan of global variables, but I put the position of the stations in the global variables `sa_pos` and `sb_pos` to demonstrate this method of sharing data with $h()$:" ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": null, "metadata": { "collapsed": true }, @@ -1931,28 +1735,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The rest of the filter consists of boilerplate code to construct the filter, run it, and plot the results:" + "Now we write boilerplate which constructs the filter, runs it, and plots the results:" ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": true }, - "outputs": [ - { - "data": { - "image/png": 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KrVYr6enpFBYWKqyLyLDX19/Hqdoj7Dn9IdUtJbR1tNDe1IXZGu6u8fXxY0Ts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\nnIiIiFw8JQeR/6G3r5e2M00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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "def moving_target_filter(pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = SigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", @@ -2001,30 +1794,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This looks quite good to me. There is a very large error at the beginning of the track, but the filter is able to settle down and start producing good data.\n", + "This looks quite good to me. The beginning of the track exhibits large errors, but the filter settles down and produces good estimates.\n", "\n", "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors at (0,0). This will cause a nonlinearity in the computation of the sigma means and the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of nearly $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "metadata": { "collapsed": false, "scrolled": false }, - "outputs": [ - { - "data": { - "image/png": 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LVkRE5IbQpYCempqK1WolPz+f7Oxs4MLjs3ft2sXzzz8PQHZ2NiaT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\ngszBpA7OINI/iaMHyvnfj/6YnTt3sm7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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "target_pos = [0, 0]\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", @@ -2035,7 +1817,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is unacceptable performance. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter explains how to handle this problem." + "This performance is unacceptable. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter demonstrates its use." ] }, { @@ -2049,12 +1831,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other than a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distribution for a 1° standard deviation in the bearing measurement for a 30° bearing." + "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other than a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. These scatter plots show the error distribution for a 1°$\\sigma$ error for two different bearings." ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 20, "metadata": { "collapsed": false, "scrolled": false @@ -2062,9 +1844,9 @@ "outputs": [ { "data": { - "image/png": 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ndQDFxcWsXbs2te1wOFKv586dy4IFC3jsscfo2rUrM2bM4Ic//CFbtmwhMzPz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\nWbEiQn6+p8GxlmXx8ssRRo6sf1j2iit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mzZvVjkZEFPbYyBMRUYc8Ho+MHTtWGhoaxOPx\niNVqldLSUlEURe1oRERhj408ERF1yul0yrBhw8RkMonD4ZDExES1IxERkXCNPBER+XHlyhUREWlr\na5PKykqV0xAR0S/8Rp6IiDr07NkzGT58uCxYsEBevnwptbW18vTpU+nVq5fa0YiIwh4beSIi+q1f\n6+M/fPggTqdT3r9/L2lpaTJ79mwpKChQOx4RUdjj0hoiIvqt3NxcefjwoZw4cUJ69OghiYmJsm/f\nPrHb7WK329WOR0QU9viNPBERtfPw4UMZN26c2Gw2OXbsmM++qVOnisPhEKfTKdHR0SolJCIiNvJE\nRERERBrEpTVERERERBrERp6IiIiISIPYyBMRERERaRAbeSIiIiIiDWIjT0RERESkQWzkiYiIiIg0\niI08EREREZEGsZEnIiIiItIgNvJERERERBrERp6IiIiISIP+B9Upn/SjtLCMAAAAAElFTkSuQmCC\n", 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8ODpm48YNHhERCly+bLo9y5YpMGOGDozVR/fuKqtaY7GmMalK161KrxUQZ4oX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\nBPQAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2086,7 +1868,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that for even very small angular errors the (x, y) positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer this for the one sensor problem as well as the multiple sensor problem. " + "We can see that for small angular errors the positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer for both the one sensor and multiple sensor problem. " ] }, { @@ -2100,9 +1882,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This is very important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you may need to revisit some of the earlier Kalman filter material in the **Multidimensional Kalman Filter** chapter.\n", + "This is very important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you may need to revisit some of the earlier material in the **Multidimensional Kalman Filter** chapter.\n", "\n", - "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible positions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target to form an intuition." + "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible positions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target." ] }, { @@ -2132,9 +1914,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately 45° line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this type of noise distribution. This graph makes it look easy because we have plotted 100 possible measurements for each position update. This makes the aircraft's movement obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", + "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately 45° line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will take that into account. \n", "\n", - "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose we set the intial position to be 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." + "This graph makes it look easy because we have plotted 100 measurements for each position update. The movement of the aircraft is obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", + "\n", + "Now consider that the bearing gives us no distance information. Suppose we set the initial estimate ti 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." ] }, { @@ -2174,7 +1958,7 @@ "source": [ "In the first plot I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. We can see how the errors in $x$ and $y$ change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the $y$ coordinate of sensor B the shape becomes strongly elliptical.\n", "\n", - "In the second plot the airplane starts very near one sensor, and then flies past the second sensor. The intersections of the errors are very non-orthogonal, and the resulting positions errors become very spread out." + "In the second plot the airplane starts very near one sensor, and then flies past the second sensor. The intersections of the errors are very non-orthogonal, and the resulting position errors become very spread out." ] }, { @@ -2188,9 +1972,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's implement the UKF equations with Python. FilterPy implements this for you, but it is instructive to learn how to go from equations to code. Plus, if you encounter a problem and need to debug your code you will likely need to step through the FilterPy code with the debugger.\n", - "\n", - "Implementing the UKF is quite straightforward. First, let's write the code to compute the mean and covariance given the sigma points. \n", + "FilterPy implements the UKF, but it is instructive to learn how to go translate equations into code. Implementing the UKF is quite straightforward. First, let's write code to compute the mean and covariance of the sigma points. \n", "\n", "We will store the sigma points and weights in matrices, like so:\n", "\n", @@ -2198,20 +1980,57 @@ "\\begin{aligned}\n", "\\text{weights} &= \n", "\\begin{bmatrix}\n", - "w_1&w_2& \\dots & w_{2n+1}\n", + "w_0& w_1 & \\dots & w_{2n}\n", "\\end{bmatrix} \n", "\\\\\n", "\\text{sigmas} &= \n", "\\begin{bmatrix}\n", - "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} & \\mathcal{X}_{0,2} \\\\\n", - "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} & \\mathcal{X}_{1,2} \\\\\n", - "\\vdots & \\vdots & \\vdots \\\\\n", - "\\mathcal{X}_{2n+1,0} & \\mathcal{X}_{2n+1,1} & \\mathcal{X}_{2n+1,2}\n", + "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} & \\dots & \\mathcal{X}_{0,n-1} \\\\\n", + "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} & \\dots & \\mathcal{X}_{1,n-1} \\\\\n", + "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + "\\mathcal{X}_{2n,0} & \\mathcal{X}_{2n,1} & \\dots & \\mathcal{X}_{2n,n-1}\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", - "In other words, each column contains the $2n+1$ sigma points for one dimension in our problem. The $0^{th}$ sigma point is always the mean, so first row of the sigmas is the mean of each of our state variables. The second through nth row contains the $\\mu+\\sqrt{(n+\\lambda)\\Sigma}$ terms, and the $n+1$ to $2n$ rows contains the $\\mu-\\sqrt{(n+\\lambda)\\Sigma}$ terms. The choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code a bit easier to code as I can refer to the ith sigma point for all dimensions as `sigmas[i]`." + "\n", + "That's a lot of subscripts to describe something very simple, so here's an example for a two dimensional problem ($n$=2):" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0. , 0. ],\n", + " [ 0.173, 0.017],\n", + " [ 0. , 0.172],\n", + " [-0.173, -0.017],\n", + " [ 0. , -0.172]])" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "points = SigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n", + "points.sigma_points(x=[0.,0], P=[[1.,.1],[.1, 1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The sigma point for the mean is on the first row. Its position is (0, 0), which is equal to the mean (0,0). The second sigma point is at position (0.173, 0.017), and so on. There are are $2n+1 = 5$ rows, one row per sigma point. If $n=3$, then there would be 3 columns and 7 rows.\n", + "\n", + "The choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code clearer as I can refer to the i$^{th}$ sigma point as `sigmas[i]` instead of `sigmas[:, i]`." ] }, { @@ -2225,7 +2044,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Computing the weights in numpy is extremely simple. Recall that the Van der Merwe scaled sigma point implementation states:\n", + "Computing the weights with NumPy is easy. Recall that the Van der Merwe scaled sigma point implementation states:\n", "\n", "$$\n", "\\begin{aligned}\n", @@ -2236,17 +2055,17 @@ "\\end{aligned}\n", "$$\n", " \n", - "Our code for these is:\n", + "Code for these is:\n", "\n", "```python\n", - "lambda_ = alpha**2 * (n +kappa) - n\n", - "Wc = np.full(2*n + 1, 1. / (2*(n+lambda_))\n", - "Wm = np.full(2*n + 1, 1. / (2*(n+lambda_))\n", + "lambda_ = alpha**2 * (n + kappa) - n\n", + "Wc = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", + "Wm = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", "Wc[0] = lambda_ / (n + lambda_) + (1. - alpha**2 + beta)\n", "Wm[0] = lambda_ / (n + lambda_)\n", "```\n", "\n", - "I use the underscore in `lambda_` because `lambda` is a reserved word in Python. A trailing underscore is the Pythonic workaround" + "I use the underscore in `lambda_` because `lambda` is a reserved word in Python. A trailing underscore is the Pythonic workaround." ] }, { @@ -2272,25 +2091,49 @@ "\n", "The Python is not difficult once we understand the $\\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i$ term.\n", "\n", - "The term $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ is choosing the column vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$.\n", + "The term $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ is choosing the column vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$: if $\\Sigma = SS$ then $S = \\sqrt{\\Sigma}$.\n", + "\n", + "We will choose an alternative definition that has numerical properties which makes it easier easier to compute. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n", "\n", "$$\n", - "\\begin{aligned}\n", - "\\text{if }\\Sigma = SS \\\\\n", - "\\\\\n", - "\\text{then }S = \\sqrt{\\Sigma}\n", - "\\end{aligned}\n", + "\\Sigma = \\mathbf{SS}^\\mathsf T \\\\\n", "$$\n", "\n", - "However there is an alternative definition, and we will chose it because it has numerical properties that makes it much easier for us to compute its value. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n", - "\n", - "$$\n", - "\\Sigma = SS^\\mathsf{T} \\\\\n", - "$$\n", - "\n", - "This method is frequently chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n", - "SciPy provides this with the `scipy.linalg.cholesky()` method. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`.\n", + "This definition is frequently chosen because $\\mathbf S$ is computed using the *Cholesky decomposition* [3]. It decomposes a Hermitian, positive-definite matrix into a lower triangular matrix and its conjugate transpose. $\\mathbf P$ has these properties, so we can treat $\\mathbf S = \\text{cholesky}(\\mathbf P)$ as the square root of $\\mathbf P$.\n", "\n", + "SciPy provides `cholesky()` method in `scipy.linalg`. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 2.005, 0.122],\n", + " [ 0.122, 2.995]])" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import scipy\n", + "a = np.array([[2., .1], [.1, 3]])\n", + "s = scipy.linalg.cholesky(a)\n", + "np.dot(s, s.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "```python\n", "sigmas = np.zeros((2*n+1, n))\n", "U = scipy.linalg.cholesky((n+kappa)*P)\n", @@ -2320,7 +2163,7 @@ "x = np.dot(Wm, sigmas)\n", "```\n", "\n", - "If you are not a heavy user of NumPy this may look foreign to you. NumPy is not just a library that make linear algebra possible; under the hood it is written in C to achieve much faster speeds than Python can reach. A typical speedup is 20x to 100x. To get that speedup we must avoid using for loops, and instead use NumPy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum, we call the built in `numpy.dot(x, y)` method. If passed a 1D array and a 2D array it will compute the sum of inner products:" + "If you are not a heavy user of NumPy this may look foreign to you. NumPy is not just a library that make linear algebra possible; under the hood it is written in C to achieve much faster speeds than Python can reach. A typical speedup is 20x to 100x. To get that speedup we must avoid using for loops, and instead use NumPy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum, we call the built in `numpy.dot(x, y)` method. The dot product of two vectors is the sum of the element-wise multiplications of each element. If passed a 1D array and a 2D array it will compute the sum of inner products:" ] }, { @@ -2364,14 +2207,14 @@ "P += Q\n", "```\n", "\n", - "This introduces another feature of NumPy. The state variable `x` is one dimensional, as is `sigmas[k]`, so the difference `sigmas[k]-X` is also one dimensional. NumPy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $\\mathbf{yy}^\\mathsf{T}$ for a 1D array $\\mathbf{y}$. An alternative implementation could be:\n", + "This introduces another feature of NumPy. The state variable `x` is one dimensional, as is `sigmas[k]`, so the difference `sigmas[k]-X` is also one dimensional. NumPy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $\\mathbf{yy}^\\mathsf{T}$ for the 1D array $\\mathbf{y}$. An alternative implementation could be:\n", "\n", "```python\n", "y = (sigmas[k] - x).reshape(kmax, 1) # convert into 2D array\n", "P += Wc[K] * np.dot(y, y.T)\n", "```\n", "\n", - "However, that code is slower and not idiomatic, and we will not use it." + "This code is slower and not idiomatic, so we will not use it." ] }, { @@ -2413,7 +2256,7 @@ " self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n", "\n", " self.xp, self.Pp = unscented_transform(\n", - " self.sigmas_f, self.W, self.W, self.Q)" + " self.sigmas_f, self.Wm, self.Wc, self.Q)" ] }, { @@ -2427,7 +2270,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The update step converts the sigmas into measurement space via the `h(x)` function.\n", + "The update step converts the sigmas into measurement space via the function `h(x)`.\n", "\n", "\n", "$$\\mathcal{Z} = h(\\mathcal{Y})$$\n", @@ -2469,7 +2312,7 @@ " sigmas_h[i] = self.hx(sigmas_f[i])\n", "\n", " # mean and covariance of prediction passed through UT\n", - " zp, Pz = unscented_transform(sigmas_h, self.W, self.W, self.R)\n", + " zp, Pz = unscented_transform(sigmas_h, self.Wm, self.Wc, self.R)\n", "\n", " # compute cross variance of the state and the measurements\n", " Pxz = np.zeros((self._dim_x, self._dim_z))\n", @@ -2613,10 +2456,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let's assume that we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n", + "Assume that we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n", "\n", - "\n", - "However, if we are collecting data and post-processing it we have measurements after the questionable one that informs us if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a turn was initiated.\n", + "If we are collecting data and post-processing it we have measurements after the questionable one that informs us if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a turn was initiated.\n", "\n", "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `FilterPy`. The algorithm that we have implemented is called an **RTS smoother**, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n", "\n", @@ -2700,7 +2542,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 45, "metadata": { "collapsed": false, "scrolled": false @@ -2711,8 +2553,8 @@ "output_type": "stream", "text": [ "sigmas: [ 0. 3. -3.]\n", - "mean weights: [ 0.6667 0.1667 0.1667]\n", - "cov weights: [ 2.6667 0.1667 0.1667]\n", + "mean weights: [ 0.667 0.167 0.167]\n", + "cov weights: [ 2.667 0.167 0.167]\n", "lambda: 2\n", "sum cov 3.0\n" ] @@ -2734,12 +2576,11 @@ "\\mathcal{X}_i &= \\mu \\pm \\sqrt{(n+\\lambda)\\Sigma}\n", "\\end{aligned}$$\n", "\n", - "Here you will appreciate my choice of $n=1$ as it reduces everything to scalars, allowing us to avoid computing the square root of matrices. So, for our values the equation is\n", + "My choice of $n=1$ reduces everything to scalars, allowing us to avoid computing the square root of matrices. So, for our values the equation is\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= 0 \\\\\n", "\\mathcal{X}_i &= 0 \\pm \\sqrt{(1+2)\\times 3} \\\\\n", - "&= 0 \\pm \\sqrt{9} \\\\\n", "&= \\pm 3\n", "\\end{aligned}$$\n", "\n", @@ -2748,7 +2589,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 46, "metadata": { "collapsed": false, "scrolled": true @@ -2792,7 +2633,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 49, "metadata": { "collapsed": false }, @@ -2801,92 +2642,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "sigmas: [ 0. 0.3606 -0.3606]\n", - "mean weights: [-99. 50. 50.]\n", - "cov weights: [-96.01 50. 50. ]\n", - "lambda: -0.99\n", - "sum cov 3.99\n" + "sigmas: [ 0. 0.004 -0.004]\n", + "mean weights: [-999999. 500000. 500000.]\n", + "cov weights: [-999996. 500000. 500000.]\n", + "lambda: -0.999999\n", + "sum cov 3.99999899999\n" ] } ], "source": [ - "print_sigmas(mean=0, cov=13, alpha=.1, kappa=0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I must admit to not fully understanding this advice. " - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sigmas: [ 0. 0.3 -0.3]\n", - "mean weights: [-32.3333 16.6667 16.6667]\n", - "cov weights: [-29.3433 16.6667 16.6667]\n", - "lambda: -0.97\n", - "sum cov 3.99\n" - ] - } - ], - "source": [ - "print_sigmas(mean=0, cov=3, alpha=.1)" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sigmas: [ 0. 3. -3.]\n", - "mean weights: [ 0.6667 0.1667 0.1667]\n", - "cov weights: [ 2.6667 0.1667 0.1667]\n", - "lambda: 2\n", - "sum cov 3.0\n" - ] - } - ], - "source": [ - "print_sigmas(mean=0, cov=3, alpha=1)" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "sigmas: [ 0. 0.2449 -0.2449]\n", - "mean weights: [-49. 25. 25.]\n", - "cov weights: [-46.01 25. 25. ]\n", - "lambda: -0.98\n", - "sum cov 3.99\n" - ] - } - ], - "source": [ - "print_sigmas(mean=0, cov=3, alpha=.1, beta=2, kappa=1)" + "print_sigmas(mean=0, cov=13, alpha=.001, kappa=0)" ] }, { @@ -2900,11 +2665,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "It is time to try a significant problem. Most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world problem. This example will not teach you how to tackle any problem, but illustrates the type of things you will have to consider as you design and implement a filter. \n", + "It is time to undertake a significant problem. Most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world problem. This example will not teach you how to tackle any problem, but illustrates the type of things you will have to consider as you design and implement a filter. \n", "\n", "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n", "\n", - "Our robot has 4 wheels configured the same as an automobile. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n", + "Our robot has 4 wheels with the same configuration as an automobile. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n", "\n", "The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", "\n", @@ -2963,7 +2728,7 @@ "\n", "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", "\n", - "If we let $\\theta$ be our current orientation then we can compute the position $C$ before the turn starts as\n", + "With $\\theta$ being the robot's orientation we compute the position $C$ before the turn starts as\n", "\n", "$$ C_x = x - R\\sin(\\theta) \\\\\n", "C_y = y + R\\cos(\\theta)\n", @@ -2994,13 +2759,13 @@ "source": [ "### Design the State Variables\n", "\n", - "For our robot we will maintain the position and orientation of the robot:\n", + "For our robot we will maintain the position and orientation:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}x & y & \\theta\\end{bmatrix}^\\mathsf{T}$$\n", "\n", "I could include velocities into this model, but as you will see the math will already be quite challenging.\n", "\n", - "Our control input $\\mathbf{u}$ is the commanded velocity and steering angle\n", + "The control input $\\mathbf{u}$ is the commanded velocity and steering angle\n", "\n", "$$\\mathbf{u} = \\begin{bmatrix}v & \\alpha\\end{bmatrix}^\\mathsf{T}$$" ] @@ -3011,7 +2776,7 @@ "source": [ "### Design the System Model\n", "\n", - "In general we model our system as a nonlinear motion model plus noise.\n", + "We model our system as a nonlinear motion model plus noise.\n", "\n", "$$\\overline x = x + f(x, u) + \\mathcal{N}(0, Q)$$\n", "\n", @@ -3069,7 +2834,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "I will design the UKF so that $\\Delta t$ is small. If the robot is moving slowly then this function should give a reasonably accurate prediction. In general, if $\\Delta t$ is large or your system's dynamics are very nonlinear this method will fail. In those cases you will need to implement this function using a more sophisticated numerical integration technique such as Runge Kutta. Numerical integration is covered briefly in the **Kalman Filter Math** chapter." + "I will design the UKF so that $\\Delta t$ is small. If the robot is moving slowly then this function should give a reasonably accurate prediction. If $\\Delta t$ is large or your system's dynamics are very nonlinear this method will fail. In those cases you will need to implement it using a more sophisticated numerical integration technique such as Runge Kutta. Numerical integration is covered briefly in the **Kalman Filter Math** chapter." ] }, { @@ -3078,7 +2843,7 @@ "source": [ "### Design the Measurement Model\n", "\n", - "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. If $p$ is the position of a landmark, the range $r$ is\n", + "Now we need to design our measurement model. We are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. If $p$ is the position of a landmark, the range $r$ is\n", "\n", "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", "\n", @@ -3096,7 +2861,7 @@ "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n", "\\end{aligned}$$\n", "\n", - "I will not implement this in Python yet as there is a difficulty that will be discussed in the *Implementation* section below." + "I will not implement this yet as there is a difficulty that will be discussed in the *Implementation* section below." ] }, { @@ -3105,7 +2870,7 @@ "source": [ "### Design Measurement Noise\n", "\n", - "This is quite straightforward as we need to specify measurement noise in measurement space, hence it is linear. It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", + "It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", "\n", "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$" ] @@ -3121,12 +2886,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Before we begin coding the main loop we have another issue to handle. The residual is defined as $y = z - h(x)$. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Subtracting them gives $-358^\\circ$. this will throw off the computation of the Kalman gain because the correct angle difference in this case is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." + "Before we begin coding we have another issue to handle. The residual is $y = z - h(x)$. Suppose z has a bearing of $1^\\circ$ and $h(x)$ is $359^\\circ$. Subtracting them gives $-358^\\circ$. This will throw off the computation of the Kalman gain because the correct angular difference is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 50, "metadata": { "collapsed": false }, @@ -3141,7 +2906,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 53, "metadata": { "collapsed": false }, @@ -3155,7 +2920,7 @@ } ], "source": [ - "print(np.rad2deg(normalize_angle(np.deg2rad(1-359))))" + "print(np.degrees(normalize_angle(np.radians(1-359))))" ] }, { @@ -3226,13 +2991,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Our difficulties are not over. The unscented transform computes the average of the state and measurement vectors, but each contains a bearing. There is no unique way to compute the average of a set of angles. For example, what is the average of 359$^\\circ$ and 3$^\\circ$? Intuition suggests the answer should be 1$^\\circ$, but a naive sum/count approach yields 181$^\\circ$.\n", + "Our difficulties are not over. The unscented transform computes the average of the state and measurement vectors, but each contains a bearing. There is no unique way to compute the average of a set of angles. For example, what is the average of 359$^\\circ$ and 3$^\\circ$? Intuition suggests the answer should be 1$^\\circ$, but a naive $\\frac{1}{n}\\sum x$ approach yields 181$^\\circ$.\n", "\n", "One common approach is to take the arctan of the sum of the sins and cosines.\n", "\n", "$$\\bar{\\theta} = atan2\\left(\\frac{\\sum_{i=1}^n \\sin\\theta_i}{n}, \\frac{\\sum_{i=1}^n \\cos\\theta_i}{n}\\right)$$\n", "\n", - "We have not used this feature yet, but the `UnscentedKalmanFilter.__init__()` method has an argument `x_mean_fn` for a function which computes the mean of the state, and `z_mean_fn` for a function which computes the mean of the measurement. We will code these function as:" + "`UnscentedKalmanFilter.__init__()` has an argument `x_mean_fn` for a function which computes the mean of the state, and `z_mean_fn` for a function which computes the mean of the measurement. We will code these function as:" ] }, { @@ -3274,7 +3039,7 @@ "\n", "With that done we are now ready to implement the UKF. I want to point out that when I designed this filter I did not just design all of functions above in one sitting, from scratch. I put together a basic UKF with predefined landmarks, verified it worked, then started filling in the pieces. \"What if I see different landmarks?\" That lead me to change the measurement function to accept an array of landmarks. \"How do I deal with computing the residual of angles?\" This led me to write the angle normalization code. \"What is the *mean* of a set of angles?\" I searched on the internet, found an article on Wikipedia, and implemented that algorithm. Do not be daunted. Design what you can, then ask questions and solve them, one by one.\n", "\n", - "You've seen the UKF implemention already, so I will not describe it in detail. There is one new thing here that is important to discuss. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", + "You've seen the UKF implemention already, so I will not describe it in detail. There is one new thing here. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", "\n", "```python\n", "points = SigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", @@ -3285,7 +3050,7 @@ " residual_x=residual_x, residual_z=residual_h)\n", "```\n", "\n", - "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once per second. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." + "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once per second. We are not using Runge Kutta to integrate the differential equations of motion, so a small time step makes the simulation more accurate." ] }, { @@ -3489,7 +3254,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "You can see that the uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can incorporate error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further away." + "The uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can incorporate more error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further away." ] }, { @@ -3532,13 +3297,13 @@ "source": [ "## Discussion\n", "\n", - "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working because of the need to handle the modular math of angles. On the other hand, if you have implemented an extended Kalman filter (EKF) you are perhaps bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. The EKF for the same problems requires some fairly difficult mathematics. In fact, for many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", + "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working because of the need to handle the modular math of angles. On the other hand, if you have implemented an extended Kalman filter (EKF) perhaps you are bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. The EKF for the same problem requires some fairly difficult mathematics. For many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", "\n", - "However, the advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is often more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", + "The advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is often more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", "\n", - "Hence my recommendation is to always start by implementing the UKF. If your filter has real world consequences if it diverges (people die, lots of money lost, power plant blows up) of course you will have to engage in a lot of sophisticated analysis and experimentation to choose the best filter. That is beyond the scope of this book, and you should be going to graduate school to learn this theory. \n", + "Hence my recommendation is to always start by implementing the UKF. If your filter has real world consequences if it diverges (people die, lots of money lost, power plant blows up) of course you will have to engage in sophisticated analysis and experimentation to choose the best filter. That is beyond the scope of this book, and you should be going to graduate school to learn this theory. \n", "\n", - "I have spoken of the UKF as *the* way to perform sigma point filters. This is not true. The specific version I chose is Julier's scaled unscented filter as parameterized by Van der Merwe in his 2004 dissertation. If you search for Julier, Van der Merwe, Uhlmann, and Wan you will find a family of similar sigma point filters that they developed. Each technique uses a different way of choosing and weighting the sigma points. But the choices don't stop there. For example, the SVD Kalman filter uses singular value decomposition (SVD) to find the approximate mean and covariance of the probability distribution. Think of this chapter as an introduction to the sigma point filters, rather than a definitive treatment of how they work." + "Finally, I have spoken of the UKF as *the* way to perform sigma point filters. This is not true. The specific version I chose is Julier's scaled unscented filter as parameterized by Van der Merwe in his 2004 dissertation. If you search for Julier, Van der Merwe, Uhlmann, and Wan you will find a family of similar sigma point filters that they developed. Each technique uses a different way of choosing and weighting the sigma points. But the choices don't stop there. For example, the SVD Kalman filter uses singular value decomposition (SVD) to find the approximate mean and covariance of the probability distribution. Think of this chapter as an introduction to the sigma point filters, rather than a definitive treatment of how they work." ] }, {