From b9f462678dbe362b28aedbde04df781e7b4e60b1 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 19 Jul 2014 00:14:32 -0700 Subject: [PATCH] Work on EKF chapter. Started developing EKF chapter. Stalled - not sure what is the best initial example to develop. Air drag seems unnecessarily 'mathy', but then you need diff eq to compute Jacobians. --- Extended_Kalman_Filters.ipynb | 147 ++++++++++++++++++++++++++++------ baseball.py | 53 ++++++++++++ ekf_internal.py | 128 +++++++++++++++++++++++++++++ exp/RungeKutta.py | 3 + exp/ball.py | 1 + 5 files changed, 307 insertions(+), 25 deletions(-) create mode 100644 ekf_internal.py diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb index 2521dca..8119b67 100644 --- a/Extended_Kalman_Filters.ipynb +++ b/Extended_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:4ca13721197346f81b4551f2897e3b34983888159a0e887ab7d3fe729999e595" + "signature": "sha256:2703ec2a794449aaabf6044e38967bdacd2cadc551c734b81dfa513e4ae2ea54" }, "nbformat": 3, "nbformat_minor": 0, @@ -41,10 +41,10 @@ " margin-right: auto;\n", " }\n", " div.text_cell code {\n", - " background: #FFFFFF;\n", + " background: transparent;\n", " color: #000000;\n", " font-weight: 600;\n", - " font-size: 13pt;\n", + " font-size: 11pt;\n", " font-style: bold;\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", " }\n", @@ -250,7 +250,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -289,7 +289,22 @@ "\n", "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n", "\n", - "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output." + "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n", + "\n", + "If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "amp(roger) &= amp(roger + 0) \\\\\n", + "&= amp(roger) + amp(0) \\\\\n", + "&= amp(roger) + non\\_zero\\_value\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "which is clearly nonsense. Hence, an apparently linear equation such as\n", + "$$L(f(t)) = f(t) + 1$$\n", + "\n", + "is not linear because $L(0) = 1$! Be careful!" ] }, { @@ -326,9 +341,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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5PlETALDBms3yn/3Zn+ndd9/turdlyxZ9+OGH+vDDD3X+/HlJkud5euONN/TBBx/ovffe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\n/ScXzBcIoyZgAs0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Pzk/Hg9OGsSAWGY/b5C2tZhsee78EAoBNd2TKHYeoF1F7ii0WC7Kzs3HkyBGY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\neVMX/n97dxPSyB2HcfxJ4iS+ZPOym3ZxK12qIii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/vyB7wHPSY8MNSIaj6mprzY5gGVb782eGji6HHvjnAdW0dOp/v3cWBbGHmGPG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\nzcWDIJ6FynqwYiCXlmYjigejmfhjN1mnh2Lw12J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wu6b3zTffRH5+PhoaGpCbm6v4zvPqj9JEpqSsgLLyKikr4Ni8DU1mnCmtbfG1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\nAQDTKp5IqGcoqt7hmCKxuELdw3LZbXLYbWrti6h3OKrRk5f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W/3Z69tlnkZiYiFOnTuGnn36Sfed59UdpIpNTVkBeeeWUFbB93tIaLVLzq5Ca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\nhIQEhIeHAwC8vLwQFxeH+Ph4AFfq+Lp7u+k+qd6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"text": [ - "" + "" ] } ], @@ -412,10 +427,7 @@ "\n", "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n", "\n", - "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the transfer function again, simulating the next step time step of the Kalman filter.\n", - "\n", - "**process function? what is the correct name**\n", - "\n" + "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter." ] }, { @@ -431,9 +443,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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ROYBJA/wwZYAf/rj7Mpp4LQmR7MmuprcreoMBF0rqsCez3FjuoFAAzk6yH9cTkQRY00vA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\nrKzApbIC15TPA4DZ4s5wdjBzegEAxmpvb7c6woRMzSWZm41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O9FKHahsMqGt2a94f00owNbaxPGFIiLtUsYiISCBqpQJ3xgdhTIQX3vhfJg5m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\neeP+a0JRXW+QOgq1gYNeIiISlqj1g1fn6uXlYlq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"text": [ - "" + "" ] } ], @@ -460,8 +472,8 @@ "output_type": "stream", "stream": "stdout", "text": [ - "input mean, variance: 0.0013, 0.9985\n", - "output mean, variance: -0.0293, 2.2394\n" + "input mean, variance: 0.0010, 1.0013\n", + "output mean, variance: -0.0291, 2.2439\n" ] } ], @@ -490,16 +502,16 @@ { "metadata": {}, "output_type": "display_data", - "png": 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hMx29PEySt+eV22lpaULlaS1fWVkZAECv1yMpKQndjYh99mUiHCNXbsv9b8ap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\nTu/AaFS/2duhbJ9bn1hcpOa+UYWCXpXmB0xHA85Y+2BEG3Y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6qacorqrHuwfTkVZcgycn9cJAf55oS/Jj05reF198EXv37kVJSQkmTZqEtWvX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\nAJDx/h+AVqun2wCHdQAAAABJRU5ErkJggg==\n", "text": [ - "" + "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ - "output mean, variance: -0.0019, 2.2466\n" + "output mean, variance: -0.0015, 2.2530\n" ] } ], @@ -509,7 +521,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Although the shapes are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results." + "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results." ] }, { @@ -532,8 +544,8 @@ "output_type": "stream", "stream": "stdout", "text": [ - "linear output mean, variance: -0.1088, 7470.5861\n", - "nonlinear output mean, variance: -2.0348, 26163.5214\n" + "linear output mean, variance: -0.0877, 7491.7787\n", + "nonlinear output mean, variance: -2.0078, 26241.0351\n" ] } ], @@ -545,6 +557,91 @@ "source": [ "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. " ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "The Extended Kalman Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n", + "\n", + "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. \n", + "\n", + "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n", + "\n", + "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: A falling Ball" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import ekf_internal\n", + "ekf_internal.plot_ball()b" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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4L1qE5s03Md9zD6YpU7D0798yaqqvgtFoZMKECfTt25f58+ff6O5ctaysLPR6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\nRohvBdEBNTzWvTcBns5Tj5m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V7Dqawjvr/6v/nzGjEdcrr+AZPVoTVvLycN52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\nBuD15fvJ9ujXIhHo1AnPffdpYtbPPsM8e/YFfU55ymdlJoWwEGVFVbE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pPTHi4uXkujnc\ne2DhIvjqq8mbOVOK4Isg16a+JJ/6knzqp6Ln8kj+Eaatm8ZLq15iypop/OfX//D2urfJcGVoXnfX\nZSeW0PxiSwZZ7uI36DiXM/MZvOoqfD17amL2f/1Ltl4uYVIIi0rjUPYx9t82lLYbV2jigZYtyfvk\nEzhtYXMhhBCVR4Yrg2nrppHpzsRutuO0OLGb7GS4M3hj7Rsc9xwveG2DeAdXVY/CGwjx+cajZ/nU\nC+d+6ilU46ml2Yx79mCdMUPXMYSWtEaICm9j+kYW7fyRK59bRq/lizXngg0bkrtwIepfK6EIIYSo\nfGZsnMHBvIMYlML3B0NqiBpRNbiz6Z0FsRLrFQbsDz+M7b33To0fF0f22rXgLNymIU6R1gghirD6\n0Go+2TKbFi+tLlQEZyXHkjN7thTBQghRiQVCAfbl7CuyCAYwKAZ2Z+0mpIYKYiV5V9gzfrx26+Vj\nx7CeVhgLfUkhHCYqem9WSQiGgnyz6zuuevcwt32/QHMuO87JpGd6sMWSVUazqzjk2tSX5FNfkk/9\nVNRceoNegmrwrK8JqAECoYAmdqm9wsXlU01IwDNypCZmmzIF8vMveAxxblIIiwprc/o26s44wJCF\nszTxHKeVd56/HXdKIr8c/KWMZieEEKI8sJvsWIyWs7/GbMds0LY/lORdYe+oUaintUIYMjKwTp+u\n6xjiBCmEw0RlX8T8QgVCKjtenMPo2R9q4u4IK9P/PYD06nEoioI36C2jGVYccm3qS/KpL8mnfipq\nLg2KgcZxjfEFi16dwRv00jSuKUoR6/leyl3hs+VTjY3FM2KEJmZ7/XVwuS5oDHFuUgiLCicYUvnm\nube5e8armrjPamb6xFs5WLcacOIBCKdZHj4QQojKrkedHkRbo/EEPJq4N+gl1h7LjbVvLPJ9JXpX\nePRoba9wejrW99/XdQwhhXDYqKi9WXoLqSoLJ/2PgZOfxKCeWhAlYDLy/tN92NskpWBfclfARaca\nncpqqhWGXJv6knzqS/Kpn4qcS6vJyqjWo2iX2g6z0UxQDWIxWuiQ0oGRLUdiNha/KsTF3hU+Vz7V\nuDi8w4drYrbXXgO3+7zHEOcm+8iKCkNVVeZPncOgF8ZhCp168CFoUPhwws382bpWQczld9EmsQ01\nomqUwUyFEEKUNxajha61utK1VldNPBAK8OuhX9mSsQUVlXox9bgq+aqCvuKTd4VX7c9h9qZ07rki\nWbc5ee67D+s776D81RJhOHIE68yZeO+9V7cxKjtZR1hUCKqqMm/G19z+2AgifKd+W1YVhUOTX+Cz\n1hbSctIIqkFirDG0S2nHZdUuK7LnSwghhAA47jnO2+vfJt+Xj8PsAMAT8GAymBjabCipUakAbDua\nzwPz/8BuNvDB7U2Jsul3n9H+9NMnVo34Sygpiew1a8Bm022MiuBi1xGWO8Ii7Kmqyhef/kC/J0dp\nimAA18svY79zKIPLaG5CCCHCk6qqTN84nWAoWFAEA9hMNlRVZcamGTx61aOYjWYaJUTQJjWS1Wm5\nzN2czpDLk3Sbh+f++7G++y7KXy0RhkOHsH74YaG2CXFxpEc4TFTk3qxLNX/hr/QaP4Jod64m7po4\nEd/QoYVeL7nUl+RTX5JPfUk+9VPZcvnn8T857j5e5EYbiqLgD/lZfXh1QeyOVokAzNucTp43UOg9\nZzrffKoJCXiHDdPEbK++Cl5Z9UgPUgiLsPbFdxvp8ve7ics7rom7H3kE75gxZTQrIYQQ4W5TxibN\nneAz2U12/sz6s+C4aaKTlklO8n1B5m3J0HUunjFjUE9rhTAcPIjlf//TdYzKSgrhMFFR12+8FPNX\n7KD9mKGkZB7SxD333otnwoRi3ye51JfkU1+ST31JPvVT2XJpVIyabZXPpKoqCtrnTO5sfeKu8NxN\nR3H5zr5b3YXkU61WDe8Z33DaJ02Su8I6kEJYhKUvf99Hy/vvof7h3Zq4d8AA3M89B/IQnBBCiEtw\nZfKVuAPFL1XmCrhoXa21JtYiyUmzahHkeoMs2KrzXeEHHkC1WguODQcOYPn4Y13HqIykEA4Tla03\n62y+2XyYWvffS6s9mzRxX7duuCZPBsPZL2vJpb4kn/qSfOpL8qmfypbLxIhEakXXKnLHuWAoSKwt\nlsZxjTVxRVG446+7wp9vPIrbX/xd4QvNp5qYiHfIEE3M9uqr4L+wHe2ElhTCIqx890cGMQ+MocO2\nVZq4v21b8t97D8zFL3ouhBBCXIi7mt5FamQqef48/CE/gVCAPH8e0bZoRrQcUeSDdJelRNIo3kG2\nJ8CX247pOh/PAw+gWiwFx8Z9+7DMmaPrGJWNrCMsyrUcbw7L0paR7cvmeE4K9Z57n9uXzdW8JtCs\nGXkLFqBGR5fRLIUQQlRk6a501hxeQ0gN0TK+JSlRKWd9/ap92Ty1aBexdhPv394Uq0m/+46OceOw\nTp9ecBxs0ICcFSvO+W1oRSfrCIsKRVVVvtr1FasOrsJsMJOVn8yV0+cVKoKDtWuT99lnUgQLIYQo\nMfGOeG6sc+N5v/7K6lHUi7Pz5zE3X28/Ru+m8brNxfPAA1hmzkQJnmi7MP7xB+Yvv8R/8826jVGZ\nVO5fH8JIZevNWnFgBb8e/BWH2UGOK4kGs/Yz8tsZmteEqlUjb/Zs1GrVLuizK1suS5rkU1+ST31J\nPvUjuTx/p/cKz1p/BF+w8OoTF5vPUM2a+G69VROzvfIKqCXyBX+FJ4WwKHdUVWXFgRXYzXayXTEk\nLMhm/NzXNa/xRNjI+/xzQrVqlc0khRBCiLNoWzOaOrE2Mlx+vt2uc6/wgw9qjk3r12P6/ntdx6gs\npEdYlDvZ3mxe+vUlCCZg+MbMy+8+jTl4apcen9XEtIl9uWPEmyiyTJoQQohywB1wszxtOWm5aRgV\nI5clXsaxnCSe/X4vcQ4zM25romuvcMTgwVgWLiw49rdtS96XX+r2+eFGeoRFheLx2zAsdfLqjCc0\nRXDQaODDx29hd7OzP6gghBBClJbtmdv5ZOsnoILVZEVVVf44/gdxtqrUju3C7kwvX27LoG+zBN3G\n9Pz975pC2LxyJaaVKwm0bavbGJWBtEaEiUrVm6U68K+pxYvvPIPD59GcmvVQd7a1qUOCI+Gi7wZX\nqlyWAsmnviSf+pJ86kdyWbRcXy4fb/kYq9GK1XRiwwtFUYgwR5DnzyUlbjMAn6w7ollX+FLzGWzd\nGn/nzpqY7ZVXLukzKyMphEW54g2EeP3jFbw4dSIxrlzNuS/uvZ51nZviDrrpXKNzMZ8ghBBClJ6f\n9v1U5HrCACaDCZ+ygXpxFrI8AeZv0Xm3uXHjNMfm777DuH69rmNUdFIIh4nKsMd7MKTy2ry1PPDv\nMVTL1v5l8d2AtvzQsxnugJtutbrRILbBRY9TGXJZmiSf+pJ86kvyqR/JZdHSctOwGC3FnjcZjLSt\nc+LGzqwNR8j3nbgrrEc+A23bErjqKk1M7gpfGCmERbmgqipvLt7GnRPvo2ZGmubc9r6d2Tp6IG1T\n2jL+qvG0T21fRrMUQgghznCOLr2QGqJBvIHmiU5yvUHmbjqq49gK7oce0oTMCxdi2L5dvzEquHMW\nwi+88ALt27fn5tMWav7qq6/o1q0b3bp144cffijRCYoTKnpv1ocr93DjU/fT5MAfmrivd28Sps3i\njmZ30rVWVyLMEZc8VkXPZWmTfOpL8qkvyad+JJdFaxTbCG/QW+x5g8FA06pNGHJ5EgCfbzxKjieg\nWz4DN9xAoHnzgmNFVbFNnqzLZ1cG5yyEu3btyrRp0wqOfT4fL7/8Mh9//DEzZszg+eefL9EJiopv\nwcbDNJswliv+XKuJ+6+9lvy33gKjsYxmJoQQQpxd2+S2mA1m1CI2tPAGvTSJa4LT4qRFkpPLUiJx\n+UPM3qjvXWHP3/+uCVk++wzDvn36jVGBnbMQbt26NTExMQXHGzZsoH79+sTGxpKUlERiYiLbtm0r\n0UmKitub9fPOTKIeeZjrNi3VxAOXXUbezJlgKb7v6mJV1FyWFcmnviSf+pJ86kdyWTSrycqIFiMw\nG83k+/IJqSH8QT8uv4v6VerTr0G/gteevCs8d3M6TS+/qriPvGD+m28mWL9+wbESDGJ9/fWzvEOc\ndME9wunp6cTHx/PJJ5/w9ddfEx8fz9GjOv5mIyqNdQdzyXr0aXr/+pUmHmzQgLxZs8DpLKOZCSGE\nEOcvPiKecVeMY3CzwTSr2oyrUq5i3JXjGNRkEEbDqW81GydEcFX1KDyBELPWH9FvAkZjod3mrB9+\niHJExzEqqIt+WG7AgAF0794dQHb3KgXh2pt1zHWMZWnLWHlgJTnenIL4zmMufn/mVYZ8/5Hm9cHU\nVHJnz0aNjS2xOYVrLssryae+JJ/6knzqR3J5doqiUD+2Pr3q96Jrra5EW6OLfN3Ju8JfbD7KsXy/\nbuP7+vcnmJp6aj5eL7Y339Tt8yuqC95ZLiEhgfT09ILjk3eIizJ69Ghq1KgBQHR0NM2bNy/4auXk\nHyg5Pr/jjRs3lqv5nOv4u5+/Y8mxJZirmjEoBvan7QfghhY30DHlFmb/33Sena1t5vdGReGZPRs1\nJaXM5y/HcizHcizH2uOTyst8wvX48LbfaRxpZWuuiY/XH6ZVaK9un+8dMwbHo49ykvW99/jx6qvx\nO53l5ufX83pctmwZ+/7qhR4+fDgXQ9m+fXvh7u4zpKWlMWrUKBYsWIDP56N79+589tlneL1ehgwZ\nwqJFiwq9Z//+/Vx22WUXNSkR3lRVZcrvU8j2ZmMymDTn8r0QXJbMK69NwO4/tWuc6nCQO38+Qblm\nhBBCVHB7jru5d/Y2jAaFD25vSlyEWZ8PdrmIbtUKQ8aptfjdjz+O5+GH9fn8cuz3338cn0R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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can artifically force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n", + "\n", + "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n", + "\n", + "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n", + "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n", + "$$\n", + "\n", + "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n", + "\n", + "\n", + "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n", + "\n", + "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] } ], "metadata": {} diff --git a/baseball.py b/baseball.py index 7ae0e67..39e494f 100644 --- a/baseball.py +++ b/baseball.py @@ -19,6 +19,59 @@ import matplotlib.pyplot as plt from numpy.random import randn import numpy as np + +class BaseballPath(object): + def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): + """ Create baseball path object in 2D (y=height above ground) + + x0,y0 initial position + launch_angle_deg angle ball is travelling respective to ground plane + velocity_ms speeed of ball in meters/second + noise amount of noise to add to each reported position in (x,y) + """ + + omega = radians(launch_angle_deg) + self.v_x = velocity_ms * cos(omega) + self.v_y = velocity_ms * sin(omega) + + self.x = x0 + self.y = y0 + + self.noise = noise + + + def drag_force (self, velocity): + """ Returns the force on a baseball due to air drag at + the specified velocity. Units are SI + """ + B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.)) + return B_m * velocity + + + def update(self, dt, vel_wind=0.): + """ compute the ball position based on the specified time step and + wind velocity. Returns (x,y) position tuple. + """ + + # Euler equations for x and y + self.x += self.v_x*dt + self.y += self.v_y*dt + + # force due to air drag + v_x_wind = self.v_x - vel_wind + + v = sqrt (v_x_wind**2 + self.v_y**2) + F = self.drag_force(v) + + # Euler's equations for velocity + self.v_x = self.v_x - F*v_x_wind*dt + self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt + + return (self.x + random.randn()*self.noise[0], + self.y + random.randn()*self.noise[1]) + + + def a_drag (vel, altitude): """ returns the drag coefficient of a baseball at a given velocity (m/s) and altitude (m). diff --git a/ekf_internal.py b/ekf_internal.py new file mode 100644 index 0000000..2608a2c --- /dev/null +++ b/ekf_internal.py @@ -0,0 +1,128 @@ +# -*- coding: utf-8 -*- +""" +Created on Fri Jul 18 23:23:08 2014 + +@author: rlabbe +""" +from math import radians, sin, cos, sqrt, exp +import numpy.random as random +import matplotlib.pyplot as plt +import filterpy.kalman as kf +import numpy as np + +def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.02): + + g = 9.8 # gravitational constant + f1 = kf.KalmanFilter(dim_x=5, dim_z=2) + + ay = .5*dt**2 + f1.F = np.array ([[1, dt, 0, 0, 0], # x = x0+dx*dt + [0, 1, 0, 0, 0], # dx = dx + [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2 + [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt + [0, 0, 0, 0, 1]]) # ddy = -g. + + f1.H = np.array([ + [1, 0, 0, 0, 0], + [0, 0, 1, 0, 0]]) + + f1.R *= r + f1.Q *= q + + omega = radians(omega) + vx = cos(omega) * v0 + vy = sin(omega) * v0 + + f1.x = np.array([[x,vx,y,vy,-9.8]]).T + + return f1 + + +class BaseballPath(object): + def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): + """ Create baseball path object in 2D (y=height above ground) + + x0,y0 initial position + launch_angle_deg angle ball is travelling respective to ground plane + velocity_ms speeed of ball in meters/second + noise amount of noise to add to each reported position in (x,y) + """ + + omega = radians(launch_angle_deg) + self.v_x = velocity_ms * cos(omega) + self.v_y = velocity_ms * sin(omega) + + self.x = x0 + self.y = y0 + + self.noise = noise + + + def drag_force (self, velocity): + """ Returns the force on a baseball due to air drag at + the specified velocity. Units are SI + """ + B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.)) + return B_m * velocity + + + def update(self, dt, vel_wind=0.): + """ compute the ball position based on the specified time step and + wind velocity. Returns (x,y) position tuple. + """ + + # Euler equations for x and y + self.x += self.v_x*dt + self.y += self.v_y*dt + + # force due to air drag + v_x_wind = self.v_x - vel_wind + + v = sqrt (v_x_wind**2 + self.v_y**2) + F = self.drag_force(v) + + # Euler's equations for velocity + self.v_x = self.v_x - F*v_x_wind*dt + self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt + + return (self.x + random.randn()*self.noise[0], + self.y + random.randn()*self.noise[1]) + + + +def plot_ball(): + y = 1. + x = 0. + theta = 35. # launch angle + v0 = 50. + dt = 1/10. # time step + + ball = BaseballPath(x0=x, y0=y, launch_angle_deg=theta, velocity_ms=v0, noise=[.3,.3]) + f1 = ball_kf(x,y,theta,v0,dt,r=1.) + f2 = ball_kf(x,y,theta,v0,dt,r=10.) + t = 0 + xs = [] + ys = [] + xs2 = [] + ys2 = [] + + while f1.x[2,0] > 0: + t += dt + x,y = ball.update(dt) + z = np.mat([[x,y]]).T + + f1.update(z) + f2.update(z) + xs.append(f1.x[0,0]) + ys.append(f1.x[2,0]) + xs2.append(f2.x[0,0]) + ys2.append(f2.x[2,0]) + f1.predict() + f2.predict() + + p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5) + + p2, = plt.plot (xs, ys,lw=2) + p3, = plt.plot (xs2, ys2,lw=4, c='r') + plt.legend([p1,p2, p3], ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)']) + plt.show() \ No newline at end of file diff --git a/exp/RungeKutta.py b/exp/RungeKutta.py index 2e1b937..2196634 100644 --- a/exp/RungeKutta.py +++ b/exp/RungeKutta.py @@ -50,6 +50,9 @@ def rk4(y, x, dx, f): return y + (k1 + 2*k2 + 2*k3 + k4) / 6 +def rk2 (y,x,dx,f): + """computes the 2nd order Runge-kutta for dy/dx""" + diff --git a/exp/ball.py b/exp/ball.py index c685c0c..cbb9d65 100644 --- a/exp/ball.py +++ b/exp/ball.py @@ -156,6 +156,7 @@ class BaseballPath(object): # force due to air drag v_x_wind = self.v_x - vel_wind + v = sqrt (v_x_wind**2 + self.v_y**2) F = self.drag_force(v)