diff --git a/14_Smoothing/14_Smoothing.ipynb b/14_Smoothing/14_Smoothing.ipynb new file mode 100644 index 0000000..3275210 --- /dev/null +++ b/14_Smoothing/14_Smoothing.ipynb @@ -0,0 +1,567 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:cf4e23aa02553cbdae69dbb8733e9b49216155470a73689c07a24c4574923bc9" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" + ] + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Smoothing" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", + "import sys\n", + "sys.path.insert(0,'../code') # allow us to format the book\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 2, + "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "It has probably struck you by now that the performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement is far from the current track, like so (I'll only consider 1 dimension for simplicity):\n", + "\n", + " 10.1 10.2 9.8 10.1 10.2 10.3 10.1 9.9 10.2 10.0 9.9 12.4" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, 10.1, 9.9, 10.2, 10.0, 9.9, 12.4]\n", + "plt.plot(data)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAtAAAAF2CAYAAABH+q/yAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\noAAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After a long period of near steady state, we have a very large change. Assume that change is larger than the aircraft's manuevering envelope. Nonetheless the Kalman filter incorporates that new measurement into the filter based on the current Kalman gain. It cannot reject the noise because the measurement could reflect the initiation of a turn. Granted it is unlikely that we are turning so abruptly, but it is impossible to say whether \n", + " \n", + "* The aircraft started a turn awhile ago, but the previous measurements were noisy and didn't show the change.\n", + " \n", + "* The aircraft is turning, and this measurement is very noisy\n", + " \n", + "* The measurement is very noisy and the aircraft has not turned\n", + "\n", + "\n", + "Now, suppose the following measurements are:\n", + "\n", + " 11.3 12.1 13.3 13.9 14.5 15.2\n", + " " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n", + "plt.plot(data+data2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsIAAAF2CAYAAABkof4nAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMSVqhAkhhBBCiClRI0wIIYQQQkzpH3j7nVHWDNJTAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " \n", + "Given these future measurements we can infer that yes, the aircraft initiated a turn. \n", + "\n", + "On the other hand, suppose these are the following measurements.\n", + "\n", + " 9.8 10.2 9.9 10.1 10.0 10.3 9.9 10.1\n", + " \n", + "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n", + "plt.plot(data+data3)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAtEAAAF2CAYAAACoOMTMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since this type of smoothing requires knowing data from \"the future\", there are some applications for the Kalman filter where these observations are not helpful. For example, if we are using a Kalman filter as our navigation filter for an aircraft we have little interest in where we have been. While we could use a smoother to create a smooth history for the plane, we probably are not interested in it. However if we can afford a bit of latency some smoothers only require a few measurements into the future prode better results. And, of course any problem where we can batch collect the data and then run the Kalman filter on the data will be able to take maximum advantage of this type of algorithm.\n", + "\n", + "## Types of Smoothers\n", + "\n", + "There are three broad classes of Kalman smoothers that produce better tracking in these situations.\n", + "\n", + "* Fixed Point Smoothing\n", + "\n", + "Fixed point smoothers start out as a normal Kalman filter. But once they get to measurement 4 (say) it then looks backwards and revises the filter output for the previous measurement(s). So, at step 5 the filter will produce a result for 5, and update the result for measurement 4 taking measurement 5 into account. When measurement 6 comes in the filter produces the result for 6, and then goes back and revises 4 using the measurements from 5 and 6. It will revise the output for measurement 5 as well. This process continues, with all previous outputs being revised each time a new input comes in.\n", + "\n", + "* Fixed Lag Smoothing\n", + "\n", + "Fixed lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will injest the first 3 measurements but not ouput a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurments 1 through 4 into account. When the 5th measurment comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account.\n", + "\n", + "\n", + "* Fixed Interval Smoothing\n", + "\n", + "This is a batch processing based filter. It requires all measurements for the track before it attempts to filter the data. Having the full history and future of the data allows it to find the optimal answer, at the cost of not being able to run in real time. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", + "\n", + "\n", + "The choice of these filters depends on your needs and how much memory and processing time you can spare. Fixed point smoothing requires storage of all measurements, and is very costly to compute because the output is for every time step is recomputed for every measurement. On the other hand, the filter does produce a decent output for the current measurement, so this filter can be used for real time applications.\n", + "\n", + "Fixed lag smoothing only requires you to store a window of data, and processing requirements are modest because only that window is processed for each new measurement. The drawback is that the filter's output always lags the input, and the smoothing is not as pronounced as is possible with fixed interval smoothing.\n", + "\n", + "Fixed interval smoothing produces the most smoothed output at the cost of having to be batch processed. Most algorithms use some sort of forwards/backwards algorithm that is only twice as slow as a recursive Kalamn filter. \n", + "\n", + "## Fixed Point Smoothing\n", + "\n", + "not done\n", + "\n", + "## Fixed Lag Smoothing\n", + "\n", + "not done" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fixed Interval Smoothing\n", + "\n", + "There are several fixed lag smoothers available in the literature. I have chosen to implement the smoother invented by Rauch, Tung, and Striebel because of its ease of implementation and efficiency of computation. This smoother is commonly known as an RTS smoother, and that is what we will call it\n", + "\n", + "Derivation of the RTS smoother runs to several pages of densely packed math, and to be honest I have never read it through. I'm certainly not going to inflict it on you. I don't think anyone but thesis writers really need to understand the derivation. Instead I will briefly present the algorithm, equations, and then move directly to implementation and demonstration of the smoother.\n", + "\n", + "The RTS smoother works by first running the Kalman filter in a batch mode, computing the filter output for each step. Given the filter output for each measurement along with the covariance matrix corresponding to each output the RTS runs over the data backwards, incorporating it's knowledge of the future into the past measurements. When it reaches the first measurement it is done, and the filtered output incorporates all of the information in a maximally optimal form.\n", + "\n", + "The equations for the RTS smoother are very straightforward and easy to implement.\n", + "\n", + " Predict Step\n", + "$$\\begin{aligned}\n", + "\\mathbf{P}^- &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n", + "\\end{aligned}$$\n", + "\n", + " Update Step\n", + "$$\\begin{aligned}\n", + "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F} \\hspace{2 mm}inv(\\mathbf{P}^-) \\\\\n", + "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{x+1} - \\mathbf{FX}_k) \\\\\n", + "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{K+1} - \\mathbf{P}^-)\\mathbf{K}_k^\\mathsf{T}\n", + "\\end{aligned}$$\n", + "\n", + "As always, the hardest part of the implementation is correctly accounting for the subscripts. A basic implementation without comments or error checking would be:\n", + "\n", + " def rts_smoother(Xs, Ps, F, Q):\n", + " n, dim_x, _ = Xs.shape\n", + " \n", + " # smoother gain\n", + " K = zeros((n,dim_x, dim_x))\n", + " x, P = Xs.copy(), Ps.copy()\n", + "\n", + " for k in range(n-2,-1,-1):\n", + " P_pred = dot(F, P[k]).dot(F.T) + Q\n", + "\n", + " K[k] = dot(P[k], F.T).dot(inv(P_pred))\n", + " x[k] += dot(K[k], x[k+1] - dot(F, x[k]))\n", + " P[k] += dot(K[k], P[k+1] - P_pred).dot(K[k].T)\n", + " return (x, P, K)\n", + " \n", + "This implementation mirrors the implementation provided in FilterPy. It assumes that the Kalman filter is being run externally in batch mode, and the results of the state and covariances are passed in via the `Xs` and `Ps` variable.\n", + "\n", + "Let's just look at an example. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "from numpy import random\n", + "import matplotlib.pyplot as plt\n", + "from filterpy.kalman import KalmanFilter, rts_smoother\n", + "\n", + "def plot_rts(noise):\n", + " random.seed(123)\n", + " fk = KalmanFilter(dim_x=2, dim_z=1)\n", + "\n", + " fk.x = np.array([[0.],\n", + " [1.]]) # initial state (location and velocity)\n", + "\n", + " fk.F = np.array([[1.,1.],\n", + " [0.,1.]]) # state transition matrix\n", + "\n", + " fk.H = [[1.,0.]] # Measurement function\n", + " fk.P = .01 # covariance matrix\n", + " fk.R = noise # state uncertainty\n", + " fk.Q = 0.001 # process uncertainty\n", + "\n", + " # create noisy data\n", + " zs = [t + random.randn()*noise for t in range (40)]\n", + "\n", + " # filter data with Kalman filter, than run smoother on it\n", + " mu, cov, _, _ = fk.batch_filter (zs)\n", + " M,P,C = rts_smoother(mu, cov, fk.F, fk.Q)\n", + "\n", + " # plot data\n", + " plt.plot(zs,'r', marker='o', linewidth=1, alpha=0.5, label='measurement')\n", + " plt.plot (M[:,0], c='b', label='RTS')\n", + " plt.plot (mu[:,0,0], c='g', linestyle='--',label='KF output')\n", + " plt.plot ([0,len(zs)],[0,len(zs)], 'k', linewidth=1, label='ideal') \n", + " plt.legend(loc=4)\n", + "\n", + " plt.show()\n", + " \n", + "plot_rts(7.)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsoAAAF2CAYAAAB3dr7TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA9j2YKvvTSH+AAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I've injected a lot of noise into the signal to allow you to visually distinguis the RTS output from the ideal output. In the graph above we can see that the Kalman filter, drawn as the green dotted line, is reasonably smooth compared to the input, but it still wanders from from the ideal line when several measurements in a row are biased towards one side of the line. In contrast, the RTS output is both extremely smooth and very close to the ideal output.\n", + "\n", + "With a perhaps more reasonable amount of noise we can see that the RTS output nearly lies on the ideal output. The Kalman filter output, while much better, still varies by a far greater amount." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_rts(noise=1.)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsMAAAF2CAYAAACLY5UZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6/9OVLodFGqNEAAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n", + "\n", + "http://arc.aiaa.org/doi/abs/10.2514/3.3166\n" + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/README.md b/README.md index c2931c2..2ec117b 100644 --- a/README.md +++ b/README.md @@ -146,7 +146,7 @@ EKF and UKF are linear approximations of nonlinear problems. Unless programmed c * [**Chapter 13: Numerical Stability**](not implemented) -* [**Chapter 14: Smoothing**](not implemented) +* [**Chapter 14: Smoothing**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/14_Smoothing/14_Smoothing.ipynb) Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches. diff --git a/table_of_contents.ipynb b/table_of_contents.ipynb index d19ad95..dbde96f 100644 --- a/table_of_contents.ipynb +++ b/table_of_contents.ipynb @@ -97,11 +97,10 @@ "\n", "*This chapter is not started. I'm likely to rearrange where this material goes - this is just a placeholder.*\n", "\n", - "[**Chapter 14: Smoothing**](not implemented)\n", + "[**Chapter 14: Smoothing**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/14_Smoothing/14_Smoothing.ipynb)\n", " \n", "Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches.\n", - " \n", - "*Not implemented. The filterpy library does contain some smothers, however.*\n", + " \n", " \n", "[**Chapter 15: Particle Filters**](not implemented)\n", " \n",