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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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      "Smoothing"
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      "#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",
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     "source": [
      "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"
     ]
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      "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()"
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DAA0AAGADDBBaBwEaAADA4hggtBYCNAAAgMUxQGgtBGgAAACLY4DQWgjQAAAAFscAobV4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f37de3d54e0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "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": 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JkydXfBwfH6+EhIRqlAgA8FTzVu1USalNcV0j1ayGIbjckzfHa+GaXVr/x0E9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\nhMjSH1GRv7hyGLV/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f37c155d208>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "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": 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JEv8PGBen1NRUpaWlKS0tTc8++2zwqwcA+M2o4EZqT3SGY4BSkhPV2NKu+qY2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\niBANAAAABIgQDQAAAASIEA0AAAAE6P8D1PjMlQOhEYsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f37c14ba5f8>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Types of Smoothers"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "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. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Point Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "not done"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Lag Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "not done"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fixed Interval Smoothing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "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. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future.\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",
      "$$\\begin{aligned}\n",
      "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F} \\hspace{2 mm}\\mathbf{P}^{-1} \\\\\n",
      "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{x+1} - \\mathbf{FX}_k) \\\\\n",
      "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{K+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n",
      "\\end{aligned}$$\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\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., 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 = 10.                     # 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 = fk.rts_smoother(mu, cov)\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], 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": 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/6y42Kwq29nZUsxnHCNQFO5csYfuePayIisLU1gbcfI9jTe3tmC9cQL0S5vTI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\n9bv116Hi//7fvycubjE7d6qUltr46U/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tvg/MlxiNqFFRyGVl/ZsZt9sxnT9Pw9e/3n/7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\n/51KZpSFEEIIIarh9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       "text": [
        "<matplotlib.figure.Figure at 0x7f37c1286320>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I've injected a lot of noise into the signal to allow you to visually distinguish 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": 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gLiKOuMpxxEXGUSe0js/mY96/n8DPP8dx6604m3kDdlRMjMKv+NSvhmGLxcKU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       "text": [
        "<matplotlib.figure.Figure at 0x7f37ba2b7080>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[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"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}