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   "source": [
    "[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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   "metadata": {},
   "source": [
    "# Smoothing"
   ]
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  {
   "cell_type": "code",
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   ],
   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function\n",
    "from book_format import load_style\n",
    "load_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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 deviates far from the current track, like so (I'll only consider 1 dimension for simplicity):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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Jt51Dnk9EpKF+aYuqZUeOpKAgItJCna8jEYC/tzvDQv0YFurP8LAALgpuj9nU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\n72O64mE28uePd7BszxEqFm3jX7cNdpm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gSaNHj9YTTzyhffv2dXdMiKLQ65w4cUJjxowx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134caa11160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, \n",
    "        10.1, 9.9, 10.2, 10.0, 9.9, 11.4]\n",
    "plt.plot(data)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('position');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After a period of near steady state, we have a very large change. Assume the change is past the limit of the aircraft's flight 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",
    "* The aircraft is turning in the opposite direction, and the measurement is extremely noisy\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",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RFPHl8Uqs/iIfdc2tkMsE/HZaEn4/Ywh8FRxNp64xrBMRERE5UbVWj6c2ncD2ggsAgJTo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\nIiIiIiKVYrFORERERKRSfwGsT23e21CaAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134ca9fae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n",
    "plt.plot(data + data2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hLL8hIulhUk9ERLJlsYjIaiyDcXTnG5vYxg2o2KueiKSEST0REclWYVU99EYLPJQKRAZp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134cae162b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n",
    "plt.plot(data + data3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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": "markdown",
   "metadata": {},
   "source": [
    "## An Overview of How Smoothers Work\n",
    "\n",
    "The Kalman filter is a *recursive* filter with the Markov property - it's estimate at step `k` is  based only on the estimate from step `k-1` and the measurement at step `k`. But this means that the estimate from step `k-1` is based on step `k-2`, and so on back to the first epoch. Hence, the estimate at step `k` depends on all of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n",
    "\n",
    "Smoothing filters incorporate future measurements into the estimate for step `k`. The measurement from `k+1` will have the most effect, `k+2` will have less effect, `k+3` less yet, and so on. \n",
    "\n",
    "This topic is called *smoothing*, but I think that is a misleading name. I could smooth the data above by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types of Smoothers\n",
    "\n",
    "There are three classes of Kalman smoothers that produce better tracking in these situations.\n",
    "\n",
    "* Fixed-Interval Smoothing\n",
    "\n",
    "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed-interval smoother will collect all the data, then estimate the state at each measurement using all available previous and future measurements. 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",
    "* Fixed-Lag Smoothing\n",
    "\n",
    "Fixed-lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will ingest the first 3 measurements but not output a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurements 1 through 4 into account. When the 5th measurement comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account. This is useful when you need recent data but can afford a bit of lag. For example, perhaps you are using machine vision to monitor a manufacturing process. If you can afford a few seconds delay in the estimate a fixed-lag smoother will allow you to produce very accurate and smooth results.\n",
    "\n",
    "\n",
    "* Fixed-Point Smoothing\n",
    "\n",
    "A fixed-point filter operates as a normal Kalman filter, but also produces an estimate for the state at some fixed time $j$.  Before the time $k$ reaches $j$ the filter operates as a normal filter. Once $k>j$ the filter estimates $x_k$ and then also updates its estimate for $x_j$ using all of the measurements between $j\\dots k$. This can be useful to estimate initial paramters for a system, or for producing the best estimate for an event that happened at a specific time. For example, you may have a robot that took a photograph at time $j$. You can use a fixed-point smoother to get the best possible pose information for the camera at time $j$ as the robot continues moving.\n",
    "\n",
    "## Choice of Filters\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 Kalman filter. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-Interval Smoothing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many 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. It is also the smoother I have seen used most often in real applications. This smoother is commonly known as an RTS smoother.\n",
    "\n",
    "Derivation of the RTS smoother runs to several pages of densely packed math. I'm not going to inflict it on you. 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 its 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. Here is it very important to distinguish between past, present, and future so I have used subscripts to denote whether the data is from the future or not.\n",
    "\n",
    "    Predict Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{P} &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n",
    "\\end{aligned}$$\n",
    "\n",
    "    Update Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F}^\\mathsf{T}\\mathbf{P}^{-1} \\\\\n",
    "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{k+1} - \\mathbf{Fx}_k) \\\\\n",
    "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{k+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n",
    "\\end{aligned}$$\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",
    "```python\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, Pp = Xs.copy(), Ps.copy(), Ps.copy\n",
    "\n",
    "    for k in range(n-2,-1,-1):\n",
    "        Pp[k] = dot(F, P[k]).dot(F.T) + Q # predicted covariance\n",
    "\n",
    "        K[k]  = dot(P[k], F.T).dot(inv(Pp[k]))\n",
    "        x[k] += dot(K[k], x[k+1] - dot(F, x[k]))\n",
    "        P[k] += dot(K[k], P[k+1] - Pp[k]).dot(K[k].T)\n",
    "    return (x, P, K, Pp)\n",
    "```\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",
    "Here is an example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Vzz//PKNHj+bEiRMkJSVRp04d2rVrJ4H/IWk0GqKiopSgv3v3brKzs0ssa2xs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Tx5EsCTJ8158sQcc/OsYTtBQVnFfsOGUFI3x/9IzppT/yX7l4p0/K5du3RFf5UqVYiMjNQtMvXh\nhx8SExNDxl8ZzJg+g507dxoy9Oda1G0RHV/uSKvqrQy6UrAQQgghhCi4Ep5F/vnOnj2Ll5cXFhb6\nn0m8vb11+/Pz6aefcuDAAb2iX6VS4eb2Ki4ukyC0GkyGJ04f8+TJFJydWzJokDnr1sGdO7BvH7z/\nPjRqVHJF//ITy2m8qDHv7X6vyOdYtmyZ7vfFixczZMgQKleuTJpTGv9d8V9q1coaTrRr1y5u3LhR\n7JgLw8bShkFNBknRL4QQQjzjl19+ISIigvv375vk/YcMGYK9vb1J3luYRqm745+cnEztXAbQV6lS\nRbe/IJycPLCz68Ddu11JSwvg9u0qUH8LeM/F/ElVBrfsSId3fqdhw3TdIlrXr2f9lDTrB9Y8zXzK\n6tOr8avoR0vnloU+R/ZQJgsLC2rXrs2pU6fQaDX0+6kff6X/xWtdXuPa0mtAVvHfsmXB3iP7A1RG\nRganTp0qdFwib5Jb45HcGo/k1ngkt7mztLTk0aNHxTpH9sKLiqIU+1yGFBcXx8yZM+nTpw9WhZkl\nxEA0mqzn7oqTk9Ka27JCrVbn+PtuZmaGu7u7Ud6v1BX+QL4Pnz7vwdQaNeZy714n7t6txd27Wdvs\n7DLx8Unhsu9crgEDGwQzsn7WB4jMzKwfU3rF/hVC3UPZdH0Ts0/NZo3vGizNLAt1juxvSDQaDcnJ\nyVSpUoWdt3Zy69EtKltVxvzm389FmJmZ5T0MKh9FOUYUjOTWeCS3xiO5NR7J7d8sLCxyrJheHIY8\nl6EoivLcuNLT07GxMc6sd4bKSWnMbWmnKEqOv+/GXBS01BX+VatWzfWufkpK1iqu2Xf+83Lz5hC0\nWjNq135M+/YP8fV9SNOmj7jy6DfejD2MucqcsDphWFoWrrA2tvGNxhObGMuV1Cusu7aO8HrhhTre\nx8eHCxcuAPDNim8IHxvOtwnfAtDVsSsbf9oIgL29PQ0aNCjw9T/bGUtbzso6ya3xSG6NR3JrPJLb\n3KlUqmLPRvdsQVqSM9vl5+OPP2b27NkANGzYULc9JiaGESNG0KBBAwYNGsScOXP47bffGD16NB99\n9BFLlixh06ZN/Pbbbzx69AgPDw/CwsIYO3Zsjn7z448/Mn/+fE6cOEFGRgbu7u6EhYUxceJEvXbP\n5uTQoUP06dOHli1b8u2332JnZ5fvdZTG3JYlKpUqx5+bmZnxRuKXusK/cePGREdHo9Fo9Mb5nzlz\nBoBGjRrle/wnn0CnTlC7dgWgAlANgMU/fAFArwa96NK6i1FiL675VvMZ9P0glv6xlLc7v53nNJ9P\nNE+48fAG1+5fIyktibDGYXz44YesWrWKzJ6ZfFfnO7778TsALLWWfP/B97r/UIYPH07r1q0LHNOp\nU6fIyMjA0tKSJk2aFP8ihY7k1ngkt8YjuTUeyW3ubty4gW0e0+p9/vnnfP755889hzGL03feeYd3\n3nmn0MeNHDkStVrNwoUL2bx5M67/f/XPBg0aoFKpOHXqFNOmTWPatGm8/PLL2NnZYWtry40bNxgw\nYAAvv/wyVlZWnDp1io8//piEhASWL1+uO/+yZcv497//jZ+fH4sXL6ZatWr8/vvvnD17VpfP7Dor\n+/X69esZNGgQQ4cOZeHChQW68/zo0SMURUGlUuX55yTyVrFiRWrWrKm3TavVolarjfJ+pa7wDwkJ\nYenSpWzatIk+ffrotq9cuRI3Nzd8fHzyPf6tt+CfH5QytZkcvX0UgPE+4w0es6EM8B7A1ye+Zv+1\n/YzfOZ7v+34PwJKjS9h7dS/X7l/j2oNr/JX6l+4YFSp6NehF7dq1+eKLLxi9e3TW4sJa4CFkHMgg\n415W0d+iRQsiIiJK/sKEEEIII3j48CG3bt0yeQxFUaNGDd047mbNmuHh4aG3PykpifPnz1OvXj29\n7c9+0NFqtfj6+lK1alXCw8OJjIykcuXKpKam8s4779CuXTv27t2r+7DTqVOnPOP59NNP+eCDD5g9\nezaTJk0q0jWJ0q/UFf6vv/46nTt3ZuTIkTx8+JA6deoQHR3Nzp07Wb16dZHGPZmbmXN8xHEOXDtA\nmxqld5EolUpFVFAUbZe3paVbS7SKFjOVGQdvHGT9ufV6bW0sbHCv5E4tx1qon6ipaluVUaNGoXJU\nMW/ePBJOJWQV/4CNjQ2DBg1i7ty5VKxY0QRXJoQQQhieg4MD1atXf247Y97xd3BwMOj5snl7e+co\n+gFOnDjBjBkzOHjwoG4YdLbff/8dHx8ffvnlFx4+fJhVFzznehVFYcSIEaxcuZK1a9fy5ptvGvQ6\nROlS6gp/gM2bN/PBBx8wffp0UlJSqF+/PtHR0fTt27fI5zRTmeHn4WfAKI2jYbWG3Hj7Bg7Wf/9D\n0rdRX5q5NKOWY62sYr9SLZxsnXL9yzyy30j+E/YfDh8+zNWrV7Gzs8PX15fKlSuX5GUIIYQQRlfQ\nYTZlcThK9tCfZ12/fh1fX19eeeUVFixYgIeHBxUqVODXX39l9OjRpKenA3Dnzh0g61uF53n69Cnr\n1q2jYcOGvP7664a9CFHqlMrC397engULFrBgwYJin+vKvSu42LtgY2mcJ+GN4dmiHyCobhBBdYMK\nfLxKpaJNmza0aVN6v90QQgghRN5yu7n3/fffk5aWxubNm3Xr8wCcPHlSr52zszMAN2/efO77WFtb\nExsbS2BgIAEBAezcuVNuFpZjpW4BL0Prv7k/Nf9bkz0Je0wdihBCCCGEjrW1NYDuTv3zZH8YyD4O\nsobqLF26VK9d27ZtqVSpEosXLy7QFJvNmjVj37593Lx5E39/f5KSkgp6CaKMKdeFf/yteA7dPMTD\nJw9pWK3h8w8QQgghhCghjRs3BmDBggUcOnSIo0eP5jubS+fOnbGysiIsLIyYmBi2bNlCYGAg9+7d\n02tnb29PZGQk+/fvJyAggO+++47Y2FiWLl3KmDFjcj23l5cXBw4cQK1W89prrxXo2wJR9pTrwn/h\nrwsB6NOoDy72LiaORgghhBDib/7+/kyZMoWtW7fSvn17WrZsybFjx/JsX79+fTZt2sS9e/cIDQ1l\n7NixNG3alC+++CJH27feeosdO3aQmZnJsGHD6N69O/Pnz893RdjatWtz4MABVCoVvr6+JCQkGOQ6\nRemhUsrwMmu5zXNasWJFzMzM+Cv1L9z/606GNoNfh/1Ky+otTRRl2SbzShuP5NZ4JLfGI7k1Hslt\n7m7cuJFjnvPCKosP95YVktviya1/51ffFle5veO/5OgSMrQZtKnRRop+IYQQQgjxwiuXhf8TzRMW\nHV0EwDifcSaORgghhBBCCNMrl4X//mv7SUxLxK2iG728epk6HCGEEEIIIUyuVM7jX1ydPTtzftR5\nrj24hqW5panDEUIIIYQQwuTKZeEP4OXshZezl6nDEEIIIYQQolQod0N91E/ynv9WCCGEEEKIF1W5\nK/wbRTUibFMYTzOfmjoUIYQQQgghSo1yV/inZ6bzp/pPrMytTB2KEEIIIYQQpUa5K/wBxvuMN3UI\nQgghhBBClCrlrvCvWbEm/3rlX6YOQwghhBBCiFKl3BX+bzV/C3Mzc1OHIYQQQgiRrxUrVqBSqVCp\nVMTFxeXYrygKderUQaVS4e/vX+Lxib/dvn2biIgITp48aepQiqXcFf79G/c3dQhCCCGEKKXS09NZ\nuXIl3bt3p3Xr1gQHB7N69WoeP35sspgqVqzIsmXLcmzft28fly9fpmLFiiaISjzr9u3bzJw5Uwr/\n0qZShUqmDkEIIYQQpdC5c+fw8vJiyJAhbN++nSNHjrBt2zYGDhxIw4YNuXDhgkni6tOnD5s2beLh\nw4d625ctW0abNm1wd3c3SVyGkp6ejqIopg5DUA4LfyGEEEKIf0pMTKR79+5cu3Yt1/0JCQl07tyZ\nO3fulHBkEBYWBkB0dLRu24MHD9i0aRNDhw7N0f7p06fMmjWL+vXrY21tjbOzM+Hh4TliX7duHV26\ndMHV1RUbGxu8vLyYPHkyaWlpeu0SEhLo27cvbm5uWFtb89JLL9GpUye9u9sqlYqIiIgcsXh5eTFi\nxAjd6+zhSz/++CNDhw7F2dkZW1tbnjx5AsAff/xBv379qFatGtbW1nh5efG///1P75xxcXGoVCrW\nrl3L+++/j6urK/b29gQHB5OYmIharWb48OE4OTnh5OREeHg4qampeudQFIWoqCiaNm2KjY0NlStX\n5o033iAhIUGvnb+/P40aNSI+Ph5fX19sbW2pXbs2c+bMQavV6uJp2bIlAOHh4brhWdn5KEj+Sgsp\n/IUQQghR7n355ZckJSUB0Lx5cw4ePIhGo2Hfvn14e3sDcOvWLb788ssSj83BwYE33niD5cuX67ZF\nR0djZmZGnz599NpqtVp69OjBnDlz6NevH9u3b2fOnDns3r0bf39/0tPTdW3/+OMPgoKCWLZsGTt3\n7mTChAmsX7+e4OBgvXMGBQVx7Ngx5s6dy+7du1m0aBHNmjXj/v37Rb6moUOHYmlpyapVq9i4cSOW\nlpacP3+eli1bcvbsWSIjI9m2bRvdunVj3LhxzJw5M8c5pk6dSlJSEitWrCAyMpK4uDjCwsLo1asX\nlSpVIjo6mkmTJrFq1SqmTp2qd+yIESOYMGECAQEBfP/990RFRXHu3Dnatm1LYmKiXtu//vqL/v37\nM2DAAH744Qdef/11pkyZwurVq4Gs/vLNN98AMG3aNA4dOsShQ4cYNmyY0fJnNEoZlpmZqdy/f1/v\nJzMz09RhlSsnT55U4uPjlZMnT5o6lHJHcms8klvjkdwaj+Q2d9evXy/2OVJTUxUnJycFUCwtLZVb\nt27p7b9y5Ypibm6uAEqNGjWK/X4F9c033yiAEh8fr8TGxiqAcvbsWUVRFKVly5bKkCFDFEVRlIYN\nGyp+fn6KoihKdHS0AiibNm3SO1d8fLwCKFFRUbm+l1arVTIyMpR9+/YpgHLq1ClFURTl7t27CqDM\nnz8/31gBZcaMGTm2u7u7K/3791fS0tL0rmnQoEE52gYGBio1atRQHjx4oLd9zJgxSoUKFZSUlBRF\nURRdLoKDg/XaTZgwQQGUcePG6W3v2bOnUqVKFd3rQ4cOKYASGRmp1+7GjRuKjY2NMmnSJN02Pz8/\nBVCOHDmi17ZBgwZKYGCg7nV2fr/55hu9dgXNX15y69/GrG/ljr8QQgghyjW1Ws3du3cBaNOmDW5u\nbnr7PTw8aNGiBQA3b97k6dOnJR6jn58fnp6eLF++nDNnzhAfH5/rMJ9t27bh6OhIcHAwGo1G99O0\naVNcXFz0ZgdKSEigX79+uLi4YG5ujqWlJX5+fgC65xmqVKmCp6cnn332GZ9//jknTpzQDXEpjl69\neum9fvz4MXv27CEkJARbW1u92IOCgnj8+DGHDx/WO6Z79+56r728vADo1q1bju0pKSm64T7btm1D\npVIxYMAAvfdxcXGhSZMmOWZQcnFxoVWrVnrbvL298xwW9ixj5c9YpPAvZTIyMjh69ChxcXE5xqEJ\nIYQQovCsra1RqVRA1nAe5R8Pmmq1Wm7fvg2Aubk5FhYWJR6jSqUiPDyc1atXs3jxYurVq4evr2+O\ndomJidy/fx8rKyssLS31fv766y/dB5zU1FR8fX05cuQIs2bNIi4ujvj4eDZv3gygGxKkUqnYs2cP\ngYGBzJ07l+bNm+Ps7My4ceNQq9VFvh5XV1e918nJyWg0GhYuXJgj7qCgIABd7NmqVKmi99rKyirf\n7dkzMyUmJqIoCi+99FKO9zp8+HCO96latWqO+K2trfWGTeXFWPkzlpLv2Ub29ddfM2DAAGxtbU0d\nSqFkZGTw2Wef8eWXX/Lnn3/qtrdv354ZM2YQEBBgwuiEEEKIssva2pq2bdty8OBBLl++zMqVKxky\nZIhu/9KlS7l58yYAnTp1wszMNPdFhwwZwvTp01m8eDEff/xxrm2cnJyoWrUqO3fuzHV/9tSfe/fu\n5fbt28TFxenu8gO5jjuvVauWbjrR33//nfXr1xMREcHTp09ZvHgxkJXD7Ad0n5WSkpJrHNkftLJV\nrlwZc3NzBg4cyOjRo3M95uWXX851e2E5OTmhUqk4cOAA1tbWOfbntq04CpK/0qLcFf5Tp07lf//7\nH2YxZ3IAABIdSURBVLt376ZatWqmDqdAMjIyCAkJYfv27Tn2/fzzzwQGBrJixQoGDhxoguiEEEKI\nsm/kyJEcPHgQyJqZZcOGDbRu3ZpffvlFr4geN26cqUKkevXqTJw4kYsXLzJ48OBc23Tv3p3vvvuO\nzMxMfHx88jxXduH9zyJ3yZIl+cZQr149pk2bxqZNmzh+/Lhuu4eHB6dPn9Zru3fv3hyz6eTF1taW\nDh06cOLECby9vXV36Y2he/fuzJkzh1u3bvHmm28a5JzZeXzetwB55a+0KHeFP8Dp06fp3bu3bjqo\n0u7zzz/XFf0qlYrg4GDq1KlDTEwMFy5cQKvV8tZbb+Hr64uHh4dpgxVCCCHKoB49ehAeHq6bnWXH\njh3s2LFDr82YMWN0w05MZc6cOfnu79u3L2vWrCEoKIjx48fTqlUrLC0tuXnzJrGxsfTo0YOQkBDa\ntm1L5cqV+c9//sOMGTOwtLRkzZo1nDp1Su98p0+fZsyYMfTu3Zu6detiZWXF3r17OX36NJMnT9a1\nGzhwIB9++CHTp0/Hz8+P8+fP8+WXX1KpUsHXT1qwYAHt27fH19eXkSNH4uHhgVqt5tKlS2zdupW9\ne/cWLll5aNeuHcOHDyc8PJyjR4/y2muvYWdnx59//snPP/9M48aNGTlyZKHO6enpiY2NDWvWrMHL\nywt7e3vc3Ny4e/dugfJXWpS7wt/FxYXk5GT279/PoUOHaNu2ralDypdGo9GbOmz37t106tQJgM8+\n+4zhw4ezbNkyMjIyWLRoEZ9++qmpQhVCCCHKLJVKxcKFC2nSpAnz5s3TDe2BrKEaEydOZNSoUaX+\nhqG5uTk//PADCxYsYNWqVXzyySdYWFhQo0YN/Pz8aNy4MZA1bn379u28++67DBgwADs7O3r06MG6\ndeto3ry57nwuLi54enoSFRXFjRs3UKlU1K5dm8jISMaOHatrN3HiRB4+fMiKFSuYN28erVq1Yv36\n9fzrX/8qcOwNGjTg+PHjfPTRR0ybNo2kpCQcHR2pW7euwT9wLVmyhNatW7NkyRKioqLQarW4ubnR\nrl27HA/yFoStrS3Lly9n5syZdOnShYyMDGbMmMGoUaMKlL/SQqX88wmXMkSr1eZ4cGL79u30798f\nyPrkvnDhQlOEVmCnT5+mSZMmAHTt2pWYmBi9/YmJibi6uqIoCk2aNCnxxSBOnTpFRkYGlpaWujiF\nYUhujUdyazySW+OR3Obuxo0b1KxZs1jnePToEYqioFKpdDPKHDlyhOTkZJydnWnVqhXm5uYGivjF\n8s/cisLJrX/nVt9WrFjRIM+elLs7/m3atNH9nr1QR2n27Op5np6eOfZXq1YNe3t71Gp1gcfRCSGE\nECJvFhYWtGvXztRhCFHiyt10nidOnND9/s/pnkojd3d33e87duxAo9Ho7d+/f7/uU5+M7xdCCCGE\nEEVV7gr/2bNn635/4403TBhJwVSvXp3OnTsDcOXKFQYMGMD169dRFIU9e/boTTf27O9CCCGEEEIU\nRrkr/K9evQpAs2bN6Nixo2mDKaCIiAjdYiHr1q2jVq1a2NjYEBAQoLseb29vevfubcIohRBCCCFE\nWVbuCn/IGhKzefPmUv9kfra2bduybt06bGxsdNueXSSjSZMm7Nixw+ALTgghhBBCiBdHuXu4d8KE\nCYwcOTLX5ZdLs9DQUC5fvsxXX33Fjh07SE1Nxd3dncGDBxMaGmrUhS6EEEKI0ix71hghyhNTTKxZ\nInf81Wo1kyZNokuXLjg7O6NSqYiIiMiz/fHjxwkICMDe3h5HR0dCQ0NJSEgo0HtNnTq1zBX92Vxd\nXZkxYwZHjhzh3LlzxMTE0LdvXyn6hRBCvLCsra2fu1qqEGVRampqiU+BWiKFf3JyMl999RVPnjyh\nZ8+e+ba9ePEi/v7+PH36lPXr17N8+XJ+//13fH19uXPnTkmEK4QQQohSomrVqty9e5eMjAxThyKE\nQSiKglqt5t69ezg6Opboe5fIUJ9atWpx7949VCoVd+/e5euvv86z7fTp07G2tmbbtm04ODgA0KJF\nC+rWrcu8efNk5VohhBDiBWJubo6zszNJSUlotdoinUOtVuuGC1WsWNHAEb7YJLdFY2trS/Xq1Ut8\n4bgSKfwLOi5Po9Gwbds2Bg0apCv6IeuDQ4cOHdiyZYsU/kIIIcQLxsbGhurVqxf5+GdXRS7uKsBC\nn+S2bClVD/devnyZ9PR0vL29c+zz9vZm9+7dPH78mAoVKpggOlEUqamp7Ny5kzt37uDk5ERgYKDe\nhzohhBBCCFEySlXhn5ycDOS+4m6VKlVQFIV79+7h6uqa5znOnTtX5K8CRU7ZYyozMjI4depUgY/T\naDRERUWxbt060tLSdNttbGzo3bs3Y8eOxdLS0uDxliVFza14Psmt8UhujUdyazySW+OR3BqemZkZ\n7u7uRjl3oQv/uLg4OnToUKC2J06coGnTpoUOKr+hQc8bNqTRaMjMzCz0e4rnK+iDVVqtlg8++ICf\nfvopx7709HS+/fZbrl69yty5c0t8bFtpJQ+tGY/k1ngkt8YjuTUeya3xSG4Nw5i1UaEL/1deeYWl\nS5cWqG1hP61kT8OZfef/WSkpKahUKr2nn3Ob/9TKykru+BuQRqPR/Z69uvDz7N27lxMnTlC1alUs\nLCwIDAykYcOGXLhwgZiYGDQaDefOnWP//v107drVWKGXekXJrSgYya3xSG6NR3JrPJJb45HcGp6Z\nWc5JNw0153+h/4RcXV0ZNmyYQd78nzw9PbGxseHMmTM59p05c4Y6deroje/PLQk1atQwSmyi4IYM\nGcKQIUNy3Td//vySDUYIIYQQoowzVOFfIvP4F5SFhQXBwcFs3rwZtVqt2379+nViY2MJDQ01YXRC\nCCGEEEKUXSX2nUxMTAxpaWm6gv78+fNs3LgRgKCgIN3KZTNnzqRly5Z0796dyZMn8/jxY6ZPn46T\nkxPvvvtuSYUrhBBCCCFEuaJSDPXdwXN4eHhw7dq1XPdduXIFDw8P3etjx47x/vvvc+jQISwsLOjY\nsSPz5s3D09NT7ziNRqM3Y4wQQgghhBDljZ2dnUGeoSixwt8YtFptjgd5VSpVgRcME0IIIYQQojRR\nFCXHmH4zM7NcH/otrDJd+AshhBBCCCEKplQ93CuEEEIIIYQwDin8hRBCCCGEeAGU6cI/NTWVCRMm\n4ObmRoUKFWjatCnfffedqcMq8+Li4nTPSvzz5/Dhw6YOr8xQq9VMmjSJLl264OzsjEqlIiIiIte2\nx48fJyAgAHt7exwdHQkNDSUhIaFkAy5DCprbIUOG5NqP69evX/JBlxF79+5l6NCh1K9fHzs7O6pX\nr06PHj04duxYjrbSbwunoLmVflt4J0+epFu3bri7u2NjY0OVKlVo06YNq1evztFW+m3hFDS30m+L\n7+uvv0alUmFvb59jn6H6bZleYi00NJT4+HjmzJlDvXr1WLt2LWFhYWi1Wvr162fq8Mq82bNn06FD\nB71tjRo1MlE0ZU9ycjJfffUVTZo0oWfPnnz99de5trt48SL+/v40bdqU9evX66aw9fX15eTJkzg7\nO5dw5KVfQXMLYGNjw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x134cb20fda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "from filterpy.kalman import KalmanFilter\n",
    "import kf_book.book_plots as bp\n",
    "\n",
    "def plot_rts(noise, Q=0.001, show_velocity=False):\n",
    "    random.seed(123)\n",
    "    fk = KalmanFilter(dim_x=2, dim_z=1)\n",
    "\n",
    "    fk.x = np.array([0., 1.])      # state (x and dx)\n",
    "\n",
    "    fk.F = np.array([[1., 1.],\n",
    "                     [0., 1.]])    # state transition matrix\n",
    "\n",
    "    fk.H = np.array([[1., 0.]])    # Measurement function\n",
    "    fk.P = 10.                     # covariance matrix\n",
    "    fk.R = noise                   # state uncertainty\n",
    "    fk.Q = Q                       # process uncertainty\n",
    "\n",
    "    # create noisy data\n",
    "    zs = np.asarray([t + 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",
    "    if show_velocity:\n",
    "        index = 1\n",
    "        print('gu')\n",
    "    else:\n",
    "        index = 0\n",
    "    if not show_velocity:\n",
    "        bp.plot_measurements(zs, lw=1)\n",
    "    plt.plot(M[:, index], c='b', label='RTS')\n",
    "    plt.plot(mu[:, index], c='g', ls='--', label='KF output')\n",
    "    if not show_velocity:\n",
    "        N = len(zs)\n",
    "        plt.plot([0, N], [0, N], 'k', lw=2, label='track') \n",
    "    plt.legend(loc=4)\n",
    "    plt.show()\n",
    "    \n",
    "plot_rts(7.)"
   ]
  },
  {
   "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",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3GtQoV4Pq5apTo1wNGlZvaN6LfW7DuZZt34OFCxcyePBgjEYjBw4c4MCBA0XK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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134caea6eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we must understand that this smoothing is predicated on the system model. We have told the filter that that what we are tracking follows a constant velocity model with very low process error. When the filter *looks ahead* it sees that the future behavior closely matches a constant velocity so it is able to reject most of the noise in the signal. Suppose instead our system has a lot of process noise. For example, if we are tracking a light aircraft in gusty winds its velocity will change often, and the filter will be less able to distinguish between noise and erratic movement due to the wind. We can see this in the next graph.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x8dSuXZshQ4Zgbm5OUlISv/zyCyNGjCAiIoL58+cDqklXzs7OtGjRgl27dpGa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134cbb74978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=7., Q=.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This underscores the fact that these filters are not *smoothing* the data in colloquial sense of the term. The filter is making an optimal estimate based on previous measurements, future measurements, and what you tell it about the behavior of the system and the noise in the system and measurements.\n",
    "\n",
    "Let's wrap this up by looking at the velocity estimates of Kalman filter vs the RTS smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gu\n"
     ]
    },
    {
     "data": {
      "image/png": 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2z61BNOBfe/6Ff+35l3l4xXUPrkOkd6RNr0vth0yQ4ZFej+CRXo8AADKKM7A7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\nIjfzf4J5+PL7RuWEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x134cbbf74e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(7.,show_velocity=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The improvement in the velocity, which is an hidden variable, is even more dramatic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed-Lag Smoothing\n",
    "\n",
    "The RTS smoother presented above should always be your choice of algorithm if you can run in batch mode because it incorporates all available data into each estimate. Not all problems allow you to do that, but you may still be interested in receiving smoothed values for previous estimates. The number line below illustrates this concept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x134ccc52dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.book_plots import figsize\n",
    "from kf_book.smoothing_internal import *\n",
    "\n",
    "with figsize(y=2):\n",
    "    show_fixed_lag_numberline()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At step $k$ we can estimate $x_k$ using the normal Kalman filter equations. However, we can make a better estimate for $x_{k-1}$ by using the measurement received for $x_k$. Likewise, we can make a better estimate for $x_{k-2}$ by using the measurements recevied for $x_{k-1}$ and $x_{k}$. We can extend this computation back for an arbitrary $N$ steps.\n",
    "\n",
    "Derivation for this math is beyond the scope of this book; Dan Simon's *Optimal State Estimation* [2] has  a very good exposition if you are interested. The essense of the idea is that instead of having a state vector $\\mathbf{x}$ we make an augmented state containing\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}\\mathbf{x}_k \\\\ \\mathbf{x}_{k-1} \\\\ \\vdots\\\\ \\mathbf{x}_{k-N+1}\\end{bmatrix}$$\n",
    "\n",
    "This yields a very large covariance matrix that contains the covariance between states at different steps. FilterPy's class `FixedLagSmoother` takes care of all of this computation for you, including creation of the augmented matrices. All you need to do is compose it as if you are using the `KalmanFilter` class and then call `smooth()`, which implements the predict and update steps of the algorithm. \n",
    "\n",
    "Each call of `smooth` computes the estimate for the current measurement, but it also goes back and adjusts the previous `N-1` points as well. The smoothed values are contained in the list `FixedLagSmoother.xSmooth`. If you use `FixedLagSmoother.x` you will get the most recent estimate, but it is not smoothed and is no different from a standard Kalman filter output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation fixed-lag: 2.616\n",
      "standard deviation kalman: 3.562\n"
     ]
    },
    {
     "data": {
      "image/png": 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kv+VidzEvlbzE7obdwWXfG/495iTOOe3ruvsZrq1ey3NHngMgxhTDZUmXMTdx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\n4/HUOWa32+nTp0+dY00l6Sc8JDxw4ECefvrpZl177CuGoyUlJTF16lS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x134ccdfcf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.kalman import FixedLagSmoother, KalmanFilter\n",
    "import numpy.random as random\n",
    "\n",
    "fls = FixedLagSmoother(dim_x=2, dim_z=1, N=8)\n",
    "\n",
    "fls.x = np.array([0., .5])\n",
    "fls.F = np.array([[1.,1.],\n",
    "                  [0.,1.]])\n",
    "\n",
    "fls.H = np.array([[1.,0.]])\n",
    "fls.P *= 200\n",
    "fls.R *= 5.\n",
    "fls.Q *= 0.001\n",
    "\n",
    "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "kf.x = np.array([0., .5])\n",
    "kf.F = np.array([[1.,1.],\n",
    "                 [0.,1.]])\n",
    "kf.H = np.array([[1.,0.]])\n",
    "kf.P *= 200\n",
    "kf.R *= 5.\n",
    "kf.Q *= 0.001\n",
    "\n",
    "N = 4 # size of lag\n",
    "\n",
    "nom =  np.array([t/2. for t in range (0, 40)])\n",
    "zs = np.array([t + random.randn()*5.1 for t in nom])\n",
    "\n",
    "for z in zs:\n",
    "    fls.smooth(z)\n",
    "    \n",
    "kf_x, _, _, _ = kf.batch_filter(zs)\n",
    "x_smooth = np.array(fls.xSmooth)[:, 0]\n",
    "\n",
    "\n",
    "fls_res = abs(x_smooth - nom)\n",
    "kf_res = abs(kf_x[:, 0] - nom)\n",
    "\n",
    "plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n",
    "plt.plot(x_smooth, label='FLS')\n",
    "plt.plot(kf_x[:, 0], label='KF', ls='--')\n",
    "plt.legend(loc=4)\n",
    "\n",
    "print('standard deviation fixed-lag: {:.3f}'.format(np.mean(fls_res)))\n",
    "print('standard deviation kalman: {:.3f}'.format(np.mean(kf_res)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I have set `N=8` which means that we will incorporate 8 future measurements into our estimates. This provides us with a very smooth estimate once the filter converges, at the cost of roughly 8x the amount of computation of the standard Kalman filter. Feel free to experiment with larger and smaller values of `N`. I chose 8 somewhat at random, not due to any theoretical concerns."
   ]
  },
  {
   "cell_type": "markdown",
   "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",
    "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n",
    "\n",
    "http://arc.aiaa.org/doi/abs/10.2514/3.3166"
   ]
  }
 ],
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