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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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      "Ensemble Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
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      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
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     "source": [
      "> I am not well versed with Ensemble filters. I have implemented one for this book, and made it work, but I have not used one in real life. Different sources use slightly different forms of these equations. If I implement the equations given in the sources the filter does not work. It is possible that I am doing something wrong. However, in various places on the web I have seen comments by people stating that they do the kinds of things I have done in my filter to make it work. In short, I do not understand this topic well, but choose to present my lack of knowledge rather than to gloss over the subject. I hope to master this topic in the future and to author a more definitive chapter. At the end of the chapter I document my current confusion and questions. In any case if I got confused by the sources perhaps you also will, so documenting my confusion can help you avoid the same.\n",
      "\n",
      "\n",
      "The ensemble Kalman filter (EnKF) is very similar to the unscented Kalman filter (UKF) of the last chapter. If you recall, the UKF uses a set of deterministically chosen weighted sigma points passed through nonlinear state and measurement functions. After the sigma points are passed through the function, we find the mean and covariance of the points and use this as the filter's new mean and covariance. It is only an approximation of the true value, and thus suboptimal, but in practice the filter is highly accurate. It has the advantage of often producing more accurate estimates than the EKF does, and also does not require you to analytically derive the linearization of the state and measurement equations. \n",
      "\n",
      "The ensemble Kalman filter works in a similar way, except it uses a *Monte Carlo* method to choose a large numbers of sigma points. It came about from the geophysical sciences as an answer for the very large states and systems needed to model things such as the ocean and atmosphere. There is an interesting article on it's development in weather modeling in *SIAM News* [1]. The filter starts by randomly generating a large number of points distributed about the filter's initial state. This distribution is proportional to the filter's covariance $\\mathbf{P}$. In other words 68% of the points will be within one standard deviation of the mean, 95% percent within two standard deviations, and so on. Let's look at this in two dimensions. We will use `numpy.random.multivariate_normal()` function to randomly create points from a multivariate normal distribution drawn from the mean (5, 3) with the covariance\n",
      "\n",
      "$$\\begin{bmatrix}\n",
      "32 & 15 \\\\ 15 & 40\n",
      "\\end{bmatrix}$$\n",
      "\n",
      "I've drawn the covariance ellipse representing two standard deviations to illustrate how the points are distributed."
     ]
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     "input": [
      "import numpy as np\n",
      "from numpy.random import multivariate_normal\n",
      "from stats import (covariance_ellipse, \n",
      "                   plot_covariance_ellipse)\n",
      "\n",
      "mean = (5, 3)\n",
      "P = np.array([[32, 15],\n",
      "              [15., 40.]])\n",
      "\n",
      "x,y = multivariate_normal(mean=mean, cov=P, size=2500).T\n",
      "plt.scatter(x, y, alpha=0.3, marker='.')\n",
      "plt.axis('equal')\n",
      "\n",
      "plot_covariance_ellipse(mean=mean, cov=P,\n",
      "                        variance=2.**2,\n",
      "                        facecolor='none')"
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nqNZWgbffLseEyXuw8J8eRmTDTowdMxK//95nED57Ssb3ZNsKNtNxauIrYdtq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9mfcTJlYvrkcvz0izfhmkvnFHwtw4X+3H9ONhiGGUlw0sEwzIgmV+B2OpKSoiIdP//KzVj48Yfw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\ncKWDYRhmm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       "text": [
        "<matplotlib.figure.Figure at 0x7f1430666c50>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As I already stated, when the filter is initialized a large number of sigma points are drawn from the initial state ($\\mathbf{x}$) and covariance ($\\mathbf{P}$). From there the algorithm proceeds very similarly to the UKF. During the prediction step the sigma points are passed through the state transition function, and then perturbed by adding a bit of noise to account for the process noise. During the update step the sigma points are translated into measurement space by passing them through the measurement function, they are perturbed by a small amount to account for the measurement noise. The Kalman gain is computed from the \n",
      "\n",
      "We already mentioned the main difference between the UKF and EnKF - the UKF choses the sigma points deterministically. There is another difference, implied by the algorithm above. With the UKF we generate new sigma points during each predict step, and after passing the points through the nonlinear function we reconstitute them into a mean and covariance by using the *unscented transform*. The EnKF just keeps propagating the originally created sigma points; we only need to compute a mean and covariance as outputs for the filter! \n",
      "\n",
      "Let's look at the equations for the filter. As usual, I will leave out the typical subscripts and superscripts; I am expressing an algorithm, not mathematical functions. Here $N$ is the number of sigma points, $\\chi$ is the set of sigma points."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initialize Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\\boldsymbol\\chi \\sim \\mathcal{N}(\\mathbf{x}_0, \\mathbf{P}_0)$$\n",
      "\n",
      "This just says to select the sigma points from the filter's initial mean and covariance. In code this might look like\n",
      "\n",
      "    N = 1000\n",
      "    sigmas = multivariate_normal(mean=x, cov=P, size=N)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Predict Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\n",
      "\\begin{aligned}\n",
      "\\boldsymbol\\chi &= f(\\boldsymbol\\chi, \\mathbf{u}) + v_Q \\\\\n",
      "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi\n",
      "\\end{aligned}\n",
      "$$\n",
      "That is short and sweet, but perhaps not entirely clear. The first line passes all of the sigma points through a use supplied state transition function and then adds some noise distributed according to the $\\mathbf{Q}$ matrix. In Python we might write"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    for i, s in enumerate(sigmas):\n",
      "        sigmas[i] = fx(x=s, dt=0.1, u=0.)\n",
      "\n",
      "    sigmas += multivariate_normal(x, Q, N)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second line computes the mean from the sigmas. In Python we will take advantage of `numpy.mean` to do this very concisely and quickly.\n",
      "\n",
      "    x = np.mean(sigmas, axis=0)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now optionally compute the covariance of the mean. The algorithm does not need to compute this value, but it is often useful for analysis. The equation is\n",
      "\n",
      "$$\\mathbf{P} = \\frac{1}{N-1}\\sum_1^N[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$$\n",
      "\n",
      "$\\boldsymbol\\chi-\\mathbf{x}^-$ is a one dimensional vector, so we will use `numpy.outer` to compute the $[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$ term. In Python we might write\n",
      "\n",
      "    P = 0\n",
      "    for s in sigmas:\n",
      "        P += outer(s-x, s-x)\n",
      "    P = P / (N-1)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Update Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the update step we pass the sigma points through the measurement function, compute the mean and covariance of the sigma points, compute the Kalman gain from the covariance, and then update the Kalman state by scaling the residual by the Kalman gain. The equations are\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\boldsymbol\\chi_h &= h(\\boldsymbol\\chi, u)\\\\\n",
      "\\mathbf{z}_{mean} &= \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h \\\\ \\\\\n",
      "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
      "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} \\\\\n",
      "\\\\\n",
      "\\mathbf{K} &= \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}\\\\ \n",
      "\\boldsymbol\\chi & = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R] \\\\ \\\\\n",
      "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi \\\\\n",
      "\\mathbf{P} &= \\mathbf{P} - \\mathbf{KP}_{zz}\\mathbf{K}^\\mathsf{T}\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is very similar to the linear KF and the UKF. Let's just go line by line.\n",
      "\n",
      "The first line,\n",
      "\n",
      "$$\\boldsymbol\\chi_h = h(\\boldsymbol\\chi, u),$$\n",
      "\n",
      "just passes the sigma points through the measurement function $h$. We name the resulting points $\\chi_h$ to distinguish them from the sigma points. In Python we could write this as\n",
      "\n",
      "    sigmas_h = h(sigmas, u)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The next line computes the mean of the measurement sigmas.\n",
      "$$\\mathbf{z}_{mean} = \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h$$\n",
      "\n",
      "In Python we can compute that with\n",
      "\n",
      "    z_mean = np.mean(sigmas_h, axis=0)\n",
      "    \n",
      "Now that we have the mean of the measurement sigmas we can compute the covariance for every measurement sigma point, and the *cross variance* for the measurement sigma points vs the sigma points. That is expressed by these two equations\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
      "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T}\n",
      "\\end{aligned}$$\n",
      "\n",
      "We can express this in Python with\n",
      "\n",
      "    P_zz = 0\n",
      "    for sigma in sigmas_h:\n",
      "        s = sigma - z_mean\n",
      "        P_zz += outer(s, s)\n",
      "    P_zz = P_zz / (N-1) + R\n",
      "\n",
      "    P_xz = 0\n",
      "    for i in range(N):\n",
      "        P_xz += outer(self.sigmas[i] - self.x, sigmas_h[i] - z_mean)\n",
      "    P_xz /= N-1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Computation of the Kalman gain is straightforward $\\mathbf{K} = \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}$.\n",
      "\n",
      "In Python this is the trivial\n",
      "\n",
      "    K = np.dot(P_xz, inv(P_zz))\n",
      "\n",
      "Next, we update the sigma points with\n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
      "\n",
      "Here $\\mathbf{v}_R$ is the perturbation that we add to the sigmas. In Python we can implment this with\n",
      "\n",
      "    v_r = multivariate_normal([0]*dim_z, R, N)\n",
      "    for i in range(N):\n",
      "        sigmas[i] += dot(K, z + v_r[i] - sigmas_h[i])\n",
      "\n",
      "\n",
      "Our final step is recompute the filter's mean and covariance.\n",
      "\n",
      "        x = np.mean(sigmas, axis=0)\n",
      "        P = self.P - dot3(K, P_zz, K.T)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementation and Example"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have implemented an EnKF in the `FilterPy` library. It is in many ways a toy. Filtering with a large number of sigma points gives us very slow performance. Furthermore, there are many minor variations on the algorithm in the literature. I wrote this mostly because I was interested in learning a bit about the filter. I have not used it for a real world problem, and I can give no advice on using the filter for the large problems for which it is suited. Therefore I will refine my comments to implementing a very simple filter. I will use it to track an object in one dimension, and compare the output to a linear Kalman filter. This is a filter we have designed many times already in this book, so I will design it with little comment. Our state vector will be\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "The state transition function is\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$$\n",
      "\n",
      "and the measurement function is\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1&0\\end{bmatrix}$$\n",
      "\n",
      "The EnKF is designed for nonlinear problems, so instead of using matrices to implement the state transition and measurement functions you will need to supply Python functions. For this problem they can be written as:\n",
      "\n",
      "    def hx(x):\n",
      "        return np.array([x[0]])\n",
      "\n",
      "    def fx(x, dt):\n",
      "        return np.dot(F, x)\n",
      "        \n",
      "One final thing: the EnKF code, like the UKF code, uses a single dimension for $\\mathbf{x}$, not a two dimensional column matrix as used by the linear kalman filter code.\n",
      "\n",
      "Without further ado, here is the code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "from filterpy.kalman import EnsembleKalmanFilter as EnKF\n",
      "from filterpy.kalman import KalmanFilter\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "import book_plots as bp\n",
      "\n",
      "np.random.seed(1234)\n",
      "\n",
      "def hx(x):\n",
      "    return np.array([x[0]])\n",
      "\n",
      "def fx(x, dt):\n",
      "    return np.dot(F, x)\n",
      "    \n",
      "F = np.array([[1., 1.],[0., 1.]])\n",
      "\n",
      "x = np.array([0., 1.])\n",
      "P = np.eye(2)* 100.\n",
      "enf = EnKF(x=x, P=P, dim_z=1, dt=1., N=20, hx=hx, fx=fx)\n",
      "\n",
      "std_noise = 10.\n",
      "enf.R *= std_noise**2\n",
      "enf.Q = Q_discrete_white_noise(2, 1., .001)\n",
      "\n",
      "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
      "kf.x = np.array([x]).T\n",
      "kf.F = F.copy()\n",
      "kf.P = P.copy()\n",
      "kf.R = enf.R.copy()\n",
      "kf.Q = enf.Q.copy()\n",
      "kf.H = np.array([[1., 0.]])\n",
      "\n",
      "measurements = []\n",
      "results = []\n",
      "ps = []\n",
      "kf_results = []\n",
      "\n",
      "zs = []\n",
      "for t in range (0,100):\n",
      "    # create measurement = t plus white noise\n",
      "    z = t + randn()*std_noise\n",
      "    zs.append(z)\n",
      "\n",
      "    enf.predict()\n",
      "    enf.update(np.asarray([z]))\n",
      "    \n",
      "    kf.predict()\n",
      "    kf.update(np.asarray([[z]]))\n",
      "\n",
      "    # save data\n",
      "    results.append (enf.x[0])\n",
      "    kf_results.append (kf.x[0,0])\n",
      "    measurements.append(z)\n",
      "    ps.append(3*(enf.P[0,0]**.5))\n",
      "\n",
      "results = np.asarray(results)\n",
      "ps = np.asarray(ps)\n",
      "\n",
      "plt.plot(results, label='EnKF')\n",
      "plt.plot(kf_results, label='KF', c='b', lw=2)\n",
      "bp.plot_measurements(measurements)\n",
      "plt.plot (results-ps, c='k',linestyle=':', lw=1, label='1$\\sigma$')\n",
      "plt.plot(results+ps, c='k', linestyle=':', lw=1)\n",
      "plt.fill_between(range(100),results-ps, results+ps, facecolor='y', alpha=.3)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CDiGEEEKIe9j1daK1WgNTpjzPnDlTaN8+EKs1m2++eZ6aNU2YzQkAPPfc0GtH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\nuvvO4wbOvn0ZvnUrywp20mXIACIjPfj00wc6O6zGOWR8L3kC28TBWK6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V3tx11/MsXfoa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\nAhaNRLMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f14189316d8>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It can be a bit difficult to see, but the KF and EnKF start off slightly different, but soon converge to producing nearly the same values. The EnKF is a suboptimal filter, so it will not produce the optimal solution that the KF produces. However, I deliberately chose $N$ to be quite small (20) to guarantee that the EnKF output is quite suboptimal. If I chose a more reasonable number such as 2000 you would be unable to see the difference between the two filter outputs on this graph."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Outstanding Questions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All of this should be considered as *my* questions, not lingering questions in the literature. However, I am copying equations directly from well known sources in the field, and they do not address the discrepencies.\n",
      "\n",
      "First, in Brown [2] we have all sums multipied by $\\frac{1}{N}$, as in \n",
      "\n",
      "$$ \\hat{x} = \\frac{1}{N}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
      "\n",
      "The same equation in Crassidis [3] reads (I'll use the same notation as in Brown, although Crassidis' is different)\n",
      "\n",
      "$$ \\hat{x} = \\frac{1}{N-1}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
      "\n",
      "The same is true in both sources for the sums in the computation for the covariances. Crassidis, in the context of talking about the filter's covariance, states that $N-1$ is used to ensure an unbiased estimate. Given the following standard equations for the mean and standard deviation (p.2 of Crassidis), this makes sense for the covariance.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &= \\frac{1}{N}\\sum_{i=1}^N[\\tilde{z}(t_i) - \\hat{z}(t_i)] \\\\\n",
      " \\sigma^2 &= \\frac{1}{N-1}\\sum_{i=1}^N\\{[\\tilde{z}(t_i) - \\hat{z}(t_i)] - \\mu\\}^2\n",
      "\\end{aligned}\n",
      " $$\n",
      "\n",
      "However, I see no justification or reason to use $N-1$ to compute the mean. If I use $N-1$ in the filter for the mean the filter does not converge and the state essentially follows the measurements without any filtering. However, I do see a reason to use it for the covariance as in Crassidis, in contrast to Brown. Again, I support my decision emperically - $N-1$ works in the implementation of the filter, $N$ does not.\n",
      "\n",
      "My second question relates to the use of the $\\mathbf{R}$ matrix. In Brown $\\mathbf{R}$ is added to $\\mathbf{P}_{zz}$ whereas it isn't in Crassidis and other sources. I have read on the web notes by other implementers tthat adding R helps the filter, and it certainly seems reasonable and necessary to me, so this is what I do. \n",
      "\n",
      "My third question relates to the computation of the covariance $\\mathbf{P}$. Again, we have different equations in Crassidis and Brown. I have chosen the implementation given in Brown as it seems to give me the  behavior that I expect (convergence of $\\mathbf{P}$ over time) and it closely compares to the form in the linear KF. In contrast I find the equations in Crassidis do not seem to converge much.\n",
      "\n",
      "My fourth question relates to the state estimate update. In Brown we have \n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\mathbf{z}_{mean} + \\mathbf{v}_R]$$ \n",
      "\n",
      "whereas in Crassidis we have\n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
      "\n",
      "To me the Crassidis equation seems logical, and it produces a filter that performs like the linear KF for linear problems, so that is the formulation that I have chosen. \n",
      "\n",
      "I am not comfortable saying either book is wrong; it is quite possible that I missed some point that makes each set of equations work. I can say that when I implemented them as written I did not get a filter that worked. I define \"work\" as performs essentially the same as the linear KF for linear problems. Between reading implementation notes on the web and reasoning about various issues I have chosen the implementation in this chapter, which does in fact seem to work correctly. I have yet to explore the significant amount of original literature that will likely definitively explain the discrepencies. I would like to leave this here in some form even if I do find an explanation that reconciles the various differences, as if I got confused by these books than probably others will as well."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [1] Mackenzie, Dana. *Ensemble Kalman Filters Bring Weather Models Up to Date* Siam News,  Volume 36, Number 8, October 2003. http://www.siam.org/pdf/news/362.pdf\n",
      "\n",
      "- [2]  Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB\u00ae excercises and solutions.* Wiley, 2012.\n",
      "\n",
      "- [3] Crassidis, John L., and John L. Junkins. *Optimal estimation of dynamic systems*. CRC press, 2011."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}