diff --git a/quantecon.egg-info/PKG-INFO b/quantecon.egg-info/PKG-INFO
index 8051d1000..aeeb04878 100644
--- a/quantecon.egg-info/PKG-INFO
+++ b/quantecon.egg-info/PKG-INFO
@@ -1,6 +1,6 @@
 Metadata-Version: 1.1
 Name: quantecon
-Version: 0.1.7.post2
+Version: 0.1.8
 Summary: QuantEcon is a package to support all forms of quantitative economic modelling.
 Home-page: https://github.com/QuantEcon/QuantEcon.py
 Author: Thomas J. Sargent and John Stachurski (Project coordinators)
diff --git a/quantecon/kalman.py b/quantecon/kalman.py
index fccefea6d..0546c57d8 100644
--- a/quantecon/kalman.py
+++ b/quantecon/kalman.py
@@ -9,41 +9,38 @@
 import numpy as np
 from numpy import dot
 from scipy.linalg import inv
-from .matrix_eqn import solve_discrete_riccati
+from quantecon.matrix_eqn import solve_discrete_riccati
 
 class Kalman(object):
     r"""
     Implements the Kalman filter for the Gaussian state space model
 
-        x_{t+1} = A x_t + w_{t+1}
-        y_t = G x_t + v_t.
+        x_{t+1} = A x_t + C w_{t+1}
+        y_t = G x_t + H v_t.
 
-    Here x_t is the hidden state and y_t is the
-    measurement. The shocks w_t and v_t are iid zero
-    mean Gaussians with covariance matrices Q and R respectively.
+    Here x_t is the hidden state and y_t is the measurement. The shocks 
+    w_t and v_t are iid standard normals.  Below we use the notation
+    
+        Q := CC'
+        R := HH'
+    
 
     Parameters
     -----------
-    A : array_like or scalar(float)
-        The n x n matrix A
-    Q : array_like or scalar(float)
-        Q is n x n, symmetric and nonnegative definite
-    G : array_like or scalar(float)
-        G is k x n
-    R : array_like or scalar(float)
-        R is k x k, symmetric and nonnegative definite
+    ss : instance of LinearStateSpace
+        An instance of the quantecon.lss.LinearStateSpace class
+    x_hat : scalar(float) or array_like(float), optional(default=None)
+        An n x 1 array representing the mean x_hat and covariance
+        matrix Sigma of the prior/predictive density.  Set to zero if 
+        not supplied.
+    Sigma : scalar(float) or array_like(float), optional(default=None)
+        An n x n array representing the covariance matrix Sigma of
+        the prior/predictive density.  Must be positive definite.
+        Set to the identity if not supplied.
 
     Attributes
     ----------
-    A, Q, G, R : see Parameters
-    k : scalar(int)
-        Number of rows of G
-    n : scalar(int)
-        Number of columns of G
-    current_Sigma : array_like or scalar(float)
-        The n x n covariance matrix
-    current_x_hat : array_like or scalar(float)
-        The mean of the state        
+    Sigma, x_hat : as above        
     Sigma_infinity : array_like or scalar(float)
         The infinite limit of Sigma_t
     K_infinity : array_like or scalar(float)
@@ -57,12 +54,23 @@ class Kalman(object):
 
     """
 
-    def __init__(self, A, G, Q, R):
-        self.A, self.G, self.Q, self.R = list(map(self.convert, (A, G, Q, R)))
-        self.k, self.n = self.G.shape
+    def __init__(self, ss, x_hat=None, Sigma=None):
+        self.ss = ss
+        self.set_state(x_hat, Sigma)
         self.K_infinity = None
         self.Sigma_infinity = None
 
+    def set_state(self, x_hat, Sigma):
+        if Sigma == None:
+            Sigma = np.identity(self.ss.n)
+        else:
+            self.Sigma = np.atleast_2d(Sigma)
+        if x_hat == None:
+            x_hat = np.zeros((self.ss.n, 1))
+        else:
+            self.x_hat = np.atleast_2d(x_hat)
+            self.x_hat.shape = self.ss.n, 1
+
     def __repr__(self):
         return self.__str__()
 
@@ -72,44 +80,8 @@ def __str__(self):
           - dimension of state space          : {n}
           - dimension of observation equation : {k}
         """
-        return dedent(m.format(n=self.n, k=self.k))
-
-    def convert(self, x):
-        """
-        Convert array_like objects (lists of lists, floats, etc.) into
-        well formed 2D NumPy arrays
-
-        Parameters
-        ----------
-        x : scalar or array_like(float)
-            Argument to be converted into a 2D NumPy array
-
-        Returns
-        -------
-        array_like(float)
-            A 2D NumPy array
-
-        """
-        return np.atleast_2d(np.asarray(x, dtype='float32'))
-
-    def set_state(self, x_hat, Sigma):
-        """
-        Set the state of the filter (mean and variance of prior
-        density).
-
-        Parameters
-        ----------
-        x_hat : scalar(float) or array_like(float)
-            An n x 1 array representing the mean x_hat and covariance
-            matrix Sigma of the prior/predictive density.
-        Sigma : scalar(float) or array_like(float)
-            An n x n array representing the covariance matrix Sigma of
-            the prior/predictive density.  Must be positive definite.
+        return dedent(m.format(n=self.ss.n, k=self.ss.k))
 
-        """
-        self.current_Sigma = self.convert(Sigma)
-        self.current_x_hat = self.convert(x_hat)
-        self.current_x_hat.shape = self.n, 1
 
     def prior_to_filtered(self, y):
         r"""
@@ -117,12 +89,11 @@ def prior_to_filtered(self, y):
         time t filtering distribution, using current measurement y_t.
 
         The updates are according to
-
         
             x_{hat}^F = x_{hat} + Sigma G' (G Sigma G' + R)^{-1}
-            (y - G x_{hat}) 
+                (y - G x_{hat}) 
             Sigma^F = Sigma - Sigma G' (G Sigma G' + R)^{-1} G
-            Sigma
+                Sigma
 
         Parameters
         ----------
@@ -131,17 +102,17 @@ def prior_to_filtered(self, y):
 
         """
         # === simplify notation === #
-        G, R = self.G, self.R
-        x_hat, Sigma = self.current_x_hat, self.current_Sigma
+        G, H = self.ss.G, self.ss.H
+        R = np.dot(H, H.T)
 
         # === and then update === #
-        y = self.convert(y)
-        y.shape = self.k, 1
-        A = dot(Sigma, G.T)
-        B = dot(dot(G, Sigma), G.T) + R
-        M = dot(A, inv(B))
-        self.current_x_hat = x_hat + dot(M, (y - dot(G, x_hat)))
-        self.current_Sigma = Sigma - dot(M, dot(G,  Sigma))
+        y = np.atleast_2d(y)
+        y.shape = self.ss.k, 1
+        E = dot(self.Sigma, G.T)
+        F = dot(dot(G, self.Sigma), G.T) + R
+        M = dot(E, inv(F))
+        self.x_hat = self.x_hat + dot(M, (y - dot(G, self.x_hat)))
+        self.Sigma = self.Sigma - dot(M, dot(G,  self.Sigma))
 
     def filtered_to_forecast(self):
         """
@@ -151,12 +122,12 @@ def filtered_to_forecast(self):
 
         """
         # === simplify notation === #
-        A, Q = self.A, self.Q
-        x_hat, Sigma = self.current_x_hat, self.current_Sigma
+        A, C = self.ss.A, self.ss.C
+        Q = np.dot(C, C.T)
 
         # === and then update === #
-        self.current_x_hat = dot(A, x_hat)
-        self.current_Sigma = dot(A, dot(Sigma, A.T)) + Q
+        self.x_hat = dot(A, self.x_hat)
+        self.Sigma = dot(A, dot(self.Sigma, A.T)) + Q
 
     def update(self, y):
         """
@@ -188,15 +159,17 @@ def stationary_values(self):
 
         """
         # === simplify notation === #
-        A, Q, G, R = self.A, self.Q, self.G, self.R
+        A, C, G, H = self.ss.A, self.ss.C, self.ss.G, self.ss.H
+        Q, R = np.dot(C, C.T), np.dot(H, H.T)
+        
         # === solve Riccati equation, obtain Kalman gain === #
         Sigma_infinity = solve_discrete_riccati(A.T, G.T, Q, R)
         temp1 = dot(dot(A, Sigma_infinity), G.T)
         temp2 = inv(dot(G, dot(Sigma_infinity, G.T)) + R)
         K_infinity = dot(temp1, temp2)
+        
         # == record as attributes and return == #
         self.Sigma_infinity, self.K_infinity = Sigma_infinity, K_infinity
-
         return Sigma_infinity, K_infinity
     
     def stationary_coefficients(self, j, coeff_type='ma'):
@@ -213,13 +186,13 @@ def stationary_coefficients(self, j, coeff_type='ma'):
             moving average or 'var' for VAR.
         """
         # == simplify notation == #
-        A, G = self.A, self.G
+        A, G = self.ss.A, self.ss.G
         K_infinity = self.K_infinity
         # == make sure that K_infinity has actually been computed == #
         if K_infinity is None: 
             S, K_infinity = self.stationary_values()            
         # == compute and return coefficients == #
-        coeffs = [np.identity(self.k)]
+        coeffs = [np.identity(self.ss.k)]
         i = 1
         if coeff_type == 'ma':
             P = A
@@ -235,9 +208,11 @@ def stationary_coefficients(self, j, coeff_type='ma'):
 
     def stationary_innovation_covar(self):
         # == simplify notation == #
-        R, G = self.R, self.G
+        H, G = self.ss.H, self.ss.G
+        R = np.dot(H, H.T)
         Sigma_infinity = self.Sigma_infinity
-        # == Make sure that Sigma_infinity has been computed == #
+        
+        # == make sure that Sigma_infinity has been computed == #
         if Sigma_infinity is None: 
             Sigma_infinity, K = self.stationary_values()            
         return dot(G, dot(Sigma_infinity, G.T)) + R
diff --git a/quantecon/tests/test_kalman.py b/quantecon/tests/test_kalman.py
index f50e5fb78..1fe917196 100644
--- a/quantecon/tests/test_kalman.py
+++ b/quantecon/tests/test_kalman.py
@@ -10,6 +10,7 @@
 import unittest
 import numpy as np
 from numpy.testing import assert_allclose
+from quantecon.lss import LinearStateSpace
 from quantecon.kalman import Kalman
 
 
@@ -18,12 +19,16 @@ class TestKalman(unittest.TestCase):
     def setUp(self):
         # Initial Values
         self.A = np.array([[.95, 0], [0., .95]])
-        self.Q = np.eye(2) * 0.5
+        self.C = np.eye(2) * np.sqrt(0.5)
         self.G = np.eye(2) * .5
-        self.R = np.eye(2) * 0.2
+        self.H = np.eye(2) * np.sqrt(0.2)
 
-        self.kf = Kalman(self.A, self.G, self.Q, self.R)
+        self.Q = np.dot(self.C, self.C.T)
+        self.R = np.dot(self.H, self.H.T)
 
+        ss = LinearStateSpace(self.A, self.C, self.G, self.H)
+
+        self.kf = Kalman(ss)
 
 
     def tearDown(self):
@@ -58,8 +63,8 @@ def test_update_using_stationary(self):
 
         kf.update(np.zeros((2, 1)))
 
-        assert_allclose(kf.current_Sigma, sig_inf, rtol=1e-4, atol=1e-2)
-        assert_allclose(kf.current_x_hat.squeeze(), np.zeros(2), rtol=1e-4, atol=1e-2)
+        assert_allclose(kf.Sigma, sig_inf, rtol=1e-4, atol=1e-2)
+        assert_allclose(kf.x_hat.squeeze(), np.zeros(2), rtol=1e-4, atol=1e-2)
 
 
     def test_update_nonstationary(self):
@@ -79,8 +84,8 @@ def test_update_nonstationary(self):
 
         new_xhat = A.dot(curr_x) + curr_k.dot(y_observed - G.dot(curr_x))
 
-        assert_allclose(kf.current_Sigma, new_sigma, rtol=1e-4, atol=1e-2)
-        assert_allclose(kf.current_x_hat, new_xhat, rtol=1e-4, atol=1e-2)
+        assert_allclose(kf.Sigma, new_sigma, rtol=1e-4, atol=1e-2)
+        assert_allclose(kf.x_hat, new_xhat, rtol=1e-4, atol=1e-2)
 
 if __name__ == '__main__':
     suite = unittest.TestLoader().loadTestsFromTestCase(TestKalman)
diff --git a/quantecon/version.py b/quantecon/version.py
index 640621751..c9aac5938 100644
--- a/quantecon/version.py
+++ b/quantecon/version.py
@@ -1,4 +1,4 @@
 """
 This is a VERSION file and should NOT be manually altered
 """
-version = '0.1.7-2'
\ No newline at end of file
+version = '0.1.8'
\ No newline at end of file
diff --git a/solutions/kalman_solutions.ipynb b/solutions/kalman_solutions.ipynb
index 47d7c9ee0..7aa4e305b 100644
--- a/solutions/kalman_solutions.ipynb
+++ b/solutions/kalman_solutions.ipynb
@@ -1,279 +1,1626 @@
 {
- "metadata": {
-  "name": "",
-  "signature": "sha256:bdb5b0e0ae63b5089d0c7a7b9dc7dfe022c47fa05d6868054caf031d2eabc3f6"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
+ "cells": [
   {
-   "cells": [
-    {
-     "cell_type": "heading",
-     "level": 1,
-     "metadata": {},
-     "source": [
-      "quant-econ Solutions: The Kalman Filter"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Solutions for http://quant-econ.net/py/kalman.html"
-     ]
-    },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# quant-econ Solutions: The Kalman Filter"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Solutions for http://quant-econ.net/py/kalman.html"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from quantecon import Kalman\n",
+    "from quantecon import LinearStateSpace\n",
+    "from scipy.stats import norm"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exercise 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "%matplotlib inline"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7f25ce580bd0>"
+      ]
+     },
+     "execution_count": 3,
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 1
+     "output_type": "execute_result"
     },
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import numpy as np\n",
-      "import matplotlib.pyplot as plt\n",
-      "from quantecon import Kalman\n",
-      "from scipy.stats import norm"
-     ],
-     "language": "python",
+     "data": {
+      "image/png": [
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+       "W4HtwKQfk+ddoZK0UNKF6f4i4L24o1wwCWZ2HHhF0tvTU1vxrN/B9PgI8M1KC1GFHAS2SFogz+i+\n",
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+       "E3IWM07/3Y6/e9vTar8ws78Yt40I7BkEQRAEQTAzyhk2IQiCIAiCYE4SClUQBEEQBMEMCYUqCIIg\n",
+       "CIJghoRCFQRBEARBMENCoQqCIAiCIJghoVAFQRAEQRDMkFCogiAIgiAIZsj/A3g6zlxHQ+PPAAAA\n",
+       "AElFTkSuQmCC\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f25ce8079d0>"
+      ]
+     },
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 2
-    },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# == parameters == #\n",
+    "theta = 10  # Constant value of state x_t\n",
+    "A, C, G, H = 1, 0, 1, 1\n",
+    "ss = LinearStateSpace(A, C, G, H, mu_0=theta)\n",
+    "\n",
+    "# == set prior, initialize kalman filter == #\n",
+    "x_hat_0, Sigma_0 = 8, 1\n",
+    "kalman = Kalman(ss, x_hat_0, Sigma_0)\n",
+    "\n",
+    "# == draw observations of y from state space model == #\n",
+    "N = 5\n",
+    "x, y = ss.simulate(N)\n",
+    "y = y.flatten()\n",
+    "\n",
+    "# == set up plot == #\n",
+    "fig, ax = plt.subplots(figsize=(10,8))\n",
+    "xgrid = np.linspace(theta - 5, theta + 2, 200)\n",
+    "\n",
+    "for i in range(N):\n",
+    "    # == record the current predicted mean and variance == #\n",
+    "    m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)]\n",
+    "    # == plot, update filter == #\n",
+    "    ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=r'$t=%d$' % i)\n",
+    "    kalman.update(y[i])\n",
+    "\n",
+    "ax.set_title(r'First %d densities when $\\theta = %.1f$' % (N, theta)) \n",
+    "ax.legend(loc='upper left')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exercise 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "heading",
-     "level": 2,
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PolyCollection at 0x7f25ce6af390>"
+      ]
+     },
+     "execution_count": 4,
      "metadata": {},
-     "source": [
-      "Exercise 1"
-     ]
+     "output_type": "execute_result"
     },
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "\n",
-      "# == Parameters == #\n",
-      "\n",
-      "theta = 10\n",
-      "A, G, Q, R = 1, 1, 0, 1\n",
-      "x_hat_0, Sigma_0 = 8, 1\n",
-      "\n",
-      "# == Initialize Kalman filter == #\n",
-      "\n",
-      "kalman = Kalman(A, G, Q, R)\n",
-      "kalman.set_state(x_hat_0, Sigma_0)\n",
-      "\n",
-      "# == Run == #\n",
-      "\n",
-      "N = 5\n",
-      "fig, ax = plt.subplots(figsize=(10,8))\n",
-      "xgrid = np.linspace(theta - 5, theta + 2, 200)\n",
-      "for i in range(N):\n",
-      "    # Record the current predicted mean and variance, and plot their densities\n",
-      "    m, v = kalman.current_x_hat, kalman.current_Sigma\n",
-      "    m, v = float(m), float(v)\n",
-      "    ax.plot(xgrid, norm.pdf(xgrid, loc=m, scale=np.sqrt(v)), label=r'$t=%d$' % i)\n",
-      "    # Generate the noisy signal\n",
-      "    y = theta + norm.rvs(size=1)\n",
-      "    # Update the Kalman filter\n",
-      "    kalman.update(y)\n",
-      "\n",
-      "ax.set_title(r'First %d densities when $\\theta = %.1f$' % (N, theta)) \n",
-      "ax.legend(loc='upper left')\n"
-     ],
-     "language": "python",
+     "data": {
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+       "jrdUCG7YRcT2ZPj4TCnla9Vh7+kMVN2x3wSOwHs5XccBz4uIG4DPA0+PiM/g/Zy2Usod1ePdwFfJ\n",
+       "YQDv59TdCtxaSvll9frLZCC5s133stMBpJVCZmrN2cAfVc//CPha0/EXRcSciNgfWAH8oob29ayI\n",
+       "CODjwJWllA82veU9naKIWNKY9R4Rc4FnARfhvZyWUspflFKWlVL2B14E/KCU8jK8n9MSETtFxILq\n",
+       "+Tzgt4DL8H5OWSnlTuCWiDioOvRM4ArgHNp0LycrxT4jZZxCZp285iCIiM8DTwOWRMQtwNuB9wJf\n",
+       "iohXAjcCLwAopVwZEV8CrgS2AK+rusU04snAS4FLI+Ki6tjb8J5Ox57ApyNiO/IvMJ8ppfxndV+9\n",
+       "lzPXuDf+uzk9S4Gv5t85mA18rpTy3Yi4AO/ndLwR+FzVgXAdWWh0Fm26lxYikyRJXdfxQmSSJEmj\n",
+       "GUAkSVLXGUAkSVLXGUAkSVLXGUAkSVLXGUAkSVLXGUAkSVLX/X9SFyTehXTAMQAAAABJRU5ErkJg\n",
+       "gg==\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f25ce7f0710>"
+      ]
+     },
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 3,
-       "text": [
-        "<matplotlib.legend.Legend at 0x7f37121404d0>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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KiooYMWIEAEuWLGHu3LmA9Sm/H/3oR43P77//fmw2m5IpEYm5PV4vfiC/nf37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\n8WL4razDEmmbEioRkThzrKaGar+ffu2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wdrEeKhnm6Rg/g4HmJhN7HW1M71q71FlUoMp+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iD29VgCagRQ6y79BoMK/bRvD+vXwwMPwC23wJ13QpwT45gqs49btOCnxETmnb+WRtM0mn/cnGNT\nj5Edm+3cokajqq2uXKlKgBVkQLMBLB6zmHsX3ctX276qsM91F0moPKSgQB2uaN0ajh9XP3k9/bRq\nwhTC1xxPOU7v6b2pEVyDn0b9VPw0H8DRo3DDDSS8+y7DAwP5vEULmppMusWQti2NuA/jaDGthYxJ\n8GIGg7oHcP9+aNBAJVmvvqp6T31BNX9/5rVpwwMHD7I3IwMAc3Mz9Z+oz96xe7EVOFkJCguDpUtV\n49q0aTpGXLpudbvx5/g/+c/q//Dc8uew2ipvPVcSqgpms6km8/bt1d/Z2bPVDewyxE74qr9P/E2P\nL3twe7vb+XLIl8XnTIH6qaNfP/KeeoqR0dGMrVmTm6OidIvBmmNl37h9NH2rKUH19Bu9INzHYoH/\n/Ac2b1Y/kLZsCZ9/XmFtQB7VJTSU/zZpwi27d5OWry5KbvB0AzRNI/a/sc4vXK8eLFsGU6bADz/o\nE6wDWlRrwYZ7NrD+xHqGzR5Gak7lvNxReqgqiM2mWj+ef15dajx1KgwcKA3nwnfZbDY+3fwpL696\nmelDp3NTi5vsv/DUKejTB9v99/PIkCH8k5XFL+3a6Vrq+//2zjw6qiJd4L/upDtLZyP7AtlMQthR\nRBFEQEBRUXyiDxdGfeqIOsq8467okXHOGVcUGQdRRwXEARwXFheegGwiMAokJBCyYSAhC1nI0p2k\nt1vvj0pMwJCFtOkE6ndOnbr3prruR3Hr3q+++uqr3Lm5WAutDPliiLJO9VF275arovPyZD57toxr\ndS7zx+xsSm02vhwyBE+9nsaiRvaO2svQNUMJvCzw7CtOT4errpL+VLfc4jqBO8DmtDH327lsP7qd\nz/77MwaHDe74R78jXfWh6knE+YimCbFxoxATJwqRkiLE6tVCOJ3ulkqhcC+1jbXi1s9uFcPfGS6y\nK7LPXDA/X4ikJCH+9jfxUkGBGLJnj6iy2VwqS8myErE7abewnXRtvQr3sG2bEBMmCJGcLMSKFUI4\nHO6W6PfD6nSKq9LSxD1ZWULTNCGEEOVrysWu+F3CVtnN5zktTYjISCE++qj7gnYBTdPEB/s+EKGv\nhorlact79N6nA/RaK5BbG6ansduFWLVKiIsuEmLQIPlM2u3ulkqhcD+7CneJ5EXJ4t6194p6W/2Z\nC6alCRETI8Q//iHeO35cxO/aJYoaG10qS+3PteKHsB+EOdPs0noV7kXThNi0SYixY6U+vnixEBaL\nu6X6faiz28Xon38W8/Lzf72W+1iu2Ddhn3Bauzl6z8oSYsAAIRYt6qaUXedA6QEx8O8DxV1f3iWq\nG6p7/P5CKIXK7dTXy86bmCjEuHFCrFunLFIKhRBCWB1WMW/zPBHxWoT498F/t19482YhwsOFWL1a\nfFpWJqJ27hQ5Lv4iNhY3ih9jfxQnPj/h0noVvQdNE2LHDiFmzBAiLEyI554TorTU3VK5nhNWq0je\nvVu8cvSoEEIIzaGJAzMOiEN3HvrVcnXWHDkiRGqqEH/+c49bBeqsdWLO+jki9s1YsfnI5h69txBd\nV6iUD5WLyM2Fd9+Vu6Rfdhk89RSMG+duqRSK3sGuwl3M+WoOsYGx/POGfxLpd4awBELIAEMvvwwr\nV/JRairP/vIL3w4bxkgXBu+0V9rZP2E/EbdHEPesCuB5PpCTA2++KRcCzZwJDz0kt/Y6VyhqbGRK\nejqzwsOZHx+PVq+xf8J+QmeEEv98fPcqr66WgT89PWV4hcBu+GedBRvyNnDfuvuYnjKdlya/RD+f\nfj1yXxWHqgex2+UmnlOnSuXJw0M6Rq5bp5QphQLgZMNJHvzqQWZ+OpNnxz/L+tvWn1mZqq+XUZuX\nLoXdu3kzKYn5BQVsHTnSpcqUo9bBgWkHCJkeQuwzsS6rV9G7SUmBd96RilV8vIxjNWqUHAjX9s1F\nZafQ39ub7RdeyJqKCh7Pz0fvq2fY+mGULi2lcEFh9yoPCpLbeCQmwujRMnR9DzItaRqZD2XiofNg\n8OLBrDiwgt5ooFEWqrMgIwM++USGO0hMhAcegJtvBi8vd0umUPQO7E47S35ewl+3/5WZg2by0pSX\nfru5cWv27YM77oDRo3G88w5Pl5SwvrKSjSNGEOvtujAGjhoHGdMzMA03kfx2slrRdx7jdMLGjTJ8\nzfffS6vVvffKIMt9+bGostuZnpFBjJcXS1NT8Si2k35lOpH3RhL3tAussStXwty58MIL8Kc/9Xhj\n7Snaw4NfP4iPwYcFVy1gTP8xv9u9umqhUgpVJykslM/RJ5/IPSRvv11G6R061N2SKRS9B01ofH7o\nc57f8jxxQXEsuGoBQ8Pb6SQOB7z+OrzxBixaROXMmcw6eBC9TsfKwYMJMbQRk+osaSxsJOPaDIIm\nBpH0VhI6fR/+aipcSmkpfPSRdNmw2eDWW2UaNqxvKleNTicP5OSQZjazdtgwIit1pE1OI3xWOPHz\n47s/kMjLkw0UFgZLlkBcz06bOzUnHx/4mOe+f47LYy/nLxP/wsDQgS6/j1KoXEhBAaxdK6f1MjPl\nCOaOO+RmnS7c2F6h6PNoQmPN4TXM3zofH4MPL058kauTrm7/R817iISFwQcfsCswkDuysrg5LIy/\nJSTg6cJOZs4wk3FdBjFzYxjw2ABlmVK0iRByNmvlSulr5e8Pt90mpwcHDepbypUQgreKinj52DGW\npKRwjTOAzBsy8U70JvXDVDx8Pbp3A7sdXn1VOqa98IJ0SvPoZp1dxGKzsHD3QhbuWci0pGk8f8Xz\npISkuKx+pVB1g+bOtGaNVKSKi+V+kTNmwNVXqyk9heJ0GuwNfHzgYxbsWkCgVyAvTHiBa5OvbV9h\nKS6WkRe/+QbeeAPrLbfwQkEBS0tLeSclxaUR0IUQlC4r5cgTR0halETEbREuq1txbqNpUudftUp+\nDwwG+T24/nq576oLjae/Kz/W1HBnVhZXBAXxRv9ESh7Kx5JpYeiXQ/GOc8F0+uHDcP/9UFMjLc2T\nJ3e/zi5Sa61l0Z5FvLXnLcbHjufxsY8zdsDYbterFKouUloqI5hv3ChzHx+48UaZLrusxxVuhaJP\nkFeVx3t732Np2lIu7X8pT4x9gvGx49tXpKqr5Yj23Xfhnntg3jy2CMEjubmk+PqyJCWFcBduZumo\nc5DzYA7m/WYGrx6M31A/l9WtOL8QQgYPX79eptxcuRhpyhSpPyQm9m7rldnh4LH8fL6tquL1xETG\nrLBS+Eohia8mEnlXZPcttkLIqZwnn5SmvBdfdMsSSovNwtK0pby5+02CfYJ54OIHmDVkFiaj6azq\nUwpVB5w4ATt3wo4dUokqKoJJk2TnmDoVLrigd3cMhcJd1Fnr+CLrC5YfWE5GWQZ3j7yb+0fdT1Jw\nUvs/LC6GhQvhgw/kSGX+fPJDQ3kiP5/9ZjOvJSYyMyzMZdNwQgjKPy8n/9F8gqcFk7QwqfvTGwpF\nK0pKYMMG6cy+ebO0Vk2eDFdeCRMmwIAB7pawbXZUV/NIbi79DAZes0QhHjqGd5w3yYuTXbOHpdUq\nfapeew1GjIB586Rlooc/qk7NyYa8Dby79112Fu7kptSbuHXorUyIn4CnvvP7ESmFqhVOp7RG7tol\nlaidO6VCddllcPnlsgNcfPG5v9+TQnG2VNRX8E3uN6zLXsemI5uYED+B2cNmc/3A6/H2bOcFLAT8\n+KO0Rn31lVzB8eij5ISF8fKxY6ytqODRAQN4tH9/fFxoBjZnmsl/LB/rcSspi1MIuqKdlYUKhQsQ\nArKzpWK1eTP88AMYjfI7M3aszC+8sPe4jDg0jfdLSvjr0aOM8fbj8U+90N4vJ/rBaGKfisXT3wUf\nxMZG6eX/+usQHCxXA86aJaeAepjCmkJWZa5i9cHVFNUWMXPQTGYNncXlsZej17Xvp3neKlQ2m1Se\n9u2DvXtlnp4OUVFyGey4cTINHqym8RSKMyGEIKcyh/U561mXvY70snQmJ0zmhoE3MD1lOqG+oe1X\nUFAAq1fD8uVyBd+cOWh33sn3ej1LiovZVlPDwzExPBITQ7ALnVDMB8wUvFhAzQ81xD4VS8zDMegN\nauWIoucRAo4ckeOJXbtkysmB1FSpWDWn4cPBz42z0A1OJ++XlPDKsWNcWufDnA/Bb3sD/efGEP1A\nNIZ+LuifTqc05b39NuzZI1d2/eEP0qLhhpVdeVV5fHrwU1ZlrqKivoKrk65mauJUJidMJsLvt/6V\n57xCZbFIxenQIcjKakkFBTJY26hRMl10kXxoezigq0LRp9CERkZZBjuO7ZDp6A70Oj3XJV/HjNQZ\nXJlwZceWqIwM+Ppr6bmbny9fmrffTvaoUXxaXs6y0lJMHh48EB3N7IgI/F1kEtZsGhVfVlD8bjH1\nWfUMeGIA0XOi8TCpEZOid2GxwIEDsH+/XPi0f7/8hsXESEUrNRUGDmw5DgnpOdmsmsYX5eUsLi7G\nnmnh4S+NDNhiJXp2JFH3ReE3wkVaX1GRjDu0YgVUVsrVXjfeKD383WC5yq3M5bv879h4ZCNbC7YS\nFxTH1MSpTIqfxJj+YwjxDen7CpWmQVmZVJBap19+kWbV8nJITpZ+b4MGSYvToEHyWm8xqSoUvRGH\n5iC3Mpe00jTSy9JJK01jz/E9hPmGMT52PFfEXcH4uPEkBCWc2Z9J06RH7s6dsGWLTEYjTJ+Offp0\ndl90ERtqa/mqspJyu52bw8K4PTycSwMCXOIjpdk0qrdUU/5ZORVrKzANMxE9J5rQG0PRG5VFStF3\nsNtlV8rOlkaC5jwrS3apgQNlSkiQYZ6aU0zM7+emkmk2s/LECTZkljFpjZMr/0/g3c9A/OxIImaE\n4Zvq6xpfx+xsOQBbu1ZOJY0cKZ3PJkyQ86Q9bLpzaA5+Ov4TG49sZNvRbfx0/Cei/KPIeSQHXKxQ\nTQMWAh7AP4FX2iizCLgGqAfuBva3UUbU1gpKS6VDX2kppxwXF0vF6dgxCAiQ1qbWKS5Obh2QkHB+\nTtlt3bqViRMnuluMPsn51nYnG06SW5VLXlUeeVV55FblcrjiMIfKDxHlF8WIyBGMjBjJiMgRXBJz\nyZm3grFaITeXrf/6FxPr6+U8eloahIYixoyheMoUMi++mN3+/uysrWVPbS0X+PgwLTiYa4KDGRsY\niEc3X76aTcOSYaF6ezXV31dTvaMa0yATYTeHEXpTKD4JPT+y7Srn2/Pnas639hNCGhWalayCAjh6\nVKZjx+TfIiPlNzE2Fvr3l+cRES15RIR0Xdq+/ezaTgjBfrOZb8orOLypnOiv6xn7Hx1Gowcek/yJ\nmhhM0qRQfONc0P/MZjkvum0bbN8u3zOpqdKpfdiwlhQe3v17dRKn5iTzRCYjo0aCCxUqDyAbmAIc\nB34CbgOyWpW5Fni4Kb8UeAtoKxa88PUVREVJv6bISJmaj6OiWhQnX9/Oin/+MH/+fObPn+9uMfok\n50LbOTUn1Y3VVDZUUlFfQWV9JWWWMopqizhee5yiOpkX1hbi1JwkhySTFJxEUr8kkkOSSQ5OZnjE\ncPy9Wu2J19jYMqopKZGOH3l5vyZRUkL1oEE8azBw/X33kZ+cTGZoKAcdDg7W12PU6RhiMnGJvz9j\nAwMZGxBA6FmGPXA2OGnIb6Aht4GGnAbqc+uxZFiwZFrwSfQhYGwA/Sb3I2hSEMYw14VW6AnOhefP\nnaj2OxW7Xc6eNStZxcWyG5eVnZpbLODlNZ/k5Pn060enk7+/tJC1ps7hYHdNDfv2VGDZUoP/z40k\npWsYhA5zsiceg3wwDTYROtyfAcMDiYjyQX+2PlINDVKpysg4NTWb7eLiTrW0xMVJJcLPz+WrCbs6\n5deR4fASIA8oaDpfBczgVIXqBmBZ0/EeIAiIAMpOr8xi6axYCkXfw6k5sTqtWB3WDvNGRyNmm5k6\nWx1mm/nXVGetw2yXeVVD1a8KVE1jDQFeAYR6BxPl2Y9oz35EGfoRawxjsGcU0V6DiYgKJDzGnwAr\n6GpqEEdrsGbUUl93gPr63RQ3NFDf2Ei9xYLFYqFeCGqio6mMjqYqLIyq8HCqkm59itQAAAaKSURB\nVJOp8PenyGikSNPw0OkwLl/OkTFjSPTxYZivL7eZTAwxmQg77a0rnAJnvRPNpqE1ajjrnDhrnTjq\nHDhrnTjrnNgr7NjKbNhO2LCXNR2XynOfBB98kn3wSfEhYHQAkXdF4nehH55+ahmuQtGMwSBnahIS\n2i9ntcLTT8tt0qqr4eTJU9Mvv7R93WyWVjKTSSY/PzCZPDGZQvDzC5HXYyF7mB3NuwZjQxW+1WaC\nN1URvqyMsiINr0Y4GaLDHKLHEuqBLcSACPbEM8CAV5ABrwADxiBPvIMMePsZ8DN5YjJ54m8yEOBv\nwDRkLIaR4/D0lDNSHnqBrvi4HOw1m+x++EH6Yx09KpfvO53SitWcQkLkdJe/v8zbOvb2lsnL69Tc\naDwr5ayjN1UM0Hqb6iKkFaqjMv1pQ6FaMnTNGW+k64wS2IELlg4QHdSjE7Svb3bCb14nOi7W4b+n\nM/dpVWxvRTbvr1rfhiw6l/x7fr1hu79v50ad/Pe0Syfu1Xy1rdvpTv9DU+H9Vbl8tOKblsutypz6\nvIhWZVru1NYz1ZmupvuNLLpWJz6AD34ijN94C4jT6hetD3QIXXMCdDos6MjR6cgBeR0QulCaH3W9\nkKZmPXLE5QHo9Xp0Oh2mEzoC03WkoMNDp8NTh1SidHoMOnntvRId9/9sRzhtaLaTCJsg16qRYxNo\nNg3RlCNA76VHZ9Sh99bj4e+BZ4DnqXmwJ8YIIwGXBGCMMGKIMGCMNOLV3wu9p/KBUihchZeXXJQ1\nenTXf2u3SwOI2Szzto8NNDSEYrWGYu0HddFQMQT2W6HBasVhNYO1HmNDI74nrfiU2DHaG/C21+Fr\n1fBt1BCNAqddYHcILHaotoHRATYD2Iwy2T1A0zclHWi6BDR9AkIHmk4nr4Ujz/UCagWiVkC+AJ1A\nJwQ6nUC+7ZuTFUSjvN78d9Fcns595Nugo+/CTKQP1R+bzmcjFapHWpVZD7wM7Gw63wQ8Cew7ra48\n4IKui6hQKBQKhULR4+QDHUQubqEjC9VxoHXM1wFIC1R7Zfo3XTudTgulUCgUCoVCcS7hidTQ4gEj\nkAYMOq3MtUDzfMoYYHdPCadQKBQKhULRV7gGudIvD3im6dqcptTM201/Twd6fkdEhUKhUCgUCoVC\noVAoFAqFoiMKgAPIgJ//ca8ofY4g4DNkqIpDtB3jS9E2A5HPXHOqAea6VaK+xzPAQSAD+Beg9iPo\nPH9Gtltm07GifT5Erg7PaHUtGNgI5ADfId+HirZpq/1uQfZfJ2r2qCPaar/XkN/edOALoFdsZvcL\nsmMous4y4J6mY096yX9oH0QPlHDqAgpF+8QDR2hRolYDd7lNmr7FUOSL2RsZtWIjapVzR4wHLuTU\nD9qryFXjAE8hV5Qr2qat9ksFUoAtKIWqI9pqv6nIbwfIZ6/d568nA7/05L6B5wqByP/kD5vOHUgr\ni6LrTEEusCjsqKDiV2oBO+CLVOZ9aXsFr+K3pCIDHTcirQPbgJvcKlHvZwdw8rRrrQNHLwNu7FGJ\n+hZttd9hpHVP0TFttd9GQGs63oOMYnBGekqhEsj4VD/TEtNK0TEJQDnwETKu1/vIj5qi69yKnLJS\ndJ4qYAFwDCgGqpH9WNExmcjBUDCyz15HBy9jRZu03nWjrOlcoXAH99AS0aBNekqhGoc0pV0D/An5\nolF0jCfSTLu4KbcAT7tVor6JEbge+Le7BeljXAD8L3LqLxrwA+5wp0B9iMPIjeS/A75F+vBp7f5C\n0RGCs4pfrVB0m3mAjQ4G5T2lUJU05eXAl8g9AhUdU9SUfmo6/ww1D342XAPsRT5/is5zMfAjUImc\nbv4CGOtWifoWHyLbcALSupftXnH6JGVAZNNxFHDCjbIozk/uRsbb7HAw2RMKlS/QvMW9CbiKU52+\nFGemFOnzk9J0PgW5YkPRNW4DVrpbiD7IYeSqUh+kD+QU5EpTRecIb8pjgf9CTTmfDetoWQhxF3Dm\nDWEVHaH8mLvONOAJYAbSH9LtJCAjrKch/Qqeab+44jRGIC1UvWrZZh/CBFTQotQrusaTtIRNWAYY\n3CtOn2I7su3SgElulqUvsBLpq2dDDiT/B+mDtgkVNqEznN5+9yCd+AuBBuQA/Vu3Sdf7aav9coGj\ntITeWew26RQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKhUKhUCgU\nCoVCoVAoFAqFQqFQKBS9lv8H7t096QdEh9kAAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f37122214d0>"
-       ]
-      }
-     ],
-     "prompt_number": 3
-    },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from scipy.integrate import quad\n",
+    "\n",
+    "epsilon = 0.1\n",
+    "theta = 10  # Constant value of state x_t\n",
+    "A, C, G, H = 1, 0, 1, 1\n",
+    "ss = LinearStateSpace(A, C, G, H, mu_0=theta)\n",
+    "\n",
+    "x_hat_0, Sigma_0 = 8, 1\n",
+    "kalman = Kalman(ss, x_hat_0, Sigma_0)\n",
+    "\n",
+    "T = 600\n",
+    "z = np.empty(T)\n",
+    "x, y = ss.simulate(T)\n",
+    "y = y.flatten()\n",
+    "\n",
+    "for t in range(T):\n",
+    "    # Record the current predicted mean and variance, and plot their densities\n",
+    "    m, v = [float(temp) for temp in (kalman.x_hat, kalman.Sigma)]\n",
+    "    \n",
+    "    f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v))\n",
+    "    integral, error = quad(f, theta - epsilon, theta + epsilon)\n",
+    "    z[t] = 1 - integral\n",
+    "    \n",
+    "    kalman.update(y[t])\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(9, 7))\n",
+    "ax.set_ylim(0, 1)\n",
+    "ax.set_xlim(0, T)\n",
+    "ax.plot(range(T), z) \n",
+    "ax.fill_between(range(T), np.zeros(T), z, color=\"blue\", alpha=0.2) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Exercise 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
     {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "Exercise 2"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Eigenvalues of A:\n",
+      "[ 0.9+0.j -0.1+0.j]\n",
+      "Stationary prediction error variance:\n",
+      "[[ 0.40329109  0.1050718 ]\n",
+      " [ 0.1050718   0.41061711]]\n"
      ]
     },
     {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "\n",
-      "from scipy.integrate import quad\n",
-      "\n",
-      "epsilon = 0.1\n",
-      "kalman = Kalman(A, G, Q, R)\n",
-      "kalman.set_state(x_hat_0, Sigma_0)\n",
-      "\n",
-      "T = 600\n",
-      "z = np.empty(T)\n",
-      "for t in range(T):\n",
-      "    # Record the current predicted mean and variance, and plot their densities\n",
-      "    m, v = kalman.current_x_hat, kalman.current_Sigma\n",
-      "    m, v = float(m), float(v)\n",
-      "    f = lambda x: norm.pdf(x, loc=m, scale=np.sqrt(v))\n",
-      "    integral, error = quad(f, theta - epsilon, theta + epsilon)\n",
-      "    z[t] = 1 - integral\n",
-      "    # Generate the noisy signal and update the Kalman filter\n",
-      "    kalman.update(theta + norm.rvs(size=1))\n",
-      "\n",
-      "fig, ax = plt.subplots(figsize=(9, 7))\n",
-      "ax.set_ylim(0, 1)\n",
-      "ax.set_xlim(0, T)\n",
-      "ax.plot(range(T), z) \n",
-      "ax.fill_between(range(T), np.zeros(T), z, color=\"blue\", alpha=0.2) \n",
-      "\n",
-      "\n"
-     ],
-     "language": "python",
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7f25ce497190>"
+      ]
+     },
+     "execution_count": 16,
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 4,
-       "text": [
-        "<matplotlib.collections.PolyCollection at 0x7f37120c0610>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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ASU83d8O9+GJWu0REpHcKIF4aMMB1iulXX3H32RNPNBfq6i2AbN3KwGJFGRlA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\nXQogIuK1yy7jgNKbb3Z9fuZMDlL1ZMo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-       "text": [
-        "<matplotlib.figure.Figure at 0x7f37121038d0>"
-       ]
-      }
-     ],
-     "prompt_number": 4
+     "output_type": "execute_result"
     },
     {
-     "cell_type": "heading",
-     "level": 2,
+     "data": {
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+       "n/WrOC6tgKTdEhW6pI7ASXj55DgerYCZ/dzMBpjZPsC/Ai+b2XnE8Wg1JHWS1DX8vzNwMt7sLa8x\n",
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+       "HhvHZScjaTguHisJj/vM7BpJvYjj0apIOg74qZmdEcej9ZC0D+6NAJc+PGBmV+c7JrFoVSQSiUQi\n",
+       "kaIoqmhVJBKJRCKRSDQmIpFIJBKJFEU0JiKRSCQSiRRFNCYikUgkEokURTQmIpFIJBKJFEU0JiKR\n",
+       "SCQSiRRFNCYikUgkEokURTQmIpFIJBKJFMX/A2mkjZ11RYHJAAAAAElFTkSuQmCC\n"
+      ],
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f25ce497050>"
+      ]
+     },
      "metadata": {},
-     "source": [
-      "Exercise 3"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from __future__ import print_function  # Remove for Python 3.x\n",
-      "from numpy.random import multivariate_normal\n",
-      "from scipy.linalg import eigvals\n",
-      "\n",
-      "\n",
-      "# === Define A, Q, G, R === #\n",
-      "G = np.eye(2)\n",
-      "R = 0.5 * np.eye(2)\n",
-      "A = [[0.5, 0.4], \n",
-      "     [0.6, 0.3]]\n",
-      "Q = 0.3 * np.eye(2)\n",
-      "\n",
-      "# === Define the prior density === #\n",
-      "Sigma = [[0.9, 0.3], \n",
-      "         [0.3, 0.9]]\n",
-      "Sigma = np.array(Sigma)\n",
-      "x_hat = np.array([8, 8])\n",
-      "\n",
-      "# === Initialize the Kalman filter === #\n",
-      "kn = Kalman(A, G, Q, R)\n",
-      "kn.set_state(x_hat, Sigma)\n",
-      "\n",
-      "# === Set the true initial value of the state === #\n",
-      "x = np.zeros(2)\n",
-      "\n",
-      "# == Print eigenvalues of A == #\n",
-      "print(\"Eigenvalues of A:\")\n",
-      "print(eigvals(A))\n",
-      "\n",
-      "# == Print stationary Sigma == #\n",
-      "S, K = kn.stationary_values()\n",
-      "print(\"Stationary prediction error variance:\")\n",
-      "print(S)\n",
-      "\n",
-      "# === Generate the plot === #\n",
-      "T = 50\n",
-      "e1 = np.empty(T)\n",
-      "e2 = np.empty(T)\n",
-      "for t in range(T):\n",
-      "    # == Generate signal and update prediction == #\n",
-      "    y = multivariate_normal(mean=np.dot(G, x), cov=R)\n",
-      "    kn.update(y)\n",
-      "    # == Update state and record error == #\n",
-      "    Ax = np.dot(A, x)\n",
-      "    x = multivariate_normal(mean=Ax, cov=Q)\n",
-      "    e1[t] = np.sum((x - kn.current_x_hat.flatten())**2)\n",
-      "    e2[t] = np.sum((x - Ax)**2)\n",
-      "\n",
-      "fig, ax = plt.subplots(figsize=(9,6))\n",
-      "ax.plot(range(T), e1, 'k-', lw=2, alpha=0.6, label='Kalman filter error') \n",
-      "ax.plot(range(T), e2, 'g-', lw=2, alpha=0.6, label='conditional expectation error') \n",
-      "ax.legend()\n",
-      "\n"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "Eigenvalues of A:\n",
-        "[ 0.9+0.j -0.1+0.j]\n",
-        "Stationary prediction error variance:\n",
-        "[[ 0.4032911   0.10507181]\n",
-        " [ 0.10507181  0.41061712]]\n"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 6,
-       "text": [
-        "<matplotlib.legend.Legend at 0x7f3711fb4d90>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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0AgoTIiKSGhs2bOC2227j4MGDE92UaUU9EyIictKora0lEAhQV1c30U2ZVhQm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\nuHHjxo0bN27cuHHjxo0bN27cDC3/H3sLA39Q2P60AAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f371205eb50>"
-       ]
-      }
-     ],
-     "prompt_number": 6
+     "output_type": "display_data"
     }
    ],
-   "metadata": {}
+   "source": [
+    "from __future__ import print_function  # Remove for Python 3.x\n",
+    "from numpy.random import multivariate_normal\n",
+    "from scipy.linalg import eigvals\n",
+    "\n",
+    "\n",
+    "# === Define A, C, G, H === #\n",
+    "G = np.identity(2)\n",
+    "H = np.sqrt(0.5) * np.identity(2)\n",
+    "\n",
+    "A = [[0.5, 0.4], \n",
+    "     [0.6, 0.3]]\n",
+    "C = np.sqrt(0.3) * np.identity(2)\n",
+    "\n",
+    "# === Set up state space mode, initial value x_0 set to zero === #\n",
+    "ss = LinearStateSpace(A, C, G, H, mu_0 = np.zeros(2))\n",
+    "\n",
+    "# === Define the prior density === #\n",
+    "Sigma = [[0.9, 0.3], \n",
+    "         [0.3, 0.9]]\n",
+    "Sigma = np.array(Sigma)\n",
+    "x_hat = np.array([8, 8])\n",
+    "\n",
+    "# === Initialize the Kalman filter === #\n",
+    "kn = Kalman(ss, x_hat, Sigma)\n",
+    "\n",
+    "# == Print eigenvalues of A == #\n",
+    "print(\"Eigenvalues of A:\")\n",
+    "print(eigvals(A))\n",
+    "\n",
+    "# == Print stationary Sigma == #\n",
+    "S, K = kn.stationary_values()\n",
+    "print(\"Stationary prediction error variance:\")\n",
+    "print(S)\n",
+    "\n",
+    "# === Generate the plot === #\n",
+    "T = 50\n",
+    "x, y = ss.simulate(T)\n",
+    "\n",
+    "e1 = np.empty(T-1)\n",
+    "e2 = np.empty(T-1)\n",
+    "\n",
+    "for t in range(1, T):\n",
+    "    kn.update(y[:,t])\n",
+    "    e1[t-1] = np.sum((x[:,t] - kn.x_hat.flatten())**2)\n",
+    "    e2[t-1] = np.sum((x[:,t] - np.dot(A, x[:,t-1]))**2)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(9,6))\n",
+    "ax.plot(range(1, T), e1, 'k-', lw=2, alpha=0.6, label='Kalman filter error') \n",
+    "ax.plot(range(1, T), e2, 'g-', lw=2, alpha=0.6, label='conditional expectation error') \n",
+    "ax.legend()\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
   }
- ]
-}
\ No newline at end of file
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}