Fixed inconsistency in covariances.

I had changed my example from (8,10) to (8,4), but did not change
it everywhere.

06_Multivariate_Kalman_filter/Multivariate_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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@@ -261,7 +261,7 @@
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@@ -395,7 +395,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3294246240>"
+        "<matplotlib.figure.Figure at 0x7f1a474cbf60>"
        ]
       }
      ],
@@ -405,7 +405,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "Here we have plotted a two dimensional multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}8&0\\\\0&10\\end{smallmatrix}]$. The three dimensional shape shows the probability of for any value of (x,y) in the z-axis. I have projected just the variance for x and y onto the walls of the chart - you can see that they take on the normal Gaussian bell curve shape. You can also see that, as we might hope, that the curve for x is wider than the curve for y, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. Also, the highest point of the curve is centered over (2,17), the means for x and y. I hope this demystifies the equation for you. Any multivariate Gaussian will create this sort of shape. If we think of this as a the Gaussian for our dog's position in a two dimensional field, the z-value at each point of (x,y) is the probability density forthe dog being at that position. So, he has the highest probability of being near (2,17), a modest probability of being near (5,14), and a very low probability of being near (10,10).\n",
+      "Here we have plotted a two dimensional multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}10&0\\\\0&4\\end{smallmatrix}]$. The three dimensional shape shows the probability of for any value of (x,y) in the z-axis. I have projected just the variance for x and y onto the walls of the chart - you can see that they take on the normal Gaussian bell curve shape. You can also see that, as we might hope, that the curve for x is wider than the curve for y, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. Also, the highest point of the curve is centered over (2,17), the means for x and y. I hope this demystifies the equation for you. Any multivariate Gaussian will create this sort of shape. If we think of this as a the Gaussian for our dog's position in a two dimensional field, the z-value at each point of (x,y) is the probability density forthe dog being at that position. So, he has the highest probability of being near (2,17), a modest probability of being near (5,14), and a very low probability of being near (10,10).\n",
       "\n",
       "We will discuss the mathematical description of covariances in the Kalman Filter math chapter. For this chapter we just need to understand the following.\n",
       "\n",
@@ -455,7 +455,7 @@
      "source": [
       "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n",
       "\n",
-      "First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2, 7) with a variance of 8 for $x$ and a variance of 10 for $y$.\n",
+      "First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2, 7) with a variance of 8 for $x$ and a variance of 4 for $y$.\n",
       "\n",
       "Start by setting $x$ to (2.5, 7.3):"
      ]
@@ -469,7 +469,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 4
+     "prompt_number": 52
     },
     {
      "cell_type": "markdown",
@@ -487,7 +487,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 5
+     "prompt_number": 53
     },
     {
      "cell_type": "markdown",
@@ -501,12 +501,12 @@
      "collapsed": false,
      "input": [
       "P = [[8.,  0.], \n",
-      "     [0., 10.]]"
+      "     [0., 4.]]"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 6
+     "prompt_number": 54
     },
     {
      "cell_type": "markdown",
@@ -528,11 +528,11 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "0.01744\n"
+        "0.02739\n"
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 55
     },
     {
      "cell_type": "markdown",
@@ -563,7 +563,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293a3e9e8>"
+        "<matplotlib.figure.Figure at 0x7f1a23301518>"
        ]
       }
      ],
@@ -616,7 +616,7 @@
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        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937da240>"
+        "<matplotlib.figure.Figure at 0x7f1a22fbf7b8>"
        ]
       }
      ],
@@ -714,7 +714,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293a8ccf8>"
+        "<matplotlib.figure.Figure at 0x7f1a23b46b38>"
        ]
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@@ -741,7 +741,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f32939bf400>"
+        "<matplotlib.figure.Figure at 0x7f1a23058668>"
        ]
       }
      ],
@@ -768,7 +768,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937ec8d0>"
+        "<matplotlib.figure.Figure at 0x7f1a23076550>"
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@@ -799,7 +799,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293a9b048>"
+        "<matplotlib.figure.Figure at 0x7f1a232bfba8>"
        ]
       }
      ],
@@ -864,7 +864,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293545cc0>"
+        "<matplotlib.figure.Figure at 0x7f1a232cab70>"
        ]
       }
      ],
@@ -2002,9 +2002,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937a8e10>"
+        "<matplotlib.figure.Figure at 0x7f1a22f8df28>"
        ]
       },
       {
@@ -2012,7 +2012,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293a2b668>"
+        "<matplotlib.figure.Figure at 0x7f1a22fa6828>"
        ]
       }
      ],
@@ -2179,9 +2179,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937a8080>"
+        "<matplotlib.figure.Figure at 0x7f1a2338e898>"
        ]
       },
       {
@@ -2189,7 +2189,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f329357c400>"
+        "<matplotlib.figure.Figure at 0x7f1a2312a0b8>"
        ]
       }
      ],
@@ -2423,9 +2423,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32939e2e48>"
+        "<matplotlib.figure.Figure at 0x7f1a233b4ba8>"
        ]
       }
      ],
@@ -2495,7 +2495,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293871278>"
+        "<matplotlib.figure.Figure at 0x7f1a23381630>"
        ]
       },
       {
@@ -2503,7 +2503,7 @@
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-        "<matplotlib.figure.Figure at 0x7f32938710b8>"
+        "<matplotlib.figure.Figure at 0x7f1a23381898>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f329357ce48>"
+        "<matplotlib.figure.Figure at 0x7f1a22f8d2b0>"
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@@ -2575,7 +2575,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32939cd940>"
+        "<matplotlib.figure.Figure at 0x7f1a230653c8>"
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@@ -2604,7 +2604,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f32938369e8>"
+        "<matplotlib.figure.Figure at 0x7f1a22f86390>"
        ]
       }
      ],
@@ -2673,7 +2673,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937c5b38>"
+        "<matplotlib.figure.Figure at 0x7f1a230e2c18>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32939145f8>"
+        "<matplotlib.figure.Figure at 0x7f1a2328f630>"
        ]
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@@ -2775,7 +2775,7 @@
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-        "<matplotlib.figure.Figure at 0x7f32938ee518>"
+        "<matplotlib.figure.Figure at 0x7f1a23270a90>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f32938ee940>"
+        "<matplotlib.figure.Figure at 0x7f1a2326c588>"
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@@ -2838,7 +2838,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f329389bba8>"
+        "<matplotlib.figure.Figure at 0x7f1a232d2ac8>"
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@@ -2869,7 +2869,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293ae8cc0>"
+        "<matplotlib.figure.Figure at 0x7f1a230032e8>"
        ]
       }
      ],
@@ -2940,17 +2940,17 @@
       {
        "metadata": {},
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f329358c4e0>"
+        "<matplotlib.figure.Figure at 0x7f1a23299b38>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293a21f98>"
+        "<matplotlib.figure.Figure at 0x7f1a2329eac8>"
        ]
       }
      ],
@@ -3025,7 +3025,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f32937949b0>"
+        "<matplotlib.figure.Figure at 0x7f1a232e3b70>"
        ]
       }
      ],
@@ -3097,9 +3097,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f3293674da0>"
+        "<matplotlib.figure.Figure at 0x7f1a23298a90>"
        ]
       }
      ],
@@ -3151,11 +3151,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f329357c2b0>"
+        "<matplotlib.figure.Figure at 0x7f1a23298518>"
        ]
       }
      ],
-     "prompt_number": 85
+     "prompt_number": 47
     },
     {
      "cell_type": "markdown",
@@ -3195,11 +3195,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f329357cc50>"
+        "<matplotlib.figure.Figure at 0x7f1a22ef1f98>"
        ]
       }
      ],
-     "prompt_number": 87
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
@@ -3229,11 +3229,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f329b700cf8>"
+        "<matplotlib.figure.Figure at 0x7f1a22fd5898>"
        ]
       }
      ],
-     "prompt_number": 88
+     "prompt_number": 49
     },
     {
      "cell_type": "heading",