Minto typos.

Courtesy of email from James Kim.

01-g-h-filter.ipynb

@@ -3048,7 +3048,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Back to filtering. The results of the filter may strike you as quite silly; of course the data will look good if we assume the conclusion, that our weight gain is around 1 lb/day! Let's see what the filter does if our initial guess is bad. Let's spredict that there is a weight loss of 1 lb a day"
+    "Back to filtering. The results of the filter may strike you as quite silly; of course the data will look good if we assume the conclusion, that our weight gain is around 1 lb/day! Let's see what the filter does if our initial guess is bad. Let's predict that there is a weight loss of 1 lb a day"
    ]
   },
   {

02-Discrete-Bayes.ipynb

@@ -361,7 +361,7 @@
     "\n",
     "I'm sure you've used probabilities before - as in \"the probability of rain today is 30%\". The last paragraph sounds like more of that. But Bayesian statistics was a revolution in probability because it treats probability as a belief about a single event. Let's take an example. I know that if I flip a fair coin infinitely many times I will get 50% heads and 50% tails. This is called [*frequentist statistics*](https://en.wikipedia.org/wiki/Frequentist_inference) to distinguish it from Bayesian statistics. Computations are based on the frequency in which events occur.\n",
     "\n",
-    "I flip the coin one more time and let it land. Which way do I believe it landed? Frequentist probability has nothing to say about that; it will merely state that 50% of coin flips land as heads. In some ways it is meaningless to to assign a probability to the current state of the coin. It is either heads or tails, we just don't know which. Bayes treats this as a belief about a single event - the strength of my belief or knowledge that this specific coin flip is heads is 50%. Some object to the term \"belief\"; belief can imply holding something to be true without evidence. In this book it always is a measure of the strength of our knowledge. We'll learn more about this as we go.\n",
+    "I flip the coin one more time and let it land. Which way do I believe it landed? Frequentist probability has nothing to say about that; it will merely state that 50% of coin flips land as heads. In some ways it is meaningless to assign a probability to the current state of the coin. It is either heads or tails, we just don't know which. Bayes treats this as a belief about a single event - the strength of my belief or knowledge that this specific coin flip is heads is 50%. Some object to the term \"belief\"; belief can imply holding something to be true without evidence. In this book it always is a measure of the strength of our knowledge. We'll learn more about this as we go.\n",
     "\n",
     "Bayesian statistics takes past information (the prior) into account. We observe that it rains 4 times every 100 days. From this I could state that the chance of rain tomorrow is 1/25. This is not how weather prediction is done. If I know it is raining today and the storm front is stalled, it is likely to rain tomorrow. Weather prediction is Bayesian.\n",
     "\n",

03-Gaussians.ipynb

@@ -5596,7 +5596,7 @@
    "source": [
     "The y-axis depicts the *probability density* — the relative amount of cars that are going the speed at the corresponding x-axis.\n",
     "\n",
-    "You may object that human heights or automobile speeds cannot be less than zero, let alone $-\\infty$ or $-\\infty$. This is true, but this is a common limitation of mathematical modeling. “The map is not the territory” is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above models the distribution of the measured automobile speeds, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. Gaussians are used in many branches of mathematics, not because they perfectly model reality, but because they are easier to use than any other relatively accurate choice. However, even in this book Gaussians will fail to model reality, forcing us to use computationally expensive alternatives. \n",
+    "You may object that human heights or automobile speeds cannot be less than zero, let alone $-\\infty$ or $\\infty$. This is true, but this is a common limitation of mathematical modeling. “The map is not the territory” is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above models the distribution of the measured automobile speeds, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. Gaussians are used in many branches of mathematics, not because they perfectly model reality, but because they are easier to use than any other relatively accurate choice. However, even in this book Gaussians will fail to model reality, forcing us to use computationally expensive alternatives. \n",
     "\n",
     "You will see these distributions called *Gaussian distributions* or *normal distributions*.  *Gaussian* and *normal* both mean the same thing in this context, and are used interchangeably. I will use both throughout this book as different sources will use either term, and I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and talk about a *Gaussian* or *normal* — these are both typical shortcut names for the *Gaussian distribution*. "
    ]
@@ -9093,7 +9093,7 @@
     "\n",
     "In this chapter I used code from [FilterPy](https://github.com/rlabbe/filterpy) to compute and plot Gaussians. I did that to give you a chance to look at the code and see how these functions are implemented.  However, Python comes with \"batteries included\" as the saying goes, and it comes with a wide range of statistics functions in the module `scipy.stats`. So let's walk through how to use scipy.stats to compute statistics and probabilities.\n",
     "\n",
-    "The `scipy.stats` module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://http://docs.scipy.org/doc/scipy/reference/stats.html. We will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function from FilterPy."
+    "The `scipy.stats` module contains a number of objects which you can use to compute attributes of various probability distributions. The full documentation for this module is here: http://docs.scipy.org/doc/scipy/reference/stats.html. We will focus on the  norm variable, which implements the normal distribution. Let's look at some code that uses `scipy.stats.norm` to compute a Gaussian, and compare its value to the value returned by the `gaussian()` function from FilterPy."
    ]
   },
   {

04-One-Dimensional-Kalman-Filters.ipynb

@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 31,
    "metadata": {
     "collapsed": false
    },
@@ -289,7 +289,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -335,7 +335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 32,
    "metadata": {
     "collapsed": false
    },
@@ -1107,7 +1107,7 @@
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+       "<img src=\"data:image/png;base64,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 truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -1139,7 +1139,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 33,
    "metadata": {
     "collapsed": false
    },
@@ -1911,7 +1911,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img src=\"data:image/png;base64,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 truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -1924,7 +1924,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Mean of readings is 9.923\n"
+      "Mean of readings is 10.039\n"
      ]
     }
    ],
@@ -1972,9 +1972,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 34,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
@@ -2744,7 +2745,7 @@
     {
      "data": {
       "text/html": [
-       "<img 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truncated
+       "<img 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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -2847,7 +2848,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 35,
    "metadata": {
     "collapsed": true
    },
@@ -2866,7 +2867,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 36,
    "metadata": {
     "collapsed": false
    },
@@ -2877,7 +2878,7 @@
        "(25, 0.530)"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2941,7 +2942,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 37,
    "metadata": {
     "collapsed": true
    },
@@ -2990,7 +2991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 38,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -3763,7 +3764,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -3815,7 +3816,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 39,
    "metadata": {
     "collapsed": false
    },
@@ -4587,7 +4588,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -4604,7 +4605,7 @@
     "\n",
     "    xs = np.arange(5, 15, 0.1)\n",
     "    ys = [stats.gaussian(x, m1, v1) for x in xs]\n",
-    "    plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(m1, v2))\n",
+    "    plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(m1, v1))\n",
     "\n",
     "    ys = [stats.gaussian(x, m2, v2) for x in xs]\n",
     "    plt.plot(xs, ys, label='$\\mathcal{N}$'+'$({},{})$'.format(m2, v2))\n",
@@ -4637,7 +4638,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 40,
    "metadata": {
     "collapsed": false
    },
@@ -5409,7 +5410,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -6222,7 +6223,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 41,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -6995,7 +6996,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -7024,7 +7025,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 42,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -7100,7 +7101,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 43,
    "metadata": {
     "collapsed": false
    },
@@ -7872,7 +7873,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img src=\"data:image/png;base64,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 truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -8000,7 +8001,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 44,
    "metadata": {
     "collapsed": true
    },
@@ -8118,7 +8119,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 45,
    "metadata": {
     "collapsed": false
    },
@@ -8890,7 +8891,7 @@
     {
      "data": {
       "text/html": [
-       "<img 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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -9080,7 +9081,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 46,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -9853,7 +9854,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -9889,7 +9890,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 47,
    "metadata": {
     "collapsed": false
    },
@@ -10661,7 +10662,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAFACAYAAACV2UtCAAAgAElEQVR4XuydB3gUVffG3yQkoZfQ5AMBRRDpRekdpAgKKIiAShEQ+BDxA0VUBP82BLvSQQUREQTpIKAgHelNiqBUEaRKDSX5P2ezO9mEbGZ2d+7u7Ox7n8fn+8jcOffc3zmz8+7dWyLAQgIkQAIkQAIkQAIkQAIkYJhAhOGarEgCJEACJEACJEACJEACJAAKaCYBCZAACZAACZAACZAACXhBgALaC1isSgIkQAIkQAIkQAIkQAIU0MwBEiABEiABEiABEiABEvCCAAW0F7BYlQRIgARIgARIgARIgAQooJkDJEACJEACJEACJEACJOAFAQpoL2CxKgmQAAmQAAmQAAmQAAlQQDMHSIAESIAESIAESIAESMALAhTQXsBiVRIgARIgARIgARIgARKggGYOkAAJkAAJkAAJkAAJkIAXBCigvYDFqiRAAiRAAiRAAiRAAiRAAc0cIAESIAESIAESIAESIAEvCFBAewGLVUmABEiABEiABEiABEiAApo5QAIkQAIkQAIkQAIkQAJeEKCA9gIWq5IACZAACZAACZAACZAABTRzgARIgARIgARIgARIgAS8IGC2gC4G4DMAtQFcAzAdwIsAruj41AhAZwBVAYiNrwB01bmnGoC1znYye9FnViUBEiABEiABEiABEiABnwmYKaCzA9gF4BiAoQByA/gIwCoAbXU8/ABAEwC/AmgBYL6OgI4EsAlAfgC5AFBA+5wCvJEESIAESIAESIAESMAbAmYK6JcADAFQGMAZpxOtAcwEUBnAVoOO7QGwTkdA9wPQHcAsAP0poA2SZTUSIAESIAESIAESIAG/CZgpoJcDuATgYTevogCcAzACwJsGvdUT0P8B8BsAEed1AAykgDZIltVIgARIgARIgARIgAT8JmCmgD4JYBIAGYl2LzLVYj+ADga91RPQ3znttHOOeFNAGwTLaiRAAiRAAiRAAiRAAv4TMFNAX3fOfX4nlVtLAdwC0NSgu+kJ6Aed0zZKAjienoA+e/ZsjoiIiLquNiMiIo4mJCSIjywkQAIkQAIkQAIkQAIhSCAyMjImMTHxTpfriYmJv8TFxV0IdFdCSUDHANgJ4EsAw5ygZM51miPQ586deyQiImJOoIGyPRIgARIgARIgARIggcAQSExMbJkrV665gWktuRUzBbTqKRwilHsCqALANZI8CEBfAAUAxDu3tHP0jgI60KnE9kiABEiABEiABEggsATsIKBXALiYahGhbDd33qRFhDLy/DSAtER/IoCRTjFNAR3Y3GVrJEACJEACJEACJBAUAnYQ0LJ48HUARdy2sWvl3MbuAQBbDJL1NAe6BIA7UtnoAqA9AJkb/ReAg67r58+fr+jeZqZMmRAVJZuCsJCAOgI3btzA/v2yZhYoUaIEoqOj1TVGyyTgJMC8YyoEgwDzLhjU2WZ8fDwk99xKpZw5cxrdKtk0gGZO4cjhnKN81LllXRwAOSBFTgt8zM1jEdmDAdwNQOpKkb2jRWSLPx8D2AdglPPaAvepGal67nEO9NmzZ0tHRkbKwS6OkjVrVgpo09KGhjwRuH79Onbs2OG4XK5cOcTEyNR9FhJQS4B5p5YvradNgHnHzAgGgWvXrkFEtKskJCSUiYuL2x1oX8wU0OL7PQA+1TnKW0SvS0AfcXa4k3NxoEzFSF3uAuCql/qa2JKR7yypL1BABzqV2J4Q4AuFeRAMAsy7YFBnm8w75kAwCNhVQAeDZZptUkBbJhRh5QhfKGEVbst0lnlnmVCElSPMu7AKt2U6SwGtOBQU0IoB03yaBPhCYWIEgwDzLhjU2SbzjjkQDAIU0IqpU0ArBkzzFNDMAcsQoJCxTCjCyhHmXViF2zKdpYBWHAoKaMWAaZ4CmjlgGQIUMpYJRVg5wrwLq3BbprMU0IpDQQGtGDDNU0AzByxDgELGMqEIK0eYd2EVbst0lgJacSgooBUDpnkKaOaAZQhQyFgmFGHlCPMurMJtmc5SQCsOBQW0YsA0TwHNHAgqgQvXLuDQ+UM4d+0czl85j98O/Obwp2SxksiZOSdyZsyJIjmKIC5THCIizN6xNKhdZ+MWIUABbZFAhJkbFNCKA04BrRgwzVNAMwcCQiAxMRH7z+zH+mPrseH4Bmz6axMOnjuIs1fPGmo/W0w23J3rblQuUBlVC1VF1YJVUSZfGURF8mRWQwBZySMBCmgmRzAIUEArpk4BrRgwzVNAMweUEYi/GY/lh5Zj3r55mLd/Ho7+6zq01Zwm82bOi+YlmuPhEg+jcbHGyBqT1RzDtBJWBCigwyrcluksBbTiUFBAKwZM8xTQzAHTCew4uQMTt0zElJ1TDI8wuzsRgQgkIq0DXT27miU6C9qVboeuFbuixp01ON3D9Kja1yAFtH1ja+WeUUArjg4FtGLANE8BzRwwhUBCYgLm7J2D4WuHO6ZpeCoijkvlLeWYglE2f1nHtIy7ct6F/FnzIzoxGr/v+R1Sp3ip4riBGzh95TT+PP8n/jz3J3b/s9sx/UME+s2Emx7bEPsDqg9Ax3IdERMVY0r/aMS+BCig7RtbK/eMAlpxdCigFQOmeQpo5oBfBETITtkxBcNWD8O+M/vStFUgawG0KNHCMdWibtG6yB6b3a+8u3rjKtYeXeuYFiL//XHujzTtFcpeCP+r9j/0vL8nMkVn8qufvNm+BCig7RtbK/eMAlpxdCigFQOmeb+EDPGFLwFZFLjg9wUYuGwgfvsnaecM95I5OjPalmrrmFJRq3AtREZE6sLyRciIH9v+3oYvtn7hmDJy/tr529q5M/udeKvBW3iy3JOG/NB1lBVsRcCXvLMVAHYmKAQooBVjp4BWDJjmKaCZA14T2HVqF55b9BxWHFqRpljtX70/ulTs4nGk2VOD/gqZazev4btd3zmmkaQl6svnL4/Pmn2G2kVqe91n3mBfAv7mnX3JsGcqCVBAq6QLgAJaMWCap4BmDhgmIFMn3lz5JkasHXHbHOQSuUvg1dqvon2Z9oiOijZs072iWUJG5mPP3z/f4atsl5e6dK/UHe81eg+5MuXyyU/eZC8CZuWdvaiwN6oJUEArJkwBrRgwzVNAMwcMEVh5eCW6zunq2LvZveTLkg9D6w5Ft0rdfBbOLntmCxkR0jN2z8CgnwY5FiK6l/xZ8mPkQyPxWKnHDPWflexLwOy8sy8p9sxMAhTQZtJMwxYFtGLANE8BzRxIl8D1W9cxZPkQvLfmvRRby0VFREGmarxW5zVki81mCkVVQkb2o/50w6cY+stQXLlxJYWvnSt0xqdNPzWtD6aAoJGAElCVdwHtBBsLOQIU0IpDRgGtGDDNU0AzBzwS2Hd6HzrM6oAtJ7akqFOlYBWMazEO5e8obyo91UJGjgzvvaA3Fh1YlMJv2UpvSuspqH5ndVP7Q2OhQUB13oUGBXoZaAIU0IqJU0ArBkzzFNDMgTQJyNSHrnO74tL1S9r12KhYvNvwXfSt2lfJEdqBEDKya8e3u751COkL8Re0vmWIzIAPGn+A56o8x0NYwuyZCETehRlSdtcAAQpoA5D8qUIB7Q893usrAb5QfCUX+vfJvs6Dlg3C++veT9GZMvnKYOqjUx2Hn6gqgcy7IxeO4OkfnsYvh39J0Z0OZTs4RtezxGRR1U3atRiBQOadxbpOd4JIgAJaMXwKaMWAaZ4j0MwBjcDZq2fRZnobLD+0PAUVGZUd/uBwZMyQUSmtQAuZWwm3MHzNcLy2/DXIgkNXKZuvLOa1n4ciOYso7S+NW4NAoPPOGr2mF8EmQAGtOAIU0IoB0zwFNHPAQeDA2QNoPrU59p/ZrxGRw1AmPDwB7cu2DwilYAmZn//8GU98/wT+ufKP1k/ZpWNu+7mQ+d4s9iYQrLyzN1X2To8ABbQeIT+vU0D7CZC3+0SALxSfsIXsTauPrEaraa1w5uoZrQ/F44pjVrtZkKkbgSrBzLujF46i7Yy22HB8g9ZdGXGXxYXc6i5QGRCcdoKZd8HpMVu1AgEKaMVRoIBWDJjmOQId5jkwa88stJ/ZHrJdnavUL1ofMx+fGfCDRoItZOQkQ9nrWhYZuhfZ5u65qs+FeabYt/vBzjv7kmXP0iNAAa04PyigFQOmeQroMM6BiVsmosf8Hinm/3ap0AVjWoxBTFRMwMlYQcjILh1DVwzF/638vxT9H1J3COS/iIiIgHNhg2oJWCHv1PaQ1q1IwK4CuhiAzwDUBnANwHQALwJIuQP/7RFpBKAzgKoAxMZXALqmqiYnDvQH0AxACQC3AGwDMATAmtQmKaCtmPb294kvFPvHeMSaEXhp2UspOvpW/bfwSu1XgiYSrZR3k7dPxjNzn0lxZHmfB/rgk2afIDIi0v4JEkY9tFLehRH2sO+qHQV0dgC7ABwDMBRAbgAfAVgFoK1OxD8A0ATArwBaAJifhoAuDWApgC8ByP5J8kncE0Bz570/u7dBAR32z1hQAPCFEhTsAWlURljf+OUNx3+uIoJwTPMx6F65e0B88NSI1fJuwf4FaDOjDWRqh6vIyYWysDIqMiqorNi4eQSslnfm9YyWrEzAjgJahmRkNLgwANeKmtYAZgKoDGCrwYDsAbAuDQGdCUCic2TbZUo+iUW0H3QKb60JCmiDtFnNVAJ8oZiK0zLGRDwPWTEEb658U/NJpmp88+g3aFOqTdD9tGLeyQLLFlNbpDh0pVP5Tpj4yESK6KBnjDkOWDHvzOkZrViZgB0FtGyAKkdvPewGXgTuOQAjACS/edKPjCcB7emuaQDuBVDRvQIFtJXT376+8YViv9iKeB68fDDeXvW21rlMGTJhzhNz8GCxBy3RYavm3fa/t6PR141w+sppjdNT5Z7Cly2/pIi2ROb454RV886/XvFuqxOwo4A+CWASgJSTA4FNAGSD1A4Gg+KNgM7gHH1eDaAjBbRBwqymjALine truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -10710,7 +10711,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 48,
    "metadata": {
     "collapsed": false
    },
@@ -10733,7 +10734,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 49,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -11506,7 +11507,7 @@
     {
      "data": {
       "text/html": [
-       "<img src=\"data:image/png;base64,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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -12386,7 +12387,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 50,
    "metadata": {
     "collapsed": false
    },
@@ -13158,7 +13159,7 @@
     {
      "data": {
       "text/html": [
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -13211,7 +13212,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 51,
    "metadata": {
     "collapsed": false
    },
@@ -13983,7 +13984,7 @@
     {
      "data": {
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truncated
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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -14035,7 +14036,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 52,
    "metadata": {
     "collapsed": false
    },
@@ -14807,7 +14808,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -14856,7 +14857,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 53,
    "metadata": {
     "collapsed": false
    },
@@ -15628,7 +15629,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -15671,7 +15672,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 54,
    "metadata": {
     "collapsed": false
    },
@@ -16443,7 +16444,7 @@
     {
      "data": {
       "text/html": [
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+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -16494,7 +16495,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 55,
    "metadata": {
     "collapsed": false
    },
@@ -17306,7 +17307,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 56,
    "metadata": {
     "collapsed": false
    },
@@ -18078,7 +18079,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -18148,7 +18149,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 57,
    "metadata": {
     "collapsed": false
    },
@@ -18166,7 +18167,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 58,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -18939,7 +18940,7 @@
     {
      "data": {
       "text/html": [
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truncated
+       "<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAFACAYAAACV2UtCAAAgAElEQVR4XuxdBXjcRhN9IYeZucGGmZmZmTkOO8xJw0mTP4wOMzNz0nDDzMyMDTn4f0+ydOfz2T6dD+Wd7+vX1rda7b4drUazM29CQYhAQCAgEBAICAQEAgIBgYBAQCBgMQKhLG4pGgoEBAICAYGAQEAgIBAQCAgEBAIQBrRQAoGAQEAgIBAQCAgEBAICAYGABgSEAa0BLNFUICAQEAgIBAQCAgGBgEBAICAMaKEDAgGBgEBAICAQEAgIBAQCAgENCAgDWgNYoqlAQCAgEBAICAQEAgIBgYBAQBjQQgcEAgIBgYBAQCAgEBAICAQEAhoQEAa0BrBEU4GAQEAgIBAQCAgEBAICAYGAMKCFDggEBAICAYGAQEAgIBAQCAgENCAgDGgNYImmAgGBgEBAICAQEAgIBAQCAgFhQAsdEAgIBAQCAgGBgEBAICAQEAhoQEAY0BrAEk0FAgIBgYBAQCAgEBAICAQEAsKAFjogEBAICAQEAgIBgYBAQCAgENCAgDCgNYAlmgoEBAICAYGAQEAgIBAQCAgEhAEtdEAgIBAQCAgEBAICAYGAQEAgoAEBYUBrAEs0FQgIBAQCAgGBgEBAICAQEAgIA1rogEBAICAQEAgIBAQCAgGBgEBAAwKuYkDXBdANQCYAXwGcAdAIwHMNcxFNBQICAYGAQEAgIBAQCAgEBAJ2R8AVDOjuAEYCGANgD4DIAIoAmAHgvt0REDcQCAgEBAICAYGAQEAgIBAQCGhAwNkGdGoAlwF0AjBLw7hFU4GAQEAgIBAQCAgEBAICAYGAUxBwtgFNz3NHALEA/HAKAuKmAgGBgEBAICAQEAgIBAQCAgENCDjbgN7vG7JB7/MAAIl9PdJ9AOzQMA/RVCAgEBAICAQEAgIBgYBAQCDgEAScbUBf9TWaPwDoBeCFbzhHOQDZAPB3Sd68eRM9VKhQRZX/DxUq1MNfv359cwhK4iYCAYGAQEAgIBAQCAgEBAJORyB06NAev3//TqoM5Pfv3wdixYr13tEDc7YBfR0A46ArANjpO/lwAG4D2AuguQLI27dvq4QKFWqjowES9xMICAQEAgIBgYBAQCAgEHBNBH7//l01ZsyYmxw9Omcb0P8CyA0gEgAfo8kv9zWs+ZskwoB2tGqI+wkEBAICAYGAQEAgIBBwbQRCqgE9F0AzMwb0CgAZAWQWBrRrK64YnUBAICAQEAgIBAQCAgFnIRBSDeiqANYBqAxgmy/44X1DOHYBaKEsyLt377L7FliR/hQxYkSECRPGWesl7usEBL5//44bN25Id06bNi3ChWO0j5CQhIDQgZC02ubnKnRA6IDQgZCtAz4+PqAOGEmOGDFinHU0Ks4O4eD9DwNIAaAfgGcAvHwLqTB8wziJMGPo0KEvKQBFiRJFGNCO1hYn3+/bt2+4cOGCNIosWbLAw8PDySMSt3c0AkIHHI24691P6IDrrYmjRyR0wNGIu9b9vn79ChrRivz69StTrFixWFPEoeJsA5qTjQFgLIBqdCwDOAmgp++/VTDevHkjDGiHqobr3Uxsmq63Jo4ekdABRyPuevcTOuB6a+LoEQkdcDTirnU/YUBrXA9hQGsETIfNxaapw0XVOCWhAxoB02FzoQM6XFSNUxI6oBEwnTUXBrTGBRUGtEbAdNhcbJo6XFSNUxI6oBEwHTYXOqDDRdU4JaEDGgHTWXNhQGtcUGFAawRMh83FpqnDRdU4JaEDGgHTYXOhAzpcVI1TEjqgETCdNRcGtMYFFQa0RsB02FxsmjpcVI1TEjqgETAdNhc6oMNF1TgloQMaAdNZc2FAa1xQYUBrBEyHzcWmqcNF1TgloQMaAdNhc6EDOlxUjVMSOqARMJ01Fwa0xgUVBrRGwHTYXGyaOlxUjVMSOqARMB02Fzqgw0XVOCWhAxoB01lzYUBrXFBhQGsETIfNxaapw0XVOCWhAxoB02FzoQM6XFSNUxI6oBEwnTUXBrTGBRUGtEbAdNhcbJo6XFSNUxI6oBEwHTYXOqDDRdU4JaEDGgHTWXNhQGtcUGFAawRMh83FpqnDRdU4JaEDGgHTYXOhAzpcVI1TEjqgETCdNRcGtMYFFQa0RsB02FxsmjpcVI1TEjqgETAdNhc6oMNF1TgloQMaAdNZc2FAa1xQYUBrBEyHzcWmqcNF1TgloQMaAdNhc6EDOlxUjVMSOqARMJ01Fwa0xgUVBrRGwHTYXGyaOlxUjVMSOqARMB02Fzqgw0XVOCWhAxoB01lzYUBrXFBhQGsETIfNxaapw0XVOCWhAxoB02FzoQM6XFSNUxI6oBEwnTUXBrTGBRUGtEbAdNhcbJo6XFSNUxI6oBEwHTYXOqDDRdU4JaEDGgHTWXNhQGtcUGFAawRMh83FpqnDRdU4JaEDGgHTYXOhAzpcVI1TEjqgETCdNRcGtMYFFQa0RsB02FxsmjpcVI1TEjqgETAdNhc6oMNF1TgloQMaAdNZc2FAa1xQYUBrBEyHzcWmqcNF1TgloQMaAdNhc6EDOlxUjVMSOqARMJ01Fwa0vKBFAew3s7aXAGQx/rswoHX2BFgxHbFpWgGazi4ROqCzBbViOkIHrABNZ5cIHdDZgmqcjjCgDQb0PgAtAVwxwvAzABrRqggDWqOG6bC52DR1uKgapyR0QCNgOmwudECHi6pxSkIHNAKms+bCgPZrQOcHcCKwNRYGtM6eACumIzZNK0DT2SVCB3S2oFZMR+iAFaDp7BKhAzpbUI3TEQa0wYBmCEc+YUBr1KAQ2FxsmiFw0U2mLHRA6IDQAaEDQgdCtg4IA9qvAf0cQFwArwBsBNAHwFtjFREe6JD9wHD27rpp/vj5C6FDhULo0KHEIgYTAXfVgWBOW1xuhIDQAaEOQgdCtg4IA1pe/2wAGgD4B8BHAHkB9APwAEAuAN8VNTE1oMOHD4/QoUOHbC0KYbPnpnnt2jVp1unSpYOHh4fLI7Dl35voNHkHPn75jsX9qqJc7lQuP2ZXHqA76oAr4+mOYxM64I6rZtsxCx2wLZ7u1puPjw9+/fqlDvvXr1+ZYsWKddnR83BFl1gpALsANAOwKCAD+v79+5JHUohAwBUR+PXrN2bvvok5e26qw4sWMRyWdy+CeNEjuOKQxZgEAgIBgYBAQCDg8gjQeZY8eXJhQAewUgzlWA6gkzCgXV6XxQBNEPjw+Tv+Wn4WR6699IdNvrRxMblVboQK5YrfrmIpBQIhD4Hz997gs89PZEsRExE9woY8AMSMBQJuhoAwoANfsCANaBHC4WYab4PhusOx3aW7L1B7yFrcefouwBlP6lgGbSvntAEiIa8Ld9CBkLcqjp2xLXVg5NLDGLLokDSB8OHCoET2P1ApfxpUyJsaiWJHdezExN0sRsCWOmDxTUVDl0FAhHAEvBRlAWwH0ATAkoA80FGiREGYMGFcZkHFQOyPgLMTR568+g9txm/B1fsv8UeCGEidOBbSJImFNIljS/997tYztB63GZ+/qqH7SBY/Oub1rIJmozfi0csPEkgRw4fFudltkTZpbPuDprM7OFsHdAanW07HVjqw7uBV1By0KkAMcqdLhCoF/kTLCtmRUBjTLqUrttIBl5qUGIw/BMavOia9W8vkToUIRqdDIolQhmoxAAaJnvNNIiSdXS8At3yp7X4IA1o8VQoCztw0rz14hXK9luD+8/cWL0jJHCmwfGBNxI0RGXtP30GpHlR3WfKkS4wjU1sgbBiRCGsxoG7MxKJljqJt4AgEtA98+OSDtuO34MW7TxjavDgKZEoaYEc8KcrXfg4+GX3sBtQ4VrSIWD2oNkrkSCGWxkUQcOa7wEUg0P0w3n/8ing1xuLb95+IEtEDi/pWQ/XC6aV5CwNaXn7S1dUHwGjwiAAeAVgHYCiA/4w1RNDY6f55CXKCzto0j156iMr9l+PNhy9BjlFp0LNuAYxsXdKPgdx5ynZMXmeoFzS0eTEMbMJq9kIsRcBZOmDp+EQ7+yMQkA54jt2M2VvPSAPwCBcGs7tXRpOyWf0NiM9x7nazceeJgSl1bLvS8Pn2E5uOXsfxq4/9XRMmdCiMb18WnWrkEfkL9l/iIO8g9oEgIXL7Bkt3X0CjkevVeVxb2AF/JosjDGhrVlYY0Nagpq9rnLFpbjh8DfWHrcXXb+phCIpn/wNJ40bHzcevcfPRG7x6z8rzskSOEA7ze1dF7WIZ/YH/xec7cnjOAr3ZFHqf/53WEjn/TKSvhbLjbJyhA3acjujaCgTM6QCfqYzNp4PsN8bSv1FhyRutcLCTk71Cn6XYfeqO2qxb7XwY156Rg7I8e/MRW47dwKp/Lvtpx9+alcuGGV0r+jlOtmIK4pJgIiD2gWAC6AaXVx+4Enz/UjKliIeL89qpoxYeaI0LKAxojYDpsLmjN03vTafQYdI2Py/l1hVzYHrXin48y+8+fsWtx2+kGOfcfyZC4rjRAkT/1PUnyN9hLvgip6RLFgdnZnkiYvhwOlwx20/J0Tpg+xmIHoOLgDkdqPnXKqw7dNVs17WLZsCCPtUQKUI49PTehbErj6ntSuVMie2jG5oNpfr9+zemrj+BrtN24qeRYZ43fWKsG1oXieKIJMPgrqW114t9wFrk3OO6/z77IG61/8Hn+09pwIObFcWgpsWEAW3t8gkD2lrk9HOdozZNvjgHztuPEUvk7HxFhjRjyEWRYB/hDl14AIMWsHaQLJ1r5sXEjuX0s1B2nImjdMCOUxBdBxMBUx04c+uF9FGqSLFsf+D41Uf44mM4NWJCYMOSmdFl2k61XYqEMXByRmvEjh4p0BHtO3MXdYasxmujEK6EsaNg/dC6yJshSTBnIy63BgGxD1iDmvtcs3LfJdQbtlYd8KV57ZAxRTxhQFu7hMKAthY5/VznqE3T1EvF+EfvbpXQqmIOm4D5/cdPFOw0DyevPZH6IyX0lQLine truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -19021,7 +19022,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 59,
    "metadata": {
     "collapsed": false
    },
@@ -19032,7 +19033,7 @@
        "(11, 7.000)"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 59,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -19057,7 +19058,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 60,
    "metadata": {
     "collapsed": false
    },
@@ -19068,7 +19069,7 @@
        "(11.350, 4.550)"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }

05-Multivariate-Gaussians.ipynb

@@ -1136,7 +1136,7 @@
     {
      "data": {
       "text/html": [
-       "<img 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truncated
+       "<img 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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -1235,13 +1235,13 @@
     "Easy, right? If we weigh the students we might find their weights to be W = [70.1, 91.2, 59.5, 93.2, 53.5]. Can we use the covariance equation to create the covariance matrix? Sure. It will look like:\n",
     "\n",
     "$$\\Sigma = \\begin{bmatrix}\\sigma_H^2 & \\sigma_{H,W} \\\\\n",
-    "\\sigma_{W,H} & \\sigma_{H}^2\\end{bmatrix}$$\n",
+    "\\sigma_{W,H} & \\sigma_{W}^2\\end{bmatrix}$$\n",
     "\n",
     "We just computed the variance of the height, and it will go in the upper left hand corner of the matrix. The lower right corner contains the variance in heights. Using the same equation we get:\n",
     "\n",
     "$$\\begin{aligned}\n",
     "\\mu_W &= \\frac{1}{5}(70.1 + 91.2 + 59.5 + 93.2 + 53.5) = 73.5 \\\\\n",
-    "\\sigma_W^2 &= \\frac{1}{5}\\left[(70.1-73.5) + (91.2-73.5) + (59.5-73.5) + (93.2-73.5) + (53.5-73.5)\\right] \\\\\n",
+    "\\sigma_W^2 &= \\frac{1}{5}\\left[(70.1-73.5)^2 + (91.2-73.5)^2 + (59.5-73.5)^2 + (93.2-73.5)^2 + (53.5-73.5)^2\\right] \\\\\n",
     "&= 261.8\n",
     "\\end{aligned}$$\n",
     "\n",
@@ -2135,7 +2135,7 @@
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -2957,8 +2957,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 10.2504   3.0537]\n",
-      " [  3.0537   2.3873]]\n"
+      "[[ 11.1301   3.1556]\n",
+      " [  3.1556   2.4903]]\n"
      ]
     }
    ],
@@ -3754,7 +3754,7 @@
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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -3767,8 +3767,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 1.0051 -0.0056]\n",
-      " [-0.0056  0.9967]]\n"
+      "[[ 0.9964  0.004 ]\n",
+      " [ 0.004   0.9992]]\n"
      ]
     }
    ],
@@ -3799,7 +3799,7 @@
     "f(\\mathbf{x},\\, \\mu,\\,\\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^n|\\Sigma|}}\\, \\exp  \\Big [{ -\\frac{1}{2}(\\mathbf{x}-\\mu)^\\mathsf{T}\\Sigma^{-1}(\\mathbf{x}-\\mu) \\Big ]}\n",
     "$$\n",
     "\n",
-    "I urge you to not try to remember this equation. We will program it in a Python function and then call it if we need to compute a specific value. However, note that it has the same form as the univariate normal distribution:\n",
+    "I urge you not to try to remember this equation. We will program it in a Python function and then call it if we need to compute a specific value. However, note that it has the same form as the univariate normal distribution:\n",
     "\n",
     "$$ \n",
     "f(x, \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp \\Big [{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 \\Big ]\n",
@@ -4582,7 +4582,7 @@
     {
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+       "<img 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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
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       "text/plain": [
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       "text/plain": [
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       "text/plain": [
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       "text/plain": [
        "<IPython.core.display.HTML object>"
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       "text/plain": [
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
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       "text/plain": [
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       "text/plain": [
        "<IPython.core.display.HTML object>"
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       "text/plain": [
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"

06-Multivariate-Kalman-Filters.ipynb

@@ -904,7 +904,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This worked. Note that the code does not distinguish between between the prior and posterior in the variable names, so after calling predict the prior $\\bar{\\mathbf x}$ is stored in `KalmanFilter.x`. If we call `predict()` several times in a row the value will be updated each time. "
+    "This worked. Note that the code does not distinguish between the prior and posterior in the variable names, so after calling predict the prior $\\bar{\\mathbf x}$ is stored in `KalmanFilter.x`. If we call `predict()` several times in a row the value will be updated each time. "
    ]
   },
   {
@@ -966,7 +966,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Inspecting the diagonals shows us that the position variance got larger. We've performed three prediction steps with no measurements, and our uncertainty grew. The off-diagonal elements became non-zero - the Kalman filter detected a correlation between position and velocity! The variance of the velocity did not change.\n",
+    "Inspecting the diagonals shows us that the position variance got larger. We've performed five prediction steps with no measurements, and our uncertainty grew. The off-diagonal elements became non-zero - the Kalman filter detected a correlation between position and velocity! The variance of the velocity did not change.\n",
     "\n",
     "Here I plot the covariance before and after the prediction. The initial value is in solid red, and the prior (prediction) is in dashed black. I've altered the covariance and time step to better illustrate the change."
    ]
@@ -2218,7 +2218,7 @@
     "\n",
     "The rest of the code optionally plots the results and then returns the saved states and covariances.\n",
     "\n",
-    "Let's run it. We will 50 measurements with a noise variance of 10 and a process variance of 0.01."
+    "Let's run it. We have 50 measurements with a noise variance of 10 and a process variance of 0.01."
    ]
   },
   {
@@ -2996,7 +2996,7 @@
     {
      "data": {
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truncated
+       "<img src=\"data:image/png;base64,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 truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"

07-Kalman-Filter-Math.ipynb

@@ -306,7 +306,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "If you've gotten this far I hope that you are thinking that the Kalman filter's fearsome reputation is somewhat undeserved. Sure, I hand waved some equations away, but I hope implementation has been fairly straightforward for you. The underlying concept is quite straightforward - take two measurements, or a measurement and a prediction, and choose the output to be somewhere between the two. If you believe the measurement more your guess will be closer to the measurement, and if you believe the prediction is more accurate your guess will lie closer it it. That's not rocket science (little joke - it is exactly this math that got Apollo to the moon and back!). \n",
+    "If you've gotten this far I hope that you are thinking that the Kalman filter's fearsome reputation is somewhat undeserved. Sure, I hand waved some equations away, but I hope implementation has been fairly straightforward for you. The underlying concept is quite straightforward - take two measurements, or a measurement and a prediction, and choose the output to be somewhere between the two. If you believe the measurement more your guess will be closer to the measurement, and if you believe the prediction is more accurate your guess will lie closer to it. That's not rocket science (little joke - it is exactly this math that got Apollo to the moon and back!). \n",
     "\n",
     "To be honest I have been choosing my problems carefully. For an arbitrary problem designing the Kalman filter matrices can be extremely difficult. I haven't been *too tricky*, though. Equations like Newton's equations of motion can be trivially computed for Kalman filter applications, and they make up the bulk of the kind of problems that we want to solve. \n",
     "\n",
@@ -811,23 +811,23 @@
     {
      "data": {
       "text/latex": [
-       "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{5}}{20} & \\frac{\\Delta{t}^{4}}{8} & \\frac{\\Delta{t}^{3}}{6}\\\\\\frac{\\Delta{t}^{4}}{8} & \\frac{\\Delta{t}^{3}}{3} & \\frac{\\Delta{t}^{2}}{2}\\\\\\frac{\\Delta{t}^{3}}{6} & \\frac{\\Delta{t}^{2}}{2} & \\Delta{t}\\end{matrix}\\right] \\Phi_{s}$$"
+       "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{5}}{20} & \\frac{\\Delta{t}^{4}}{8} & \\frac{\\Delta{t}^{3}}{6}\\\\\\frac{\\Delta{t}^{4}}{8} & \\frac{\\Delta{t}^{3}}{3} & \\frac{\\Delta{t}^{2}}{2}\\\\\\frac{\\Delta{t}^{3}}{6} & \\frac{\\Delta{t}^{2}}{2} & \\Delta{t}\\end{matrix}\\right] \\Phi_s$$"
       ],
       "text/plain": [
-       "⎡         5           4           3⎤       \n",
-       "⎢\\Delta{t}   \\Delta{t}   \\Delta{t} ⎥       \n",
-       "⎢──────────  ──────────  ──────────⎥⋅\\Phi_s\n",
-       "⎢    20          8           6     ⎥       \n",
-       "⎢                                  ⎥       \n",
-       "⎢         4           3           2⎥       \n",
-       "⎢\\Delta{t}   \\Delta{t}   \\Delta{t} ⎥       \n",
-       "⎢──────────  ──────────  ──────────⎥       \n",
-       "⎢    8           3           2     ⎥       \n",
-       "⎢                                  ⎥       \n",
-       "⎢         3           2            ⎥       \n",
-       "⎢\\Delta{t}   \\Delta{t}             ⎥       \n",
-       "⎢──────────  ──────────  \\Delta{t} ⎥       \n",
-       "⎣    6           2                 ⎦       "
+       "⎡         5           4           3⎤      \n",
+       "⎢\\Delta{t}   \\Delta{t}   \\Delta{t} ⎥      \n",
+       "⎢──────────  ──────────  ──────────⎥⋅\\Phiₛ\n",
+       "⎢    20          8           6     ⎥      \n",
+       "⎢                                  ⎥      \n",
+       "⎢         4           3           2⎥      \n",
+       "⎢\\Delta{t}   \\Delta{t}   \\Delta{t} ⎥      \n",
+       "⎢──────────  ──────────  ──────────⎥      \n",
+       "⎢    8           3           2     ⎥      \n",
+       "⎢                                  ⎥      \n",
+       "⎢         3           2            ⎥      \n",
+       "⎢\\Delta{t}   \\Delta{t}             ⎥      \n",
+       "⎢──────────  ──────────  \\Delta{t} ⎥      \n",
+       "⎣    6           2                 ⎦      "
       ]
      },
      "execution_count": 3,
@@ -880,10 +880,10 @@
     {
      "data": {
       "text/latex": [
-       "$$\\left[\\begin{matrix}\\Delta{t} \\Phi_{s}\\end{matrix}\\right]$$"
+       "$$\\left[\\begin{matrix}\\Delta{t} \\Phi_s\\end{matrix}\\right]$$"
       ],
       "text/plain": [
-       "[\\Delta{t}⋅\\Phi_s]"
+       "[\\Delta{t}⋅\\Phiₛ]"
       ]
      },
      "execution_count": 4,
@@ -916,18 +916,18 @@
     {
      "data": {
       "text/latex": [
-       "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{3}}{3} & \\frac{\\Delta{t}^{2}}{2}\\\\\\frac{\\Delta{t}^{2}}{2} & \\Delta{t}\\end{matrix}\\right] \\Phi_{s}$$"
+       "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{3}}{3} & \\frac{\\Delta{t}^{2}}{2}\\\\\\frac{\\Delta{t}^{2}}{2} & \\Delta{t}\\end{matrix}\\right] \\Phi_s$$"
       ],
       "text/plain": [
-       "⎡         3           2⎤       \n",
-       "⎢\\Delta{t}   \\Delta{t} ⎥       \n",
-       "⎢──────────  ──────────⎥⋅\\Phi_s\n",
-       "⎢    3           2     ⎥       \n",
-       "⎢                      ⎥       \n",
-       "⎢         2            ⎥       \n",
-       "⎢\\Delta{t}             ⎥       \n",
-       "⎢──────────  \\Delta{t} ⎥       \n",
-       "⎣    2                 ⎦       "
+       "⎡         3           2⎤      \n",
+       "⎢\\Delta{t}   \\Delta{t} ⎥      \n",
+       "⎢──────────  ──────────⎥⋅\\Phiₛ\n",
+       "⎢    3           2     ⎥      \n",
+       "⎢                      ⎥      \n",
+       "⎢         2            ⎥      \n",
+       "⎢\\Delta{t}             ⎥      \n",
+       "⎢──────────  \\Delta{t} ⎥      \n",
+       "⎣    2                 ⎦      "
       ]
      },
      "execution_count": 5,
@@ -1302,9 +1302,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2d813f60b38>"
+       "<matplotlib.figure.Figure at 0x226f12795c0>"
       ]
      },
      "metadata": {},
@@ -1329,16 +1329,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2d81401cb38>"
+       "<matplotlib.figure.Figure at 0x226f0d73160>"
       ]
      },
      "metadata": {},
@@ -1364,7 +1364,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 15,
    "metadata": {
     "collapsed": true
    },
@@ -1381,7 +1381,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -1411,16 +1411,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2d8145d4208>"
+       "<matplotlib.figure.Figure at 0x226f10e2550>"
       ]
      },
      "metadata": {},
@@ -1440,7 +1440,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
@@ -1523,7 +1523,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false
    },
@@ -1561,7 +1561,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -1575,9 +1575,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2d814f8d860>"
+       "<matplotlib.figure.Figure at 0x226f2f68ef0>"
       ]
      },
      "metadata": {},

08-Designing-Kalman-Filters.ipynb

@@ -1144,7 +1144,7 @@
     {
      "data": {
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -4238,7 +4238,7 @@
     "\n",
     "I must mention that this is only true for simulated systems. Real sensors are not perfectly Gaussian, and you may need to expand your criteria to, say, $5\\sigma$ with real sensor data.\n",
     "\n",
-    "So let's run the first order Kalman filter against our first order system and access it's performance. You can probably guess that it will do well, but let's look at it using the standard deviations.\n",
+    "So let's run the first order Kalman filter against our first order system and access its performance. You can probably guess that it will do well, but let's look at it using the standard deviations.\n",
     "\n",
     "First, let's write a routine to generate the noisy measurements for us."
    ]
@@ -30204,7 +30204,7 @@
     {
      "data": {
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truncated
+       "<img 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truncated
       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"

09-Nonlinear-Filtering.ipynb

@@ -320,7 +320,7 @@
     "\n",
     "These facts were not lost on the early adopters of the Kalman filter. Soon after Dr. Kalman published his paper people began working on how to extend the Kalman filter for nonlinear problems. \n",
     "\n",
-    "It is almost true to state that the only equation anyone knows how to solve is $\\mathbf{Ax}=\\mathbf{b}$. We only really know how to do linear algebra. I can give you any linear set of equations and you can either solve it or prove that it haas no solution. \n",
+    "It is almost true to state that the only equation anyone knows how to solve is $\\mathbf{Ax}=\\mathbf{b}$. We only really know how to do linear algebra. I can give you any linear set of equations and you can either solve it or prove that it has no solution. \n",
     "\n",
     "Anyone with formal education in math or physics has spent years learning various analytic ways to solve integrals, differential equations and so on. Yet even trivial physical systems produce equations that cannot be solved analytically. I can take an equation that you are able to integrate, insert a $\\log$ term, and render it insolvable. This leads to jokes about physicists stating \"assume a spherical cow on a frictionless surface in a vacuum...\". Without making extreme simplifications most physical problems do not have analytic solutions.\n",
     "\n",
@@ -386,9 +386,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba331e8f60>"
+       "<matplotlib.figure.Figure at 0x249b00622e8>"
       ]
      },
      "metadata": {},
@@ -440,9 +440,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba2f9b5518>"
+       "<matplotlib.figure.Figure at 0x249b0062128>"
       ]
      },
      "metadata": {},
@@ -467,7 +467,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -475,9 +475,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba34f8bf60>"
+       "<matplotlib.figure.Figure at 0x249ae1e0630>"
       ]
      },
      "metadata": {},
@@ -508,16 +508,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba353fd160>"
+       "<matplotlib.figure.Figure at 0x249b33eaa20>"
       ]
      },
      "metadata": {},
@@ -550,16 +550,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba354e7860>"
+       "<matplotlib.figure.Figure at 0x249b32ff748>"
       ]
      },
      "metadata": {},
@@ -582,7 +582,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -591,8 +591,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "input  mean, variance: 0.0026, 1.0028\n",
-      "output mean, variance: -0.1285, 2.4110\n"
+      "input  mean, variance: -0.0026, 1.0002\n",
+      "output mean, variance: -0.1206, 2.4042\n"
      ]
     }
    ],
@@ -614,16 +614,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAloAAAEjCAYAAADqnq9+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba3503c748>"
+       "<matplotlib.figure.Figure at 0x249b0ebbef0>"
       ]
      },
      "metadata": {},
@@ -633,7 +633,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "output mean, variance: -0.0038, 2.2563\n"
+      "output mean, variance: 0.0040, 2.2504\n"
      ]
     }
    ],
@@ -657,7 +657,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -666,8 +666,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "linear    output mean, variance: -0.2211, 7502.7249\n",
-      "nonlinear output mean, variance: -9.5909, 30606.5870\n"
+      "linear    output mean, variance: 0.2282, 7483.2071\n",
+      "nonlinear output mean, variance: -8.6559, 30530.7638\n"
      ]
     }
    ],
@@ -695,7 +695,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -703,9 +703,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba351caa20>"
+       "<matplotlib.figure.Figure at 0x249b0fe3da0>"
       ]
      },
      "metadata": {},
@@ -745,16 +745,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba351d5048>"
+       "<matplotlib.figure.Figure at 0x249b11b5470>"
       ]
      },
      "metadata": {},
@@ -778,16 +778,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba356aef60>"
+       "<matplotlib.figure.Figure at 0x249b10f89b0>"
       ]
      },
      "metadata": {},
@@ -808,16 +808,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba35115048>"
+       "<matplotlib.figure.Figure at 0x249b159a9e8>"
       ]
      },
      "metadata": {},
@@ -838,16 +838,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x2ba35199d30>"
+       "<matplotlib.figure.Figure at 0x249b1015518>"
       ]
      },
      "metadata": {},

10-Unscented-Kalman-Filter.ipynb

@@ -1090,7 +1090,7 @@
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -1139,7 +1139,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's look at the problem in terms of a 2D covariance ellipse. I choose 2D merely because it is easy to plot; this extends to any number of dimensions. Assuming some arbitrary nonlinear function, we will take random points from the first covariance ellipse, pass them through the nonlinear function, and plot their new position. Then we can compute the the mean and covariance of the transformed points, and use that as our estimate of the mean and probability distribution."
+    "Let's look at the problem in terms of a 2D covariance ellipse. I choose 2D merely because it is easy to plot; this extends to any number of dimensions. Assuming some arbitrary nonlinear function, we will take random points from the first covariance ellipse, pass them through the nonlinear function, and plot their new position. Then we can compute the mean and covariance of the transformed points, and use that as our estimate of the mean and probability distribution."
    ]
   },
   {
@@ -2732,7 +2732,7 @@
     {
      "data": {
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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -2745,7 +2745,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Difference in mean x=-0.023, y=43.732\n"
+      "Difference in mean x=-0.066, y=43.079\n"
      ]
     }
    ],
@@ -12144,7 +12144,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Tracking Manuevering Aircraft"
+    "### Tracking Maneuevering Aircraft"
    ]
   },
   {
@@ -15489,7 +15489,7 @@
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       "text/plain": [
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@@ -19710,7 +19710,7 @@
     "\n",
     "This graph makes it look easy because we have plotted 100 measurements for each position update. The movement of the aircraft is obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n",
     "\n",
-    "Now consider that the bearing gives us no distance information. Suppose we set the initial estimate ti 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements."
+    "Now consider that the bearing gives us no distance information. Suppose we set the initial estimate it 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements."
    ]
   },
   {
@@ -20495,7 +20495,7 @@
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