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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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     "source": [
      "The g-h Filter"
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import sys\n",
      "sys.path.insert(0,'../code') # allow us to import book_format\n",
      "import matplotlib.pyplot as plt\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "Building Intuition via Thought Experiments"
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     "source": [
      "Imagine that we live in a world without scales - the devices you stand on to weigh yourself. One day at work a coworker comes running up to you and announces her invention of a 'scale' to you. After she explains, you eagerly stand on it and announce the results: \"172 lbs\". You are ecstatic - for the first time in your life you know what you weigh. More importantly, dollar signs dance in your eyes as you imagine selling this device to weight loss clinics across the world! This is fantastic!\n",
      "\n",
      "Another coworker hears the commotion and comes over to find out what has you so excited. You explain the invention and once again step onto the scale, and proudly proclaim the result: \"161 lbs.\" And then you hesitate, confused.\n",
      "\n",
      "\"It read 172 lbs just a few seconds ago\" you complain to your coworker. \n",
      "\n",
      "\"I never said it was accurate,\" she replies.\n",
      "\n",
      "Sensors are inaccurate. This is the motivation behind a huge body of work in filtering, and solving this problem is the topic of this book. I could just provide the solutions that have been developed over the last half century, but these solutions developed by asking very basic, fundamental questions into the nature of what we know and how we know it. Before we attempt the math, let's follow that journey of discovery, and see if it does not inform our intuition about filtering. "
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     "source": [
      "#### Try Another Scale\n",
      "\n",
      "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n",
      "\n",
      "Well, what are our choices?\n",
      "\n",
      "* We could choose to only believe A, and assign 160lbs to our weight estimate. \n",
      "* we could choose to only believe B, and assign 170lbs to our weight.\n",
      "* We could choose a number less than either A or B\n",
      "* We could choose a number greater than either A or B\n",
      "* We could choose a number between A and B\n",
      "\n",
      "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A more than B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they measure. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n",
      "\n",
      "In mathematics this concept is formalized as *expected value*, and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we made one million separate readings. Some of the times both scales will read too low, sometimes that will both read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n",
      "\n",
      "We will deal with this more formally later, but for now I hope it is clear that our best estimate is just the average of A and B. $\\frac{160+170}{2} = 165$.\n",
      "\n",
      "Let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not just use it instead of B? Can B possibly improve our knowledge over A alone?\n",
      "\n",
      "The answer, perhaps counter intuitively, is yes, it can. Consider this case. We know scale A is accurate to 1 lb. In other words, if we weight 170 lbs, it could report 169, 170, or 171 lbs. We know that scale B is accurate to 9 lbs. We do a reading, and A=160, and B=170. What should we estimate our weight to be?\n",
      "\n",
      "Well, if we say 160 lbs we would be wrong, because B can only be 9 pounds off, and 170 lbs - 160 lbs is 10 lbs. 160 is not a possible measurement for B. In fact, the only number that satisfies all of the constraints is 161 lbs. That is 1 lb within the reading of A, and 9 lbs within the reading of B. \n",
      "\n",
      "This is an important result. With two relatively inaccurate sensors we were able to deduce an extremely accurate result. Now sure, that was a specially constructed case, but it generalizes. What if A is accurate to 3 lbs, B is accurate to 11 lbs, and we get the measurements of A=160 lbs and B=170 lbs? The result can only be from 159 lbs to 163 lbs, which is better than the range of 157 lbs to 163 lbs that is the range of values that A alone allows.\n",
      "\n",
      "> So two sensors, even if one is less accurate than the other, is better than one.\n",
      "\n",
      "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. \n",
      "\n",
      "So, what if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 1,000,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. I will not prove it, but it can be proved that the average of a large number of weighings will be extremely close to my actual weight. Consider a simple case - the scale is accurate to within 1 lb. If I weigh 170, it will return one of either 169, 170, or 171. The average of a bunch of 170 is 170, so we can exclude those. What is left is measurements of 169 and 171. But we know there will be as many 169s as there are 171s. The average of those will also be 170, and so the average of all must be 170, my true weight. It's not that hard to extend this to any arbitrary accuracy.\n",
      "\n",
      "Okay, great, we have an answer! But it is not a very good answer. No one has the patience to weigh themselves a million, or even a hundred times. \n",
      "\n",
      "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n",
      "\n",
      "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise - bad measurements. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! \n",
      "\n",
      "Shall we give up? No, let's play 'what if'. Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it, but it seems pretty likely that my weight held steady.\n",
      "\n",
      "Another what if: what if the readings were 158.0, 164.2, 160.3, 159.9, 162.1, 164.6, 169.6, 167.4, 166.4, 171.0? Let's look at a chart of that and then answer some questions."
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      "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6,\n",
      "           169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
      "plt.plot(weights)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.show()"
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xcXHEx8cD4O7uTkRERKlfo0SFOzk5mcjISAD2799PYGAgjz/+ODt37mTTpk2l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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751b90a90>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. Lets look at that in a chart. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n",
      "\n",
      "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should just average all the measurements. Let's look at that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "ave = np.sum(weights) / len(weights)\n",
      "plt.plot(weights,label='weights')\n",
      "plt.plot([0,12], [ave,ave], c='r', label='hypothesis')\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2NBGmiIiIlKlpn20hJ89M9N1NVGyLoIJbREREytCP+0+wautRPN1deH5oe6Pj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\nMm2KAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7518df2b0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That doesn't look very convincing. \n",
      "\n",
      "Now, let's assume we we gained weight. How much? I don't know, but numpy does! We just want to draw a line through the measurements that looks 'about' right. numpy has functions that will do this according to a rule called \"least squares fit\". Let's not worry about the details of that computation, or why we are writing our own filter if numpy provides one, and just plot the results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = range(len(weights))\n",
      "line = np.poly1d(np.polyfit(xs, weights, 1))\n",
      "plt.plot(weights, label='weights')\n",
      "plt.plot (xs, line(xs), c='r', label='hypothesis')\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5YnxcXl4e/fr147333gPg+++/55tvviE/P5++ffsyfvx4U5UshBBCiGKSp9Ux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\nIiIiIiI2pIZbRERERMSG/h8r4M+OGeafCAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751596160>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks much better, at least to my eyes. It seems far more likely to be true that I gained weight than I didn't gain any weight. Did I actually gain 13 lbs? Who can say? That seems impossible to answer.\n",
      "\n",
      "\"But is it impossible?\" pipes up a coworker.\n",
      "\n",
      "Let's try something crazy. Let's just assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, just assume I know it somehow. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's just see if we can make use of such information if it was available.\n",
      "\n",
      "The first measurement was 158. We have no way of knowing any different, so let's just accept that as our estimate. If our weight today is 158, what will it be tomorrow? Well, we think we are gaining weight at 1 lb/day, so our prediction is 159, like so:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a lot of the plotting code is not particularly useful to read, \n",
      "# so for each chapter I have placed the uninteresting code in a \n",
      "# file named xxx_internal. I import this  file and call whatever \n",
      "# function I need.\n",
      "\n",
      "import gh_internal\n",
      "gh_internal.plot_estimate_chart_1()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vJUuWuHRwLS0teumllxQTE8M3vALodhhhBwB0hEu9QV1dnWw22zXTrVarLl26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\nA/dUyQPEFONTAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7518c8da0>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Okay, but what good is this? Sure, we could just assume the 1 lb/day is accurate, and just predict our weight for 10 days, but then why use a scale at all if we don't incorporate its readings? So let's look at the next measurement. We step on the scale again and it displays 164.2 lbs."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.plot_estimate_chart_2()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lpqYqMzNT1dXVysrK0h133NGiY9tstrYoEc0QHBwsibEPFMY/sBj/wGHsA4vx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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751770c88>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here the measurement is in blue, the previous estimate (output of the filter) is black, and the estimate is red. So we have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right?. If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n",
      "\n",
      "> The key insight to this entire book follows. Read it carefully!\n",
      "\n",
      "So what do we do? If we only take data from the measurement than the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of blend of the prediction and measurement. \n",
      "\n",
      "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should like between 159 (the prediction) and 164.2 (the measurement). \n",
      "\n",
      "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when A was much more accurate than B - we scaled the answer to be closer to A than B. Let's look at that in a chart."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.plot_estimate_chart_3()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FYpw+fRq7du1Ceno6Jk+eDMB8kZ9IJMJ3332HOXPmADCv5fz3v/8doaGhCA4O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\nJCIW4EREREREIvp/bTsez/4XC3MAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751841208>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try a randomly chosen number: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n",
      "\n",
      "$$ \\verb,new estimate, = \\verb,prediction, + \\frac{4}{10}(\\verb,measurement, - \\verb,prediction,)\n",
      "$$\n",
      "\n",
      "The difference between the measurement and prediction is called the *residual*, which is depicted by the black vertical line in the plot above. This will become an important value to use later on, as it is an exact computation of the difference between measurements and the filter's output. Smaller residuals imply better performance.\n",
      "\n",
      "Let's just code that up and see the result when we test it against the series of weights from above.. We have to take into account one other factor. Weight gain has units of lbs/time, so to be general we will need to add a time step $t$, which we will set to 1 (day)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n",
      "           169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n",
      "\n",
      "time_step = 1 # day\n",
      "scale_factor = 4/10\n",
      "\n",
      "def predict_using_gain_guess(weight, gain_rate): \n",
      "    # store the filtered results\n",
      "    estimates = []\n",
      "\n",
      "    # most filter literature uses 'z' for measurements\n",
      "    for z in weights: \n",
      "        # predict new position\n",
      "        prediction = weight + gain_rate * time_step\n",
      "\n",
      "        # update filter \n",
      "        weight = prediction + scale_factor * (z - prediction)\n",
      "\n",
      "        # save for plotting\n",
      "        estimates.append(weight)\n",
      "\n",
      "\n",
      "    # plot results\n",
      "    n = len(weights)\n",
      "    plt.xlim([1, n])\n",
      "\n",
      "    plt.plot (range(1, n+1), estimates, '--', label='filter')\n",
      "    plt.plot(range(1, n+1), weights, c='r', label='measurements')\n",
      "    plt.plot([1, n],[160, 160+n],c='g', label='actual')\n",
      "    plt.legend(loc=2)\n",
      "    plt.xlabel('day')\n",
      "    plt.ylabel('weight (lbs)')\n",
      "    plt.show()\n",
      "\n",
      "predict_using_gain_guess (weight=160, gain_rate=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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s2Xh89hmWWrWI2r4dQ5kyQOHu58xKRrDqILIW3KhPBV1tBrQLoFermvh4FO46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\nIgpuAAAAIIr+BDZN3fAXJldbAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751547748>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is pretty good! The blue dots, showing our estimates, are not a straight line, but they are straighter than the measurements and somewhat close to the trend line we created. Also, it seems to get better over time. \n",
      "\n",
      "This 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 see what happens if I predict that there is no weight gain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "predict_using_gain_guess (weight=160, gain_rate=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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atShaLXFz54IDfy2XkpG8MaaZ2fbreZbvOE3kpbsAeLtrSUwx4u3havPrO03C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G4AAADAiwjcAAAAgBcRuAHAz+3evVtms9nXZQDArEXgBgAAALyIwA0AAAB4UZCvCwAAeI7dbtdn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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751574b38>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly a filter that requires us to correctly guess a rate of change is not very useful. \n",
      "Even if our initial guess was useful, the filter will fail as soon as that rate of change changes. If I stop overeating the filter will have extremely difficulty in adjusting to that change. \n",
      "\n",
      "But, 'what if'? What if instead of just leaving the weight gain at the initial guess of 1 lb (or whatever), we compute it from the existing measurements and estimates. On day one our estimate for the weight is:\n",
      "\n",
      "$$\n",
      "(160 + 1) + \\frac{4}{10}(158-161) = 159.8\n",
      "$$\n",
      "\n",
      "On the next day we measure 164.2, which implies a weight gain of 4.4 lbs (since 164.2 - 159.8 = 4.4), not 1. Can we use this information somehow? It seems plausible. After all, the weight measurement itself is based on a real world measurement of our weight, so there is useful information. Our estimate of our weight gain may not be perfect, but it is surely better than just guessing our gain is 1 lb. Data is better than a guess, even if it is noisy.\n",
      "\n",
      "So, should we just set the new gain/day to 4.4 lbs?  Hmm, sounds like our same problem again. Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n",
      "\n",
      "$$\\verb,new gain, = \\verb,old gain, + \\frac{1}{3}\\frac{measurement - predicted~weight}{1~ day}\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weight = 160  # initial guess\n",
      "gain_rate = 1.0 # initial guess\n",
      "\n",
      "time_step = 1\n",
      "weight_scale = 4/10\n",
      "gain_scale = 1/3\n",
      "estimates = []\n",
      "\n",
      "for z in weights:\n",
      "    # prediction step\n",
      "    weight = weight + gain_rate*time_step\n",
      "    gain_rate = gain_rate\n",
      "    \n",
      "    # update step    \n",
      "    residual = z - weight\n",
      "    \n",
      "    gain_rate = gain_rate + gain_scale   * (residual/time_step)\n",
      "    weight    = weight    + weight_scale * residual\n",
      "  \n",
      "    estimates.append(weight)\n",
      "\n",
      "# plot results\n",
      "n = len(weights)\n",
      "plt.xlim([1, n])\n",
      "    \n",
      "plt.plot(range(1, n+1), estimates, '--', label='filter')\n",
      "plt.plot(range(1, n+1), weights, label='measurements')\n",
      "plt.plot([1 ,n], [160,160+n], label='actual')\n",
      "plt.legend(loc=2)\n",
      "plt.xlabel('day')\n",
      "plt.ylabel('weight (lbs)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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v7M99QzrSrZ2PzZJ8KRmpP6r4+PgWsUpJYmIiERERle5LT0/H19e3gSMSrYkt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\nAPAjAjcAAADgR/8LA8JgCQNEwUQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7518e43c8>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I think this is starting to look really good. We used no methodology for choosing our scaling factors of $\\frac{4}{10}$ and $\\frac{1}{3}$ (actually, they are poor choices for this problem), and we 'luckily' choose 1 lb/day as our initial guess for the weight gain, but otherwise all of the reasoning followed from very reasonable assumptions.\n",
      "\n",
      "One final point before we go on. In the prediction step I wrote the line\n",
      "\n",
      "    gain_rate = gain_rate\n",
      "    \n",
      "This obviously has no effect, and can be removed. I wrote this to emphasize that in the prediction step you need to predict next value for **all** variables, both *weight* and *gain_rate*. In this case we are assuming that the the gain does not vary, but when we generalize this algorithm we will remove that assumption. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The g-h Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This algorithm is known as the g-h filter. *g* and *h* refer to the two scaling factors that we used in our example. *g* is the scaling we used for the measurement (weight in our example), and *h* is the scaling for the change in measurement over time (lbs/day in our example)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This filter is the basis for a huge number of filters, including the Kalman filter. In other words, the Kalman filter is a form of the g-h filter. So is the Least Squares filter, which you may have heard of, and so is the Benedict-Bordner filter, which you probably have not. Each filter has a different way of assigning values to *g* and *h*, but otherwise the algorithms are identical. For example, the $\\alpha$-$\\beta$ filter just assigns a constant to *g* and *h*, constrained to a certain range of values. Other filters will vary *g* and *h* dynamically, and filters like the Kalman filter will vary them based on the number of dimensions in the problem.\n",
      "\n",
      "\n",
      "**Let me repeat the key insights as they are so important**. If you do not understand these you will not understand the rest of the book. If you do understand them, then the rest of the book will unfold naturally for you as mathematically elaborations to various 'what if' questions we will ask about *g* and *h*.\n",
      "\n",
      "* Multiple measurements are more accurate than one measurement\n",
      "* Always choose a number part way between two measurements to create a more accurate estimate\n",
      "* Predict the next measurement based on the current estimate and how much we think it will change\n",
      "* The new estimate is then chosen as part way between the prediction and next measurement\n",
      "\n",
      "Let's look at a visual depiction of the algorithm."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gh_internal.create_predict_update_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ro0c3+JjVpk2bhi1btuDo0aNmpa8KCgowb948AMDHH3+MoKAgrFixAqWlpfD3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\nqrCwUIWFhZyrCkQ4QiuAiBUVFaURI0ZoxIgRam9v16FDh1RRUaFDhw6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       "text": [
        "<matplotlib.figure.Figure at 0x7fc751679198>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I'll begin to introduce the nomenclature and variable names used in the literature. Measurement is typically denoted $z$, and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $\\mathbf{z_k}$ is the data for this time step. A bold font denotes a vector. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our data, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "Finally, a hat '$\\hat{}$' indicates an *estimate*. So the output of the predict step time $k$ at is the *estimate* of our state $\\mathbf{\\hat{x}_k}$, and again this is a vector of all the state variables. So for our scale example it contains the estimate of both the weight and the gain rate.\n",
      "\n",
      "So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$. We then enter a loop, predicting the state for time $k$ from the values from time $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{\\hat{x}_k}$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Write Generic Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the example above, I explicitly coded this to solve the weighing problem that we've been discussing throughout the chapter. For example, the variables are named \"weight_scale\", \"gain\", and so on. I did this to make the algorithm easy to follow - you can easily see that we correctly implemented each step. But, this is specialized code. Rewrite it to work with any data. Use this function signature:\n",
      "\n",
      "    def g_h_filter (data, x0, dx, g, h)\n",
      "        \"\"\"\n",
      "        Performs g-h filter on 1 state variable with a fixed g and h.\n",
      "\n",
      "        'data' contains the data to be filtered.\n",
      "        'x0' is the initial value for our state variable\n",
      "        'dx' is the initial change rate for our state variable\n",
      "        'g' is the g-h's g scale factor\n",
      "        'h' is the g-h's h scale factor\n",
      "        'dt' is the length of the time step \n",
      "        \"\"\"\n",
      "\n",
      "Test it by passing in the same weight data as before, plot the results, and visually determine that it works."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def g_h_filter (data, x0, dx, g, h, dt=1., pred=None):\n",
      "    \"\"\"\n",
      "    Performs g-h filter on 1 state variable with a fixed g and h.\n",
      "    \n",
      "    'data' contains the data to be filtered.\n",
      "    'x0' is the initial value for our state variable\n",
      "    'dx' is the initial change rate for our state variable\n",
      "    'g' is the g-h's g scale factor\n",
      "    'h' is the g-h's h scale factor\n",
      "    'dt' is the length of the time step \n",
      "    'pred' is an optional list. If provided, each prediction will\n",
      "    be stored in it\n",
      "    \"\"\"\n",
      "    \n",
      "    x = x0\n",
      "    results = []\n",
      "    for z in data:\n",
      "        #prediction step\n",
      "        x_est = x + (dx*dt)\n",
      "        dx = dx\n",
      "        \n",
      "        if pred is not None:\n",
      "            pred.append(x_est)\n",
      "        \n",
      "        # update step\n",
      "        residual = z - x_est\n",
      "        dx = dx    + h * (residual) / dt\n",
      "        x  = x_est + g * residual\n",
      "        \n",
      "        results.append(x)\n",
      "        \n",
      "    return results\n",
      "\n",
      "def plot_g_h_results(measurements, filtered_data, title=''):    \n",
      "    plt.plot(filtered_data, '--',label='filter')\n",
      "    plt.plot(measurements,label='measurement')\n",
      "    plt.legend(loc=4)\n",
      "    plt.title(title)\n",
      "    plt.show()\n",
      "\n",
      "\n",
      "plt.xlim([0,10])\n",
      "plt.plot([0,9],[160,170],label='actual')\n",
      "data = g_h_filter(data=weights, x0=160, dx=1, g=6./10, h = 2./3, dt=1.)\n",
      "plot_g_h_results(weights, data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7WiJZ8dpWVhQ6OVZe63vc4H4x5GU7yMtycMPAwLWEiw8bgoWNAdHjGNX3q8SFXX7ddE9i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\nffONzmSMYUfZKxy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9iA7t57fxulpx2VlfL+MDpVW+48nxkeRmpZOX7WDU4D4dukpuDR+L\n7Se/xvzpd5jNH2I2f4DZ/AEEh8DwsVhjJ2KNmYAVHeuPt9SrmbXLwLkP4hKx7nsk0OVIN6GQLCIi\n7WKqq774eHrRg1gxPfuqb0eVVtSycnMxKwqd7DpU7jseHxXK3Inp5GU5mHBTMjab/5aPeLe1/j5m\nziLMji2YnZuhuMi7a9+nWzGWDYYOwxo7CWvcJKykZL+9dm9hDh/ArPoTALZvfg8r8tLLXeT6opAs\nIiLtYl5/AepqvF0AsqYFupyAqKxpZPUWbzDeUlSGObeHbVRYMDNvSSMvayi3jRxIcFDn3gBmJQ/C\nmj0IZi/EVFV6A/LOzbB3FxzY491e+c3fw8A0b1geO8m7SUYvWe/dXqapCc+L/wVuN9Yd87CGjw10\nSdKNKCSLiMg1M59tx2zdCCEh2P7mOx0KW8YYyuo+IzlyVI8IbbUNzazdfoQVhU42fn6MFrc3GYcG\n27ljbCp52Q6mjU0hPCQwf8VacQlYU2bBlFmYhnrM5x/Djs2Yz7bD8SOY40cwq1+HhCTvkoyxE+GG\nEVhB118kMMtfhrJj0D8Fa8H9gS5Hupnr7/8IERHpENNY771ZD7By7+vwR/jFZz5k+4nfMzjuNiYO\nfNgfJfpdQ3ML63eWkF/gZP3OozS63ADYbRZTRw8iN9vBrPGDiY7oXht8WOERWJm3QeZtGJcLij7D\n7NyM2bkVKk97O2SsXw0RUVijM6+rG//M7h3e9263e3tOh4QGuiTpZhSSRUTkmpj8V6GyHNKGYt0x\nv0Nj1TWXs/PkHwFIjhrlj/L8xtXiYdPu4+QXOlm77TC1jS7fuYk3JZOb7WDuhCEkxoQHsMqrZwUH\nw8ibsUbejLn3ETh8wBuYd2yBsmPX1Y1/pq4Gz0tPA2DN+5o2ZZE2KSSLiMhVM8593qtvNpt36+kO\nbGJxftOQFk8jA6NvITVmkh8rbR+Px7Btfxn5hU5WbzlEZU2j79zoIX3IzXIwb1I6AxOjAlhlx1k2\nG6TfhJV+Eyz4BubEMczO6+PGP2MM5pXnoKoSHMOwZi0MdEnSTSkki4jIVTEtLu/W08ZgzVyAlZre\nofGKz3zAybrPCbFHccuABwK2HtkYw2eHy8kvcLJyczEnKut854YOiCMvy8H8rHQc/Xtv9w6r/yCs\n/tfHjX9m60bM9k0QGobtwce1W6FckkKyiIhcFbN2GZQehaRkrHn3dGwsYzhUtQmA8f3vJyyo6z/S\nP1haRX6Bk/zCgxwqq/YdH5gYRW5WOrlZQxmRltAjg2BH9OYb/0zlacyr/w2AtXgJVt/+Aa5IurPu\nP6NFRCTgzIljmDVvAHiXWXTwJifLspg6+AlKqreS0oXLLI6X17Ki0El+oZPdRyp8x/vEhDNv0hBy\nJzkYf0M/v/Yy7sl6041/xuPB8z9PQ0MdjJmANXlGoEuSbk4hWURELst4PN5lFi0tWJNnYA0b7Zdx\n7bZgBsfd6pexLuf02XpWbzlEfoGT7QdO+o7HRIQwO3MweVkOsocPIMjeub2Me7qefuOfWb8K9u2C\n6Fhs93esbaFcHxSSRUTksszGd+DgHoiJw/rKNwNdzlU5W9fE2u2HyS9wsml3KZ5zu3yEhdiZMS6N\nvGwHU8ekEBqs9ajt0dNu/DPHj2KW/QE490lITHxA6pCeRSFZREQuyZypwCx7CQDb1x7Giuy+XR0a\nmlp4b4d3k4/1O0tobvEAEGS3mDoqhbzsocwcn0ZkWHCAK+19uvONf6bFhefF/4QWF9Ztd3rXUItc\nBYVkERFpkzEGz6vPQWMDjJkA4zu2NOJU3V7iwtIIsUf4qUJodrl57xNvMH7n4yPUN7UAYFmQPbw/\neVlDuWvCYOKjut8a2d6qu934Z1b+EUoOeW84XfRgp7yG9E4KySIi0rZPCuDTrRAWju3eRzp01a+u\n+TR/PfpLgm0R3On41w51s3B7PGzeW8baHVvJ31R0QS/jcY4kXy/j5PjIdr+G+Eegb/wzB/Zg1i4H\ny4btwb/DCvPfL2jS+ykki4jIRUxdLZ4//Q4Aa+E3sBL6tH8s42Fr6Qu0eBrpHzW6XQHZGMPO4tPk\nFzhZtbmYk1X1vnM3DYonN8tBbpaDwf1i2l2ndK6uvvHPNNTjefGX3r7ed30Fa+hwP78j6e0UkkVE\n5CJm2Utw9gwMzcDKmdWhsZxn1nOqbg+h9mhu7v+Na3ruvpJK8gudrCx0cuRUje94alI099wxksW3\nDyc5Wl0pepquuPHPvP4CVJzyrn3uYF9vuT4pJIuIyAXMvl2Yv74LQUHeTgC29ofQ2uZTfHryNQDG\n93+AsKArX+k9cqqaFYVOVhQ42XfsjO9437hw5k1ykJflYJwjiT59vFe3KyoqLjWU9BD+vvHP7NiM\n+WgdBAVje+j7WEG6WVOunUKyiIj4mOYmPP/7DADWnEVY/VM6NF5pzQ5aPE2kxEwkJXbCJR938kw9\nq7YUk1/gZIfzlO94XGQod2UOJjfbQVZGf+wdCOzSM3T0xj9PVaW3rzfnlgoNSA3k25EeTCFZRER8\nzOrX4NQJGJCKNWthh8e7MXEmMaEDiAtLu+jcmdpG3tp6mPzCgxTuPcG5VsZEhAYxc3wauVkOpowe\nREiQehlfr671xr/GnOk0vr8GaqshYwzWtLmBfgvSgykki4gIAOZoMeadv4BleZdZ+Okj6uSoUb6v\n6xpdvPvxEfILnWzYdQyX29vLOCTIxtQxKeRmOZgxLpUI9TKWVq7mxr/qzR94HxwRie2B73VoqZCI\nQrKIiGDcbu9H1B4P1rS5WI5hfhu7yeXmw09LyC908t6OozSc62VssyxyRg4kN8vB7MzBxEaG+u01\npXe71I1/9s+303L4ILb7v9uhjiwioJAsIiKAeX8VHDkICX2w7v56h8drcXso2FNKfqGTt7cdprq+\n2Xfulhv6kZftYO7EISTFqm+tdNz5G/8Svv4woJs5xT8UkkVErnPmdBlmxSsA2O7723ZvuGCMoXD/\nXj7YVcQb6+sor27wnRuemkBetoP5kxykJEX7pW4Rkc6kkCwich0zxuB55VlobsaakIM1OvOan7/n\naKW3ZVvhQXJnFTBk2FkG7ssgKtxBXra3ZdsNA+M76R2IiHSOy4bkdevW8fzzz7Nnzx7mzp3Lz372\nM9+5l156iZdffpmqqiqGDBnCsmXLfP0KCwoK+PnPf05JSQl9+vTh//7f/8uwYf5b3yYiIv5hCj+A\nPTshMhpr8ZKrfl5x2VlfL+MDpVUATL7lOI7Us7S4wnnqvq8xbsjgDm1lLSISSJcNyTExMSxZsoSC\nggIaGxt9x9esWcNLL73Es88+y/Dhw9m/f7/vB+GxY8f47ne/y1NPPcXMmTOprKzEprtLRUS6HVNd\nhXnjRQCsRQ9ixcRd9vGlFbWs3FzMikInuw6V+47HR4WyICeRkWMLMcCU9IcZFDOkM0sXEel0lw3J\nEyZ4G7/v3r37gpD82muv8e1vf5vhw737oN94442+c3/5y1/Iyclh9uzZAL4dkUREpHsxr78AdTXe\nfrJZ09p8TGVNI6u3eIPxlqIyXy/jqLBgZt6SRl7WUCaP6M+mYz/ndL2L1NgsBsXc0oXvQkSkc1zV\nmmRz/qfiOUVFRUycOJEZM2bQ0tLCggUL+O53v+s7l5iYyKJFizh+/DiTJk3ipz/9KVFRUW2OnZiY\n2MG3IL1JcLC3N6rmhXyZ5oX/NX1cwNmtGyEklMTv/gj7ly5oVNc1sbJwP29u2Mv7nxym5Vwv49Bg\nO3dNHMqi2zOYlekgPNT73+VMfQnVzccJD45n+vDvERZ85a2n/UHzQlrTnJC2nJ8X1+qqQnLrNWU1\nNTVs3LiR119/naamJu677z4yMjKYPn06NTU1bNu2jZdffpm0tDQef/xxnn76aX70ox+1OfaTTz7p\n+zonJ4cpU6a0642IiMjV8TTUUfPbXwAQ9bVvYU8eSEOTi7XbnLzx4V7e3uqksdnby9hus7jzlnQW\n3Z7B/KwbiWmjl3F8RAr3jH+O6sayLgvIIiKXs2HDBjZu3AiA3W4nJyfnmsdo15Xk8PBwFixYQEJC\nAgB33nknW7ZsYfr06YSHh3Prrbf6btRbtGgRTz/99CXHfvTRRy/4Xr0Nr2/nf/vXPJAv07zwL89r\nz2PKT2JSHbwVeSP5/7aMtdsOU9vo8j1m0rBk5mc5mDthCIkx4QC4GmupaKy95LghJHfpfyPNC2lN\nc0LOGzlyJCNHjgS882LTpk3XPEa7riSnpqZe8P2XQ3Rqairl5eUXnGsdskVEJDDcB/dh3l+NB4t7\nj6VT+Iv3fOdGD+lDbpaD+ZPSGZDY9hI5EZHrxWVDssfjweVy4Xa7cbvdNDc3Y7PZmD59Om+++Saz\nZs2iqamJdevW8cQTTwAwY8YMHnnkEfbv309aWhp//vOfmTRpUpe8GRERuZgxhs8Ol7Ny034W/fW/\ncWD4rWsoha4whg6IIy/LwfysdBz9L9/dQkTkenLZkJyfn88Pf/hD3/crV65k6dKlPPzwwxw/fpzp\n06cTFhbGPffcw/Tp0wHIzMzkO9/5Dg8++CAul4vJkyfz2GOPde67EBGRixwsrSK/wEl+4UEOlVXz\nWNB+HCFnOWZFUT99Ae9MzmBEWsI19zL2GA/HqreQEjMRy1KLTxHpnayioqKArYUoKSkhIyMjUC8v\n3ZDWk0lbNC+u3vHyWlYUOskvdLL7yBd/XrdEu3jD8x5Bxg3ffxJ7xph2v0ZRxVp2lr1KSsxEslOW\n+qPsdtG8kNY0J6Qt59ckp6SkXNPztC21iEgPd/psPau3HCK/wMn2Ayd9x2MiQpidOZi8SUPIfvsZ\nrINurMkzsHUgINc0lfHZyTcBSIvN7nD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d3ZkyZQrJycknvF5K2elLPP2RzN4OWzeCmwfi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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75183cb38>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Choice of g and h"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The g-h filter is not one filter - it is a classification for a family of filters. Eli Brookner in *Tracking and Kalman Filtering Made Easy* lists 11, and I am sure there are more. Not only that, but each type of filter has numerous subtypes. Each filter is differentiated by how g and h are chosen. So there is no 'one fits all' advice that I can give here. Some filters set g and h as constants, others vary them dynamically. The Kalman filter varies them dynamically at each step $k$. Some filters allow g and h to take any value within a range, others constrain one to be dependent on the other by some function $f(\\dot{}), \\mbox{where }g = f(h)$.\n",
      "\n",
      "The topic of this book is not the entire family of g-h filters; more importantly, we are interested in the *Bayesian* aspect of these filters, which I have not addressed yet. Therefore I will not cover selection of g and h in depth. Eli Brookner's book *Tracking and Kalman Filtering Made Easy* is an excellent resource for that topic, if it interests you. If this strikes you as an odd position for me to take, recognize that the typical formulation of the Kalman filter does not use g and h at all; the Kalman filter is a g-h filter because it mathematically reduces to this algorithm. When we design the Kalman filter we will be making a number of carefully considered choices to optimize it's performance, and those choices indirectly affect g and h. Don't worry if this is not too clear right now, it will be much clearer later after we develop the Kalman filter theory.\n",
      "\n",
      "However, it is worth seeing how varying g and h affects the results, so we will work through some examples. This will give us strong insight into the fundamental strengths and limitations of this type of filter, and help us understand the behavior of the rather more sophisticated Kalman filter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: create measurement function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's write a function that generates noisy data for us. Recall from chapter 0 that we model a noisy signal as the signal plus white noise generated by `numpy.random.randn()`.  We want a function that we call with the starting value, the amount of change per step, the number of steps, and the amount of noise we want to add. It should return a list of the data. Test it by creating 30 points, filtering it with `g_h_filter()`, and plot the results with `plot_g_h_results()`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "def gen_data(x0, dx, count, noise_factor):\n",
      "    return [x0 + dx*i + random.randn()*noise_factor for i in range (count)]\n",
      "\n",
      "measurements = gen_data(0, 1, 30, 1)\n",
      "data = g_h_filter(data=measurements, x0=0, dx=1, dt=1, g=.2, h=0.02)\n",
      "plot_g_h_results(measurements, data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PXDIMFxUV8dJLL+FwOJg5cyYAJpOJp59+mjfeeIOHH34Yr9dLWloaP/vZzzoNkRAREREZ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\neeCBBwgLC+O6666rr+G1117jj3/8I8HBwcyePZsnn3ySRYv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       "text": [
        "<matplotlib.figure.Figure at 0x7fc7518fd3c8>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Bad Initial Conditions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now write code that uses `gen_data` and `g_h_filter` to filter 100 data points that starts at 5, has a derivative of 2, a noise scaling factor of 10, and uses g=0.2 and h=0.02. Set you initial guess for x to be 100."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data (x0=5, dx=2, count=100, noise_factor=10)\n",
      "data = g_h_filter(data=zs, x0=100., dx=2., dt=1.,g=0.2, h=0.01)\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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W38NLBx9KtoDLTitnTsGN/HRrDxdVRnji7gs4f/oE2tvbR2SM6bYs8l3n0Nyz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\n3wBhlPVDtHPfwAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7516167f0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The filter starts out with estimates that are far from the measured data due to the bad initial guess of 100. You can see that it 'rings' before settling in on the measured data. 'Ringing' means that the signal overshoots and undershoots the data in a sinusodial type pattern. This is a very common phenomena in filters, and a lot of work in filter design is devoted to minimizing ringing. That is a topic that we are not yet prepared to address, but I wanted to show you the phenomenon."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Extreme Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rerun the same test, but this time use a noise factor of 100. Remove the initial condition ringing by changing the initial condition from 100 down to 5."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data (x0=5, dx=2, count=100, noise_factor=100)\n",
      "data = g_h_filter(data=zs, x0=5., dx=2., g=0.2, h=0.02)\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C0ij8wtkKb1H10hd7TbLzB2C+murwFM5Ux6YpNuqf09vEpQn6ZTV9UP259y3H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BBGnA8qz2TnOFNtGaXFVCezmWqCRv88NJWdCAAYShzOeh1Ql6YYg4hy+TV5cPC45AJ6MBzHLQ++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\nhBBCCCExoqCaEEIIIYSQGP1/pZqna2eWgZYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75178d9e8>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This doesn't look so wonderful to me. We can see that perhaps the filtered signal varies less than the noisy signal, but it is far from the straight line. If we were to plot just the filtered result no one would guess that the signal with no noise starts at 5 and increments by 2 at each time step. And while in locations the filter does seem to reduce the noise, in other places it seems to overshoot and undershoot.\n",
      "\n",
      "At this point we don't know enough to really judge this. We added **a lot** of noise; maybe this is as good as filtering can get. However, the existence of the multitude of chapters beyond this one should suggest that we can do much better than this suggests."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: The Effect of Acceleration"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Write a new data generation function that adds in a constant acceleration factor to each data point. In other words, increment dx as you compute each data point so that the velocity (dx) is ever increasing. Set the noise to 0, $g=0.2$ and $h=0.02$ and plot the results. Explain what you see."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def gen_data(x0, dx, count, noise_factor, accel=0):\n",
      "    zs = []\n",
      "    for i in range(count):\n",
      "        zs.append(x0 + dx*i + random.randn()*noise_factor)\n",
      "        dx += accel\n",
      "    return zs\n",
      "   \n",
      "predictions = []\n",
      "zs = gen_data(x0=10, dx=0, count=20, noise_factor=0, accel = 2)\n",
      "data = g_h_filter(data=zs, x0=10, dx=0, g=0.2, h=0.02, pred=predictions)\n",
      "plt.xlim([0,20])\n",
      "plot_g_h_results(measurements=zs, filtered_data=data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Dtc5m/rw2F5/PMDuKtJOOKIuIiMg3cqBmGztK/4nb5yQ8uC+X959HZGii2bH8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\n//znwP/h2WefZcSIEWzZsoXhw4cH9X/ggQeYOnU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dltTbiUg6fsQuISGBysrK\nwO3Kyko5f4qIOf74FKIr8Pv9vPvuuyQkJHDJJZcE2tt7/oxIomw0Gunfvz95eXl4PB7y8/OJjY2V\n6eFExLlcLvbs2YPX68Xr9fL5559jtVpJSkqKdGiiB/L7/Xg8Hvx+P4qi4PV68fl85OTksHHjRlwu\nF0VFRRQXFzNw4MBIhyt6mBMdnzt27MDpdOL3+9m9ezf79u0jKysr0uGKHmb16tWBWayO1d7zZ8SW\nsJZ5lEVX5HA4eP3116mpqUGj0WC327n88stJTEyMdGiiB/r+++/54IMPgtomTZrExIkTZR5lEXEn\nOj4rKyspKCjA7/djs9mYMmUK559/foSiFD1RXV0dL730EjqdLqj9jjvuwG63t+v8GbFEWQghhBBC\niK5MlrAWQgghhBAiDEmUhRBCCCGECEMSZSGEEEIIIcKQRFkIIYQQQogwJFEWQgghhBAiDEmUhRBC\nCCGECEMSZSGEEEIIIcKQRFkIIYQQQogwJFEWQgghhBAijP8PW4o/MzDrA64AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7518411d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Each prediction lags behind the signal. If you think about what is happening this makes sense. Our model assumes that velocity is constant. The g-h filter computes the first derivative of $x$ (we use $\\dot{x}$ to denote the derivative) but not the second derivative $\\ddot{x}$. So we are assuming that $\\ddot{x}=0$. At each prediction step we predict the new value of x as $x + \\dot{x}*t$. But because of the acceleration the prediction must necessarily fall behind the actual value. We then try to compute a new value for $\\dot{x}$, but because of the $h$ factor we only partially adjust $\\dot{x}$ to the new velocity. On the next iteration we will again fall short.\n",
      "\n",
      "Note that there is no adjustment to $g$ or $h$ that we can make to correct this problem. This is called the *lag error* or *systemic error* of the system. It is a fundamental property of g-h filters. Perhaps your mind is already suggesting solutions or workarounds to this problem. As you might expect, a lot of research has been devoted to this problem, and we will be presenting various solutions to this problem in this book.\n",
      "> The 'take home' point is that the filter is only as good as the mathematical model used to express the system. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise: Varying g"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's look at the effect of varying g. Before you perform this exercise, recall that g is the scale factor for choosing between the measurement and prediction. What do you think of a large value of g will be? A small value? \n",
      "\n",
      "Now, let the `noise_factor=50` and `dx=5`. Plot the results of $g = 0.1\\mbox{, } 0.5,\\mbox{ and } 0.9$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solution and Discussion"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = gen_data(x0=5, dx=5, count=100, noise_factor=50)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.1, h=0.01)\n",
      "plot_g_h_results (zs, data, 'g = 0.1')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.5, h=0.01)\n",
      "plot_g_h_results (zs, data, 'g = 0.5')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0., dx=5., dt=1.,g=0.9, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.9')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p/CP62khw2jrgGu9k6LpOg7f70BcAm8XIv117Hh5fiFuvPIfcjL6DW5sxJ9Lz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lFJNUC0cTw5ZQc5nv8JfQOua3O1CYfDyZJ3PuHeO2soq1Bz/+Qx/L+bBmNz5rMjbWej7coT+4Ww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\nooMkqRZCCCGEEKKD/g8pnXlLagQniwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751684438>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9nl9Y9xYljdt5+9gvKKh9s92xiBqmOaiVbFx+5qJ+Z74NiqmlVZ7KicaPga7r\nqaF1qqInWEOK08Luwko2vvEZJX0YBKNnqg+XhHFazf1ad39JUC2EEEKIQaWqEQ7XvArA9IyLSLdP\nRsFIg6+EYLj7jYWxtLZqG4/NYmLN+bNobNKC6u7KP/QR5UVlQR76914uWTQJUGhqNrdcO/AlIHp/\n6gz7NP786n6KKxqZNiaV5+++lPu/sZyM5N6NBVcUAzZTKtC7VoLuljrniBpm18m/srPsr4Qj2pCW\npkAlKmEc5kx+cM2S/nxbUXoJyAn3LqCHoNqilWw0B6vJnzSKK8+egj8Y5t6/be/185oDWqa6wW1j\nzqT+teXrLwmqhRBCCDGoyps+wR0ow25KZ3zyQkwGK2n2iaio1HgL+3y/jq3alswegzsaVPdc/tHs\nNZGXm8niWaPJSLZR79aD6oEtAVFVlWpv69CXrBQ7o9Od3Pe1c1g4I6fP99PrqnvTks7t14Lq0zIv\nw6CYKax7k7eP/QJfqKHNJMUxfV5DR3pbPf1nHaudnk6vg/YEa1DVCD+6bhE2i5EXtxfxwWcne3yW\nP9SEJ1RNKKwwypWN0yaZaiGEEEKcwg7VbAZgWvoqDIrWVSLTPg3oX111NKhuyYKePWs0EzK1zhO9\n2ajY5DFzxvQsDAaF269ewMTMnB6vTQRPsAZfqB6L0UmSJYf/uCiP7Q9ex8J+ThPU66ofevld1vx6\nc5fnhSMhPMEqFBROG3UF5+X+GLspjWrPYV4rvDvakaU/kxQ70gfA6LrLVJsMNqzGJCJqCF+ogbEZ\nLr55qVbOc8/GDwhHIt0+q7z5E0DlaEkKebl9/1ASLwmqhRBCCDFo6n0lVDR/ilGxMCV9RfT1TIcW\nVPenA0i0/KMlC5qRbOee61cC4A32IlPtMbNwuhaErV15GrlZWoZ2oMs/oq307FOiQ1+MBkO/h5bo\nXTUKykt5a28JDc3+mOc1B6tQUXGYMzEazGQ4prBq8k9Js07BG6qlpFErt0hIUG1tDW5tplSspqRu\nz+/Yq/rmS/KZNyWLr12Uh0L3P5eT7j0AfFaQztzJo+JZdr/E38hQCCGEEKKX9FrqSannYDE6o69n\ntATVNd4CImoEQ4zJgrGEIgGaAhWAASXcWkNr78UQF19IL/8wc8a01uzwYI0qr25TT50IdrNWUz11\nnIE3P4Qdhytidu5wB7RSCqc5m+0HT7Jtfxnb9p9gb9EYLl/ZzFlztdKQlARnqrvLUuuclkzqfEV4\ngtXANOyWpBfUAAAgAElEQVRWE//+78t6/KARUSOcbNoHwC+/so4UW/ylK30lmWohhBBCDApfqIFj\nDe8DMD3jQgDqm/3ceP9rbHqvEoc5g2DEG63p7Y1GfxkqKpU1Ns741tPUNGobHbWMqII/7CaihmNe\nq48o//LyeWSnOaKv20z6qPKBDarbjidPBL2melzL54MPu6hDbvJrEw73FkS46mcvcv+zH/PRoQqC\nQQOHD56NM3gVMzO/QLp9cvxrMmdES3xSuhj60lY0Ux2oib7Wm8x9rbeQQLgJlyWL8em5pDit/Vxx\n/0mmWgghhBCDorD2TSJqkDGuudFpewVl9by66xiv7jrGg3eMAXMN1Z4jXU7d60ivpy6rdDB7Qka0\nW4ZBMWE1uvCH3fhD7mgWt61AWKupXjlvVrvXo100wgNX/hGKBKjzakNf0m3xB6/QOpo7LVlrqffh\nwfKY5+mdP3KSxzF9rI2ls8eydPYYzpo1OuHBqEEx4LJk0egv612m2tzaAaQv9NKP0a7T+10+Ey/J\nVAshhBBiwIUjQQrq3gC0Nnq6M6Zl81/XngHAc+9ofaGrPYd7fd/Glnrqk5VOrl3WvoyipxZzek21\nzdi+zlfPVHuDDYTC3W+O6686XzEqYQyRLFb+8EWe2db/aZI6PVNtMjdjNCgcOF6DNxDqdJ4eVC87\nLZ+37ruWn91wNheeMXDZ3XHJi7Aak8lx5fV4bmuv6p6DalVV2fLxMSIRlbKmvQCMTpob32LjIJlq\nIYQQQgy44w0f4As1kGIdT5bztHbHvn35XCrqPLz+iRbklrtjT/mLpcJdDEB1XRKXntk+4xsKaSUd\nL3y0jxuW53a61t9SU23pFFRrNdWHykqweE6yLC/+2uKO9C4nRSVJFJ5soMYd/6AZPRvvDzfw9J0X\nc9rETOyWzqGe3k4v2To4HTLmZF3NnKyre3Vux42KHQVDER57/QCTc1J4eUcRf3v7EHd8cTqjpx7D\nqFjIcsxM2Lr7SoJqIYQQQgy4w7WvATAj46JOv55XFIWfrl1M2QON+AN7wVKNL9QQDW67U918HKMZ\npmVN75RpDQbsYIQ9RUXcsLz9daGIn7AawKCYMRnaX6c/1+UI8PrHxwYoqNbqqT/4xIDFZOCapfFv\nVjQZbJgNDoIRD/OmJ2E1WTqdE4r48YZqMSjGaAA7nDgtrZlqVVU7vVf+9vZB7tn4AYoCqgo2s5Hx\nYysIAdmu2RgNnb/nwSLlH0IIIYQYUM2Baup9xzAZbExIWRzzHJPRwEO3riTo07KnvWmtFwg3YzQ3\nEQ4bufzMBZ2Oj03X7lXnqabZF2x3rMmvbUK0Gl2dAjezwQEYsVnDvLm3CFVVe1xLX7Qd+lJUmswl\niyb1exR4R3qvam+o/QCYT4tr+MNL+6JZaqc5C4NiTMgzE8lscGAy2AhF/NGa97a+tHwGudnJqCrk\npDl57p5Lyc4qA2C0a+hKP0CCaiGEEEIMsIrmAwBkOU/DaDATCIUJhjrXKjtsZhZNXgj0bghMg0/b\npJjpnMC5+Z1bx6XYtI17LkeAjw6137T30IsfAOD3d64jVhQl2pKv3lvL4RM9TyjsC33oi9dnpqrW\nzpfPm9XzRb0Ua6pioyfATb97nZ89tZ1/79TGhScNUulHXymKgtOs9ZhuDtZ0Om41G/nLbav45mVz\neflnVzB7YioVzZ8CMCbp9EFda0cJC6p37tzJzJkz+ec//wlAMBjkzjvvZP78+axYsYJXXnml3fmP\nP/44S5YsYdGiRdx///2JWoYQQgghhpnK5v0AZLfUUj/11iHOuf0fvLKjqNO5+hCYqt4E1R3Gk3dk\na6kxTnIFeP9AWbtjhRVauzmz0RX72pagOskZ4PXdx3tcS1/oQ1+qqtOZPDqVs2YmLsDVM9Welky1\nqqrc9sd3KK5oZPbEDOZO00I/l2V4BtXQ2gGkq82KM8al86MvLSQ7zUGV5yChiJ8U6/jomPOhkpCa\n6lAoxG9+8xumTJkS/RXKo48+SkFBAVu3buXAgQPcdNNNzJs3j5ycHPbu3cuGDRt46qmncLlcXH/9\n9cyaNYvVq1cnYjlCCCGEGCZUVaUiGlTnEQiFeejfezlR00QkRlWF3rO5zldEOBLEaDDz4Wcn2X6o\nnMvOmsyknNY66+gkxS5atbUNjN97v7Vnc7MvQJVby4JmuNK7uFbrAJKeEsbtDcY8p7/0oS8Xz1vK\njYsvTGgLuNZMdS0ADz6/m1d2FpNkN/On76ykMvQPoPP48OHEYel+s2JbJ91a14+hzlJDgjLVTzzx\nBCtWrCA9vfWNuXnzZtasWYPL5WLRokXMmzePLVu2RI9dcMEFTJkyhezsbK699lpefvnlRCxFCCGE\nEMNIo/9Ey6bDVJKtY3h2WwEnapqYNiaV1WfkdjrfYnSSbB1LRA1R5ysG4Mm3DnLfP3ey9PtPc/FP\nnuMPL+3jRE1Tj5lqvYRjylgTf75tVfT1HYdO4rBpgbLDkhzzWj0g/+1NC/jhFxf263vvij70JdMx\nLdpXO1Faa6rr2fpJKb/+l1bucf9Ny8nNTo6200uyZHd5j6EWbasX6DmojrbSG+J6akhAprqqqopn\nn32Wf/3rX2zbti36enFxMZMmTeL222/nvPPOY8qUKRQVFUWPLVy4kMcee4zy8nIWLFjAiy++GO9S\nhBBCCDHMtGapZxNRVf73BW1Ix7cun4vBEDtDm+mYRqP/BNWeI2Q6pkU7Y7y66xh7j1az92g1b+49\nzpeu0DLVqdbYg2L0PtUms4ectNaR6B/sL8Xp0IJqa4d2eq3XasF2GHfM4+FIhJpGHw3NfiblpGAy\n9i5P2eA7QZ23GAVDQiYWduRoU1O9YFo25+aPY+nsMVy8cBLQ2k5PH74zHLW21etcU92W219OU6Ac\ni9GZsKmU8Yg7qP7Vr37FzTffjMXSvoWJ1+vF4XBw5MgR8vLycDqdlJeXtztWUFBAWVkZy5Ytw+Px\nxLsUIYQQQgwzFW3qqf/94VGKKxqZmJXE5YundHlNpn0aR+vejnYAWZ4/juX54/AGQry1t4RNHxSy\nq6CQkOrBYnBGg+eOzAYHBsVMKOIjFPFhMmgdNsprm3E5tKEoXQXV1pZMtS/Ufqril3/1CgdLaqlq\n8BJuqV+ZOiaVP377fGaOj11KovMHg3x04s+oRJictgKzMbFZamjf/cNpM/PkD1pLawNhD/5wI0bF\ngr2Ln9lw0DpVsarb88qatA9oOa78YdHJJK6geteuXZSWlnLxxRdHX9PbztjtdrxeL5s2bQLg3nvv\nxel0Ro95PB7uuusuALZs2YLD4Yj5jIyMoS06F8OL2WwG5H0h2pP3hYhF3hdDL6KGqTp4EIAZ45ZS\n39hE/uQsvvGF+WRnjeryOqN9IR+V/R+1vkLS09Pb1RyvGZ3NmovO4HDFdl4/tI3MpElkZnbdb9lp\nScPtr8TmMpBiz8BsNvPQ9y7huY8/4nhdGRmpo2O+R0aFx0I5qAZvu+M1bj/ldVoicEymmbMXFPHJ\nwTBzpk0guYuJhKFwhKfe+JRNO5/i/KVHsJvTOHfmzdjMsQP6eNj8wFHwh+s7fV+VLXXkqY6xZGZ2\n/fMfavYkAxSBN1Tb7d/f6hNaV5lpOUvi+nuu/78iXnEF1Z9++il79uxh5szW6TU7duzgyJEj5Obm\nUlhYyOzZswEoLCzk/PPPByA3N5ejR49GrykoKGDy5Ni/AvnZz34W/fOyZctYvnx5zPOEEEII0Zmq\nqrj9lSRZR6Eog9tJt9J9mGDYS6p9LEm2UaycP4rzN+QSibVDsY0U+1hs5mS8wToafeWk2DuXKniC\nJwBId0zs9l6OlqDaE6htd59wROuBbDfHHjCjTyf0BtuPOH/iziuwW03kpLnYX/4sHxS9wfKF1SjG\nBiCr3bmRiMqz2w7y08ff5WRdOT/4hhYELp3yjQEJqAHsllQUDHiDDdGNnrp6r/YzS7GPGZBnJ4rd\nnIrRYMEfchMMe2Nm9INhL2UNnwAKE9I79yjvyTvvvMPWrVsBMBqNLFu2LN5lxxdU33DDDdxwww3R\nr9esWcPll1/ONddcwyOPPMLGjRtZsWIFBw4cYM+ePfzyl78EYPXq1Xz9619n3bp1JCUl8cwzz/D9\n738/5jNuueWWdl/X1HRfXyNObfonUXkfiLbkfSFikfeF5njDdj4o/T2ZjumcOfYmXJasni9KkMOV\n7wOQYZvZ5/8O6baplAU/pqBsB7mpSzodL6vVRplbyez23ia035JX1Jag+LKwOZNIddlo8mkt53ye\nCDWRztcHfFp23O2taXf/TAdACHdjPYWVHwIQjDTywt6fcP6kn0QDwEhE5ed//4g/vLQPgJu+dByH\nPUSOM580w+wBfV/aTCl4Q3WcqDganVAIcLJG2yBpJW3Y/71wmNJxB8opKT8ccyNqaeNOImqIDPtU\nPI0hPPTt+8nLyyMvLw/Q/l/Rdl9gfw3YR9Z169Yxbdo0li9fzg9/+EPWr19Pdra20zQ/P59bb72V\ntWvXcumll3LxxRdLOz0hhBB91uArpbkXHQI+zypbBq9Uew7zauGPKa7flvAJgV3R66lzXLP7fG2m\nXducWO053O51VVU52bSPiiZt4EdKF5sUdXq99YeHjnDaNx7jp4+/C4A/rG1A7Hqjol5T3RDzeDDs\na1mbgsuSTYO/hA9Kf09EDWvrROWdfaXkpDm57z9HM2NKGUbFwoIxNyS0hV4srXXVte1e1zt/uCzD\nd5OirnWzYuy/362t9Ia+64cuIX2qdRs3bmy9scnE+vXrWb9+fcxz165dy9q1axP5eCGEEJ8jnmAt\nW47ejcuSw0VTY/9bI6Depw0uSbVNpN53jO0n/kiZew9njPkqFqOzh6v7LxTxtQw5URjl6PvEQH0I\njL5ZUQum97C/6nlqvVoJaZIlhzR7brf3ifaqdgTw+EO8s+84qqoSiAbVsYe/WIxOFAwEI55OZRQA\nVZ6DRNQw6fbJLB53C68f/W9ONu1jd/mTLBi9Fo8vxLevmMt5c3N4+/hPaA5CXtZVg/KbglhTFQGa\nAhXA8G6np4u21YsRVGvvBb2V3tD3p9YlNKgWQgghBktJ40eE1SBNgfKeT/6ciqiRaFB97sQfcMK9\nm93lGylp3E615whnjrspOuUw0ao8h4moYazKePwBC9Y+Rhxp9kkoGGnwl1Jc/x6Hal6h3ncM0LLL\nMzIvZmra+ZgMsTcH6vRMdWqy1kJvf3EVh0+cJKKGMRlsGA2WmNcpigGrKRlfqB5/uBGHof1GuPIm\nrawjx5WPy5LNkgnf5e3iX1BQu4UkSw7TMy7gsrOmsLf87zQHq0ixjmd6xoV9+yH0U8epiqDX1uvt\n9Ibv4Bedw6L9vCua9uOy5GA3pWE3p2I2OKj3HccbqsNuSiPV1n1N/WCSoFoIIcSIVNLwEQBhNUgo\n4u8xuPo8agpUEFYDOMwZWE1JTE5bRpZzBh+W/oEabwFvF/+SmZmXkJ/1xYSXJFQ2aaUfb+8ycdeD\nf+fFn15BbnbsQSuxmAwW0uwTqfUeZfuJPwBa1nlmxiVMSV8RbY/XE30ATDDSCGjPP+/2P/LjW7rO\nUutsphR8oXp8oYZOI7DLmz4BIMc1B4BRjuksGvN1PjzxMHvKn8BlycJhTudQzSuAwsIx/4FBGZyw\nS89U+9pkqv1hN8GIB7PBjtXY+/8OQ0XPppe6d1Lq3hl93aiYMbb8XR/tOn3AS2n6YnC3AQshhBAJ\n4AnWtpQWaALh5iFczfClZ3ZTbROir7ks2Zw36S5mj7oSBYWD1S9ywr0r4c8ub6mn3nPQRW52MhOz\n+t7tQv/Vvt2UxvyctVwy7X5mZK7udUANreUf3lADd1yjdYn4zyu0chRLF/XUrddqwWfHXtXNgSrc\ngXLMBgcZ9tZ+2xNTz2b2qCtRUfmgdAMflj6MSoSp6SvJcHTdlzvR7GatX3bbTHVrPXXOsApEuzI2\naQF5o65iQspishyzSLLkYDLYCKtBAmGtc8uElLOGeJXtSaZaCCHEiFPauKPd14FwEw5z94M3Po+i\nQbV1QrvXDYqRvKyrMBms7K34O0X1WxmXfEbCnusPuan3HScYMlBcmszffnhmvwK5WZmXkeOaQ5ot\nt1NNc2/p5R++UD3funwuqxbNYNzok2z+DKymHoJqY+zNiidbstTZztM6DR2ZPepKmgKVHGt4jwZ/\nKXZTGvlZ1/Zr7f3liFFT3TSCSj8AjAYLs7Ou7PR6MOzFF9LaHA63qZCSqRZCCDHilDRqpR8KWqAm\nmerYopsU7bHrTnNTl6Jg4KR7b5ddLvpD6ziiUlSazDl5uSye1b/gx2gwkemY1u+AGtpnmw0KLMuf\n0GaTYm8z1e1/Nh1LP9pSFK3UY5RjBgoG5o9eOyCTE7sT7bEdI1OdZBkZQXVXzEY7SdbRwy6gBgmq\nhRBCjDDeYB3VniMYFDNZLZvs9F8Hi/bqWoLqNNuEmMdtphRGu/JRiXCs/v2EPbe4TtvEV1Ccyo++\ntDBh9+0Po8GC2eBAJRz98KWXc/SUqY41qjyihqiMtgrM7+KZZlbk3skXpv9PQn8D0Ft2k/ZbG2+w\nLto+sbX8Y/h3/hipJKgWQggxopQ07gBURrvyo5vH/JKp7sQXasAXqsdksOE0dz2SOjf1HACKG+If\nfqFrDGqjyZdMW8JpE4Z+TLxeAuJtKRvwBrXMc8+Zai2o9rfJVNd4CglGvCRZRrcbrNKRohiGrCTJ\nbLS31B8HCEa0keqtnT+GX4b3VCFBtRBCiBGltKX0Y1zyQiwt3RskU91Za3/qCd2OJx+TNA+L0Um9\n7zh13mM93tftr+DNonv5rOpFVDXS6XhzoIqmQCVmg4Ovrbqg/99AAtk7DHLxBVsy1T12/2gp/wi3\nBtXdlX4MJ217VatqZET1qB6pJKgWQggxYniD9VR5DmNQzIxNmh8dXiI11Z21Daq7YzSYmZCsdVEo\nrn+3x/vuKX+CKs8h9lX+g/dKfkcw7G13XJ+imOWciaGbYH4w2cz6ZsUOQXVPGxVjlH+UN4+QoLpN\nXbU3VE9YDWA1Jg3owJ/Pu+HxbhdCCCF6obSl9CPHNQez0d6aqQ5Jprqjumg7vZ6HY+SmLQPgWMP7\nRNRQl+dVNh+krGkP/oABj9fECfcuHvnwe3z5N0+w7revUlbTREXLWPRsZ14CvovEaA2OtfIPPaju\nuaVe+wy3P+Sm1luEQTGR5Zw5UMtNCL2u2hOsa9dOTwwcCaqFEEKMGCWN2wEYn7wIaP31vZR/dFbf\nwybFttJtk0i2jsEfdnPSvS/mOaqqsrfi7wBUl8/jd4/N52SVg/TUZlateJ0y924MikJFy9CXbNfA\nTGrsj7a9qgG80fKP7oNqizEJBYVAuImIGmrJwqtkOqb3qVf2UNCnKvpCdSNqkuJIJkG1EEKIEaG1\n9MPEmKR5AFL+0YVQJIDbX4aCgWTruB7PVxSFsa4lALy6/wU8vmCnc0obd1DrLcRmSuGbF9zEx7/7\nJmsW3EeaeS52W5j/uHY/xZ4n8YcbsZvSSLKMSfj31V9te1UD+PSNiqbua6oNiiGazfaH3COmnhpa\na6o9wTqaTpF2esOdBNVCCCFGBG1UsVb6YTE6AKLlH37JVLfT4C9FRSXJOhqTwdLp+O827eZXT+/A\nHwxHXzteOpFIBKzOo6z68ZM8+14BWz8pBbQ2cvsq/wlow00sRjuKopCRlMKqabeRn/VFQOFYg1aT\nneU8bVhN7Wu7UTGihvGFtD7Vlh42KkL7LPeICqpbMtXeUN0p06N6uJOJikIIIUaE0gat64de+gHD\nP1Nd5t6DL9TIpNRzBjXI7G6T4v5jNfz2mV2EwirnnT6ehTO0QOsLZ5zOCwdm4FUPMW5sMd96KIii\nwKZ7LiM54xOaAuUkWXKYnLa83f0URWHWqEtJtU3kg9INBCOeYRd0tq2N9oeaABWL0dlpGmLsa5Np\n8ENl8368oTpsppROEyqHo7bdP0IRPwAuq3T+GEgSVAshhBj2fKEGqjwHMShGxiTNj74+nFvqlTbu\n4L2S3wGgAJNaNgMOBn08eVqHTYrBUITv/fEdQmGVdatOiwbUurljz+eD0kNceZ6HQwV2HFYT/qCX\n/ZXPATAn+4sYlNihw+ikfC6c8nMqPQeZkLJ4AL6r/msbVPt6WU/d8dri+vcAyHHOGVZZ+K44zHr5\nRzXBiNahRdrpDSwJqoUQQgx7pY07UFHJcbaWfgCYDFYMipGwGiAcCWCMUeowFGq9xXxY+ofo1x+X\nbyTTMYOkQcoUdpWp/t9Nu9l/rIYJo5K487pFna4bk7QAs8FB0HySN3/7TVKt4zlQ/RwlVY1k2Kcy\nLqn76YBOSyaTLEsT940kiNWYhIKBQLiJZn8N0HPnj+i1LUF1g78EGBmlH6B/GFDwt4xkt5vShv3m\nypFOaqqFEEIMeyUtA1/Gp7QPBBVFaZOt9gz6umLxBGvZdvx+wmqA3NSljE8+k1DEx4cnHu62XV2i\nqGokZlD9aXEND27aDcBvv7EMp83c6VqTwcL4lDMBKGl4j0CkkUM1LwNwevZ1IyJDG4uiGKIZ51qP\nlsXvqUe1Th8A03Insl3Dp1VgdwyKqd3apZ564EmmWgghxLDmCzVQ1ayVfoxtU/qhsxidWq1s2B0d\neDFUQhE/244/gDdUxyjHDM4YfSNhNUCNt4BabyH7qzYxJ+vqAV1DU6CKUMSHzZQaDSQBMlNsnJs/\nnnGZLs4+revOHJNSz+Fo3VsUN7xHMOIjFPEzJmkeo5wzBnTdA81mSsEbqqO2uSWo7sUmRf06XZot\nt0OQPbzZTWnRHtsuaac34CSoFkIIMayVNu5sKf3IazcN7o09WjbWnKxnquPfrHikZgsqEaZnXNjn\na1U1wvYTf6TOV4TTnMWS8d/BaDBjxMyZY2/ireJf8FnVJnKceQMaoNb7Y/enzklz8uj3LyAUVru9\nPsM+FZclh6ZAOYV1b6KgtHT3GNn04LhGz1T3tqba2BpUj5TSD53dnEadrxiQeurBIOUfQgghhrUT\njbuA9l0/AH7zr12s/fWrNDRp/5TFu1kxGPbycflGdpc/QVXzoT5f/0nlM5Q27sBscLBs4m1sev8k\nP370PcKRCFnOWczK/AIqKh+eeJh39xdy7c9fZMvHx+Jacyz13q4nKSqKgtnU/T/9iqIwKfWc6Ne5\nqeeQYuu51/VwFy3/aC4G+lf+MeKC6pYOIABJltFDuJLPBwmqhRBCDGv6uO0sZ+uEvuOVjewrqsZp\nMzM6NROIP1PtDlQAWhZ3b8U/UNXuM7ptFdVv47PqF1AwcPb4b7LrYITb/28rj245wJt7tA1ueVlX\nkWabhCdYQ2Hj33n/wEl+9tT2uNYcS30fxpN3JTd1CQoGjIqZvAEuVxks+gCYYFjrhNHbjYp2czoK\nCmaDg0zH1AFb30DQe1UDg7ZJ9vNMyj+EEEIMW4FwM/5wI0bFgsOcHn395R3FAKycNwG7pbzl3Pgy\n1U2Biuifa7xHKHN/zNjkBT1eV+U5zM6yPwMwb/Qayity+MaDLxKOqNx66emsmq8FtwbFxOJxt/Bq\n4Y+xJx9k/myVj/dDrdtHelLiujLUddOjurcc5gzOzf1hp5/7SNa2Nhp6nqbYel0yi8d/C6sxqct2\ngsOVnqlWUHCas4Z4Nac+yVQLIYQYttz+kwAkWXNQlNZ/sl7cXgTA6ZMzefptLYiMN1Otj3LWM5p7\nK54mooa7uwR/qIkPSjYQUUNMTV+FKbCQtb/ZjMcf4uqlU/nRlxa2Oz/JmsP80WsA+NLFhaSneNl5\npCLWrfvFH3LjDdViVCy4LNk0NPspKm/oU9Zdl+WcRYZjSsLWNtTspvabWHtbUw0wPnkhWc6ZiV7S\ngNMz1Q5zJkZD524vIrEkqBZCCDFsNUbHK7fWg56obmJ3YSV2q4lrlk6j4IQ2Lc4bdMf1LH2U82mZ\nl+E0Z+EOlFFU/26X56uqys6Tf8EbqiXdPoV5Odfz0ye3U9Po49z8cfz268tjtqCblLqccUlnYDaH\nuOz8InYdTlxQ3baVnkEx8MqOYpZ+/2nueKTr7+PzolOmug9B9UiVYZ+Cy5LFxGE2jOdUJUG1EEKI\nYas1U90aVKe6rDxw83K+d+U8MpLtuGzaRrLapvo4n6UFt8m2seRnXwPA/spnoyOeOyqq30pp4w5M\nBhuLx/0nBsXE/9y8nBtWnsafvrOyyw2BiqKQl6Xdf0x2E8WVjXGtu62O/anf3lcKQN7EjIQ9Y6Sy\ndcxU93Kj4khmMTq5ZNpvmZN97VAv5XNhZBUHCSGE+FxxB1qC6jaDK5w2M9eeMz36dXayFjA2+uIL\nqpuiWfEcshwzOWh7mTpfMUdqXmPWqEvbr8tfzu7yjQDMH30DrpZ2ZalOK+u/uqTHZzkt2ubKUWkh\n/vCt8+Jad1t1bTYphiMR3t1/AoBl+SO/e0e82maqFQyYDY5uzhai7yRTLYQQYtjSM9XJ1q7bgY3L\nGAWAL9j/jYqBsAd/2I1RsWA3paIoBvKzvwTAZ9Uv4g+1lpaEIyE+KH2IUMTPhOSzyE3pOYjuyGSw\nYjG6UAnhCw1MpvqTohrqm/xMGJXEpOyRM7BkoJiNNkwGKwA2c8qInQ4phi8JqoUQQgxLETXS0uau\n+x67U3K0YxH6P6Zcz1K7LNnRDZE5rjyynXkEIx4+q/539Nz9Vc9Q5yvCYc5kbs7afgdnDrOWYfeE\navu97rbCkSCN/jJAIdU2jrf3aa38ls0ZKwFkCz1bbTfLhwyReBJUCyGEGJY8wWoiahC7KQ2z0d7l\neWfNmARAsivS72e1Bu/te/nq2eojtVtoDlRT0XyAz6pfQkHh491nc8efdhAK9++50aA6WNPvdbfV\n6D+BSpgkSw4mg41RKQ5mT8zgXCn9iNLrqm0SVIsBIDXVQgghhqW27fQAvP4QigI2S/t/ulIdySgY\nCEV8hCMhjIa+/9PW5G/JVFtz2r2ebs9lQspijjd8wO7yJ6n1HgVUKsoW8KcX6rGZ3dx8SR15uX3f\nCHsWIpUAACAASURBVBgNqgPVfb42lo79qb983ky+fN7IawM3kPRMtQTVYiBIploIIXqpvOkTXjz8\nfWo8BUO9lM+FxugmRa2845/vHub0/3yCP7y0r915iqJgMToBCEb616u6q0w1wJysazAoRk64d+IN\n1eJtzua+xxxYTAb+fNuqfgXUAM6WoLopUMOewirqmnz9uo+udZJi/4e+nOokUy0GkgTVQgjRSwer\nX6I5WElh3dtDvZTPhY7t9F7eUUyTL0iaq/P0QYtRm47X36mK7mhNdU6nYy5LFlPStA4dkbCF3z42\nAYPBwB+/s5Jz88f363lAdFLhewc/45K7n+edlvZ3/aUH1WlxjCc/1bks2lTBZBnZLQaAlH8IIUQv\nBMLNVDYfBKDK89kQr+bzQW+nl2wZTa3bx/sHyjAZFS5Y0DkTq2eq/f2cqtgUzVR3DqoB8rKuxh/y\n8td/Q0OjkYe/dT4XzI8veNXLP9JTAgDsOFzBFWdP7de9VFWl3qdtTEyVoLpLU9JWkJU2nglpZ+Bu\n8A71csQpRoJqIYTohTL3HlS0kdVNgUo8wZpoUCQGhrulzjnJOpp/v19MOKJybv64bjPVlQ01jOpj\n+2F/qIlAuAmTwdpp6l7r/Z0sHn8Tc74a4PqlFXFlqHUOs9ar2mrTPgjEM668OVhFMOLBakzq8nsQ\nWivDqRnLWr6SoFoklpR/CCFEL5xw7wJAwQgQzVqLgREMe/GG6jAoZhzmTF7aXgTAJYsmxTzf1DLI\n4ycb38AfDPfpWe3b6XXfes5ltyQkoAatvlfBQAQ3FrPKgWO1NPuC/bpXnVf7+aTZJ7F5ZzG/+McO\nDpYkplWfEKJ3JKgWQogehCIBypu0zXFT01cCUNl8YCiXdMprnaSYjYKCw2bGYTVx0Rm5Mc+3t4yc\ntlmDFJT1bbKivknR1WaTYkWdh+KKxA1licWgGLCb0wBYNMtORFX5uKCyX/eqbQmq0+2T+de2I/z+\nhT39vpcQon8kqBZCiB5UNu8nFPGTZptEbuqSltdGXqZaVdWhXkKvNbbZpKgoCn/6zko++cMa0pM6\nl35Aa/mHwx7ks+N9y9C2HU+uqipPbz3Miv/6J9966C3Ckf73vu4NvYTo7Lwkls8Zi9nYv3+Wa31a\nUJ1smch7+8sAWD5H+lMLMZikploIIXpQ2rgTgHHJC0i1TcRssNMcrKQ5UI3TkjnEq+tZRA2x6+Tj\nlDbu4Lzcu0ixjR3qJfXIHQ10WycpduxP3Za+UdFhC3HgeA0wrQ/Pas1Uf3PDWzz/QSEAqU4rTd4g\nKU5rX5ffa3pQfdmSTL5zydJ+3UNVI9HyjxPlSbi9QaaOSWVspith6xRC9CzuTPXtt9/O0qVLWbBg\nAZdddhlvvPEGAMFgkDvvvJP58+ezYsUKXnnllXbXPf744yxZsoRFixZx//3/j73zDoyrvtL2c6c3\naUZdtixbcsMNG9vYFIMNGAOGQNgAgRBw2ISUxUl2k0CW8BFCAnGWbCBtSdlNo4UkxFRjHAwEFzAd\n9ypZclHvmt7u/f64uqNRGdVp4N/zl6S5984ZeTx658x73vPQeMsQCASClCArMvXuDwEoy1mMTtJR\nZDsNgBZf9nerw1E/W489yNGOfxKKejjZ/U6mSxoR/eP0hsNk0DrVkVF3qrWByPZOG8/uqMZmNvDz\nr1zAo3dcmlJBDfFbFce+AMYTaiIs+7Ea8nhjrxuAFadn/xsngeDjxrg71bfeeivr1q3DZDLxxhtv\n8OUvf5l33nmHJ554gqqqKrZu3cr+/fv58pe/zMKFCyktLWXXrl08/PDD/PnPf8bhcHDjjTcye/Zs\nVq9enYzHJBAIBEmjzXeEYNSNw1RCrlkVKkX22dR7dtLsPUCFa2zdxXTgC7ez9dhP6AqeQEKPQpRm\n30HmZrqwEdAbpzd4xF1/tE61wxZBrxt62DAeRVFicXpv7FaXr3zynGlce/7IO93joVdUj32osD1u\nSFHLul4urB8CQdoZd6d61qxZmEwmFEUhHA5jt9uRJIlNmzZx880343A4WLp0KQsXLmTz5s0AbNq0\niUsuuYRp06ZRUlLCddddx8aNG8f9YAQCgSDZnHSr1o+ynMWxZIhi+2wgu33VnYETvHL0+3QFT5Bj\nKmVl5XcBaPNVEZUjGa5uaBRF7hOnNxI0T/WSWU4e/8+RN2iCUTdh2YdBZ8FsyKU0z87qJRWjrnms\naAtgfOG2MV9D81PnWyr52Vcu4Ac3n8M5s0f2exMIBMkjKZ7qe++9l/Xr12OxWPjtb3+L1WqltraW\nyspKbr/9di666CKmTZtGTY36H7+2tpYlS5bwyCOP0NjYyOLFi9mwYUMyShEIBIKkoSgKdd1qlN6k\n3MWxn6u+alvW+qqbPPt448TPCct+Cm0zOa/8PzAbcsg1l9EdrKMjcJRC28xMl5kQX7idqBLCrM/l\nG79+myvOquTyJYNH6WmYtTXlo9yoGD+keM0VC/jS6vkopG+gs7dTPQ5R7T8KQL61kgk5LqZPdCWl\nNoFAMDqSJqrvvvtu/vrXv3LHHXewceNG/H4/NpuNI0eOMG/ePOx2O42N6ouXdltVVRX19fUsX74c\nn8836LULCsRyBUEvRqMREM8LQV9S9bxo9dTgDbdgNeYxY9JSdJI+dluZ63Rq29/GpzvJ5ILTknq/\n4+FQ06tsPf5zZCXCtMLzWDnrdgw6EwDl7QvY11CHRznOaQXnZLjSxPg61HXb0Ughz+6oprk7yM2X\nnTnkOfawCY5AWPbFngcjeV60hNXFKwU5kzPyumIPm6Aa/JF27I5cnnnjMIdOtHHv55YPfzIgK1E6\nD6i/r2kTF2M1icUvwyH+jgj6oz0nxkvS0j8MBgOf/exnefzxx9mxYwdWqxW/389zzz0HwP3334/d\nrnYSrFYrPp+Pu+++G4DNmzdjsw2+Auu+++6Lfb18+XJWrFiRrJIFAoFgSGra3gSgsuCsPoIaYGKP\nqK7v3M2skpWZKC9GMOLhSPMWDjZtptl9GIAFkz7FuZWfR5JUl19zp5eTDaqIaOjaC1yfqXKHpcOn\n+oJPNKh/6K45f9aw55gNdiR0hKI+onIEvW5kf966/HUAOK0Tx1jt+DAbHBh0FsJRP1H8rP35JnzB\nMLd9cjHFLvuw53f6ThKRg+SYi4WgFghGwZYtW9i6dSsAer2e5ctH9kZ2KJIeqacoCoqiUFFRQXV1\nNXPnqiMx1dXVrFyp/uGpqKjg6NGjsXOqqqqYOnXqoNe77bbb+nzf1jb2j8gEH320zoJ4HgjiSdXz\n4kjTdgAKTfMGXNvOFABOtO/MyPNRUWSavQeo6dzKye53iSrqJj6jzsrpJZ9mhvNi2ts7APAFwqz+\n7rM0dzdx79ehvmsfLa3NA94opBpZkekI1OIwFmHuWdYyGI0dVQB8eEj1fi+fUzSi37FRbyMU9dDY\ncgKLIXdEz4vmrloA9FFnxl5XbMZ8uoP1NLZWc8a0Qt7c38Arbx/k0gSLbuKp6VSTaZzmKeJ1cYSI\nvyMCgHnz5jFv3jxAfU5s37593Ncc16Bia2srTz31FB6Ph0gkwl/+8hfa29tZuHAhq1ev5rHHHsPt\ndvP222+zc+dOVq1aBcDq1avZvHkzVVVVNDU1sX79epH8IRAIsgpvqIXOwDEMOgvF9jkDbndZJvf4\nqlvwhsYehzYWjrRtZsORb/H6sf/iWNebRJUwJfa5nFX2Fa467ZfM6Nn6qHHPYzuoqu+k22PG43EQ\nkQN0Bo6lrd7uYB27m/7KhsPf4JWj32Pr8Z8MebwWp1ffYuHMGSVMLBhZ3rI2rFjX3sJrO08QGsG6\nci35Iydum2K6iU8AOXOGWsd7R5pGdK7mp25tc6V8UY1AIBiacXWqdTodGzZs4MEHHyQcDjN9+nR+\n9atf4XK5uOWWWzh69CgrVqzA6XSybt06SkrUF4v58+ezdu1a1qxZQyQS4YYbbhCiWiAQZBUn3eqA\n4gTHAvS6gX47naSjyH4a9e4PafYdpNKUnmi9YMTNB42PAqoYq3Qtp8J1Hg5T8aDHP7ejmidfP4TF\nqOe+z53LtDKo7dpKs/cg+dbBPyFMVp3Hu96ipnMbHT3pFBrt/qN0+I+RZ50y6Lna4pfmNhtrrxh6\nQDEeLVbvP/+wmR179LxTOYH5UxOLZUVRYve1fksbNyyfnPJc6sGwGXqzqpfMVP357x4eqahWf7c/\nfaqRx1/cyFP/7xOpKVIgEAzLuER1fn4+jzzyyOAXNhhYt24d69atG/T2NWvWsGbNmvHcvUAg+AjS\n7q9l2/EHOaP0RqY4s3dYTkv9KItL/ehPsW22Kqq9+6lMU161J9QMgNM8iUun/TDmmR4MRVF4ZPN+\nAO656WxuvHAWNZ2t1HZtpcV3kFlcnpIa9zT9nQOtG1BQO8VGnZVy51lUOM/jeNcOqjpepbZz26Ci\nOiIH8IXbkNBz382rWTpz5F5nLQFk+iQLO/aE2XO0ZUhRHYx2q/cXMLDuyT3csHzhKB9pcojvVC+a\nob452l3TSjAcxWxMbNGRlQidgeMAnGx0sObTFSmvVSAQJEasKRcIBGmlybuXQKSTk93vZq2oDkbc\ntPoOoZP0THAsSHicllfd4j2QrtLwhlVRnWMqHVJQA0iSxJ/vXM367VXceKHaAS3WtkF6D6Eo8rDX\nGC2KonC4/R8oRJngmE+F63wm5iyKJZDodEaqOl7lWNebLCi9AZ3U98+QO9hjxzCXsHru6BawaPaP\nilIDEGZvTfOQx2tZ2K3tVs6bOykjXWrom1Xtspu5/drFTC11oihDR/t1BeqQlTAt7RYKc/L47EWz\n01GuQCBIgBDVAoEgrQQi3UCvlzUbqXN/iIJCiX0OJv3gyUQAzpivuhVvqAW7qSjltXlCLQDYE9g9\n+mMxGfjsRb3pGXZTETZjAb5wG53BE+RZBrdgjJVApJOIHMCkd7B8yh0Dbs+3VMbyshvcuynLXdTn\ndm2TYo5p9MtLNPvHhAL1jcLu4UR1z3Owpd0ybA52KumfVf2Nf1k01OExmj3qQOeJhhxuv+bMIbva\nAoEg9SS3RSEQCATDEIh0AqqoHq4TlynqevzUZTl9rR8N7V5++OTb/HXLYU62uHt81apgbfalZ7ui\nt0dUO8Yh4Itsas1Vzbv50s9foaVr8D0BY6F7GFEsSVJstXtN57YBt2tDiiPdpBiP1qku6Nl9srem\nZcjj271qnF5rh5VLFyf3zcVosBnV5UGjXQCz89guAIK+Yv5l2bSk1yUQCEaH6FQLBIK0Eoh0ARCR\ngwQiXViN2bX9LSIHaPLsAQaK6gfXv8+Trx+KfT+5KIdrVpkor4Bm7wEqXeenvD5Pj/3DbhxZp3ow\niuyzONb1Bjuq3uLFdyrw+EM8/u3V6HTSuOtzB+sByB1CFFc4l7Gn6W80eD4kGHH3idcbTpQPhdap\ntprDnDmjhJmTCwmGEq9kr22rBQM4LRModFpHfX/JwmbMA8AX7kBWZHQjtOS48trpDMAVZy5DrxM9\nMoEg04j/hQKBIK1oohqy0wLS5qsmqoTJs1QOEPyKomAx6Tl/Xhm5NhPHW9x8eFC1h/T3VR880c5X\nH36N7/xxOz/667vsrB66azpSvD2DioN1qmVZ4Vcv7MLtCw15jeKeTvWkCR3k55jZsqeOX23YlZT6\nunt8ykN1mq3GPEocpyMrUY517ehzW2O3OniXay4d9X1rneqQ7OW5e6/iD3dcidmUuHfksKsrzT91\n9tJR31cy0etMmPW5KERjn+TEE47IvN8vYi8qh+gOngQkLpg99LZJgUCQHoSoFggEaSVeVGtxZtlE\nV1C1BAyWTPHgl1aw97drePLO1ez97c28dP/V3HbZKkx6e8xXrXG8xc0zb1bz6CsH+J/nd/Kln78y\nbruLrER6LAJSzDIQz59fP8gP//IOn/mvl4a8L4epBIvBSVh28+BX1AVdD65/H28gPK76ANyhnk71\nMJ1mratf29m7cMEfDMeGB8OBvFHft1kT1VHPsMcqioI3rArVs2bMHfV9JZv4BJB4QpEon3/oZa69\nfwPb99XFft4ZOIGsRMk1T8Soz1yXXSAQ9CJEtUAgSBtROdJH8GRjp7pbsy+YBo9ys5oMSJKEXqdj\nfmURy+ZOoqgnUaM5rls9b0oBP//KBdz/uXNx2c3UtXk41uweV22+cBsKCjZj/oDsbG8gzIPrVS/4\nrZfNRZISWzkkSYr5qqdO7mTB1EJCEZldR8ffTR/KE+32hfj8Qy/zjd9uodCyAKPORkeghs7ACQC2\n7D2I2RQlEDAxIX/0nnHN/hGKeoc9Vh2oDGLSO2LnZZL+w4oaRr2OyglOQhGZLzy0mb216qKh9p7s\n73xL5gYsBQJBX4SoFggEaSMY7e7zfTZ2qns9wSPPRy7qidZr9vWK6okFDq49fwafXVnJJUstmE0R\n3txfP67atIxqu3Gg4PzfjXto7vRzxtQirjp7+KE1bcCyxXeIRdOLcdpMtHT5x1VfRA7h7cmYHmwZ\nzc+e/ZB/vH+MN/bVYzNbmew8G+jtVm8/tBsAnTKwCz8STEN0qnfXtHDoZG8XWHvuOTK4STGeXlHd\ndzunJEnc+9mzuersqXgCYW768SaON3fT0bP0Jc8qRLVAkC2IQUWBQJA2NL+ohB6FaEwkZhPdodGL\n6mKbKqqbPPs42Poi3cEGPKFG3KFGApEuzj4Hzj9rKpdMH98Gw97kj76CtaXLF/NE333jWSMaONR8\n1S3eg3zn07fyg5vPHfegoifUCCg4TEUD8qerGzr5/aa9AHzrGnUAtMJ1HtUdr3Gs6w1Oy7+GY601\nnA5MdI0tiSNRp9oXCPNvv3yNhnYv377uTL64el4sTi/HNHrvdiqwJ7B/AOh0Ej/7ygW0uwNs31fP\nvz74Mrffqq4nzxeiWiDIGkSnWiAQpA3NT635lbMtVi8U9RKIdKGXTLHO4UhwWcox6e34Ix3savoL\nNZ1baPEd6rmWatOQ9SexWwauOx8NnrCWUd23U/2P94/hC0ZYtWgy58weWWpGrrkMsz4Hf6QDRd+R\npOQPzfox8A3JD554m3BU5oYVM7l+xUwACqzTyTGVEoh08c7RN8nNVTvME12Tx3T/xpio9iErcuzn\nCnDO7AkEw1Hu+/PbnPXvf+FgnZrxnJM1nereBTCDYTbq+d1/rOKMqUU0d3XRHapDQocryTnjAoFg\n7IhOtUAgSBv+HlGday7DE2qKidhsidXT/NQ55gl9Ng3+afN+8hxmLl44eVBhLEk6zii5kZPd72I3\nFZNjKiXHPIEcUyk2Yz7PHPw3wrKPYLQbi8E55vq8CewfN100m9PK8sjPtYz4WpIkUWg7jTr3ezR7\nDybFBtHdI6pz+3V/X999glc+PI7DYuQ/P72kTw0VrvPZ0/wUinkXpYX+nvNHH6cHoJN0GHU2wrKP\ncNQLqL8nu8XIT764nEsXT+GO322jod3Lm4f3Mf80cIwhZSQVJPJUx5NjM/Hs966ivvsAbzW8jtNS\nHttUKRAIMo8Q1QKBIG0Ee0S11eDEYSqh3X8UT6gp60R1vPUjHJF54G/v0u0L8cZD1yfsNlfmLacy\nb/mgt9lNRXQGjuENtY5LVHsS2D8Alpw2enFYbJ9Fnfs9WrwHmZq3Ysx1acS2IfbrVM+bUshnL5rF\n1FInxa6+GyorXMvY0/x3Wvw7mTPVSkQZ2+IXDZPeQVj2DTqsuGrRFF57oIR7Hn2TsuIP1VqzplM9\nsgUwRoOOoHISgDwxpCgQZBXC/iEQCNKG1qm2GFyxzmg2JYAMlvzx3pEmun0hpk1wUlGSO6brap1l\nb3h86RresJZRPfbFL/FoqSUtSdoG2Z0g+aPQaeXHXzifr1wxf8A5NmMBJfY5yEqEiOJGQjeuxTa9\nvurBY/Xycyz88rYLKM4PAODIEk+1xZCLTtITjLqJyEPnjLf3DCnmW8fn0RcIBMlFiGqBQJA2tEFF\ni8EZ6xC6s1FUx3VaX9upLiNZecbYfL7Q64H2hlrx+ENj8pGHol5CUS96SV0UkgyclskYdTa84VY8\noRZqGrt4tefxjhZFUWKd6tHaNyriNlHaTcXodWP/ENVs0BJAEsfq+SMdRJUwZn0OJr0t4XHpRJJ0\nWA2qr9o/TLe63S+GFAWCbESIaoFAkDYCsU61M9YhzMpOdZyofnWnmqG8cmH5mK9r7/lof8N7HzDn\nS49S3dA1zBkDibd+SJJEKBIdcz0aOklHoU0dGjzRuZ/zb/8bt/50M8Hw6K+t5j4HMOkdfdaOj4RJ\nuYsx6FQ/eH8/9mjRYvWCQyyA0RbMZEuXWiPRAph4wlE/7lADOsmA0zwpXaUJBIIRIES1QCBIG31F\ntdapzo6s6qgcwhtuQUIXE1snW9wcOtmBw2Jk6Rg8yxraSnGH3UtUVnhjDHnV3ljyRzHhiMyldz3N\n//vTG3j8Q1sFhqO4J6/aE65ixkQXoYgcWzAyGmJDnmMYMjToLJTnqqvCc81loz4/npEsgInF6Zmz\nw0+toYlq7xCd6o5ALQBOc/mABUACgSCzCFEtEAjSRryozonzVGdDrJ47lrHcaz/Iz7Hw26+v5DvX\nL8Fk0I/52toQmsup+njHsgQmPvnjidcOcLiuk6176zAbxzdvHu+rXjRd9TJ/UDX6/PCY9cM8AUVR\nuOfRN0d1nfkln2ZWwRXMLLhs1Pcdz1ALYDQ8PW/ksiWjWiPRAph4eq0fwk8tEGQbQlQLBIK0EJED\nROQAOsmIUWfDpHdg1NmIyIEBmxYzwWDWD5vFyCfOmsotl8wd17W1QUW9oRsJhR0HGkb9RkJblGPR\nF/LQMx8AcNf1SzAaxvcynmetQC8ZcYcaWTRDTSb5sHr0A5XxQ4ovvlPD7/+xj8/95B/4Q5ERnW8x\nOFlQesO4k2CGG1SE3jztj6L9o3dIUfipBYJsQ4hqgUCQFgIRVThbDE4kSUKSpDgLSOZ91YOJ6mRh\n1Fsw63NQiDB1op627gCH6zpGdQ1tm+KxBvX8WZPyuOzMinHXppMMsUHK2RVqN/6DqtH/e8Ti9Eyl\n/Pip9wC449rFWE3pTW7t7VQPbv9QFIVWv7r4JduE6XALYCJyiGbvfkB0qgWCbESIaoFAkBbikz80\ncszZM6zYu/gl+aIaehNAls23Ueyy0tCe2PM7GJ6eOL239qkLUlYvqUSSxr8FEXo76YX5Ac6ZPYFL\nFlcQicrDnNUXrfvb1GqjuqGLwlwrN144Kyn1jQbzMJ1qd6iBUNSDxeAasEQn0wy3AOZY15sEo27y\nLBViSFEgyELE8heBQJAW4v3UGrGs6mD2iOr4jOpkYjcW0e4/yi2XlbHupvNHJYhlRY75bIPBHCym\nVi47M3nrqTXB7w+38ve7PzHq8yNyCG+4DQk9m99TP5FYvaQCgz79fRvN/hFM0Klu8R0GoMg2M2lv\nSpKFPW4BjKIofepTFIXDbZsAmFlwWdbVLhAIRKdaIBCkCf8QojrTCSCyIsdqyDVPRFEU/MGReYFH\niiaYIrSPWhD5w+3IShSLwcV//euF7P3tGuZOKUhibeNbTuOJG/J85YM6AD5xVmasFSa9GueXyP7R\n6j0EEIsSzCaMeitGnZWoEhrQaW/y7qU7WIfF4KI896wMVSgQCIZCiGqBQJAW4leUa/QmgIw+bSKZ\n+MItyEoYqyEPo97K4boO5n75Uf79N68n7T56F8CMXrhqYlfbpGg1GZLaqXSMozboO6T4zD1X8quv\nXsTZs8a+anw8DDeoqHWqC3tST7KNRMOKh3q61DPyV41rOY5AIEgdQlQLTmlCUS+yktyOpGBwhupU\ne0KNGY3V6z+k+OqHJwiGoyTzA/aYqB4iLi0Rnrg4vVSgXdczxk615qfONU0gx2bik+dMy4j1A3pF\ndTjqRVH6+sL94Q684WYMOgsuy9iX+aSSwXzV3cE6Gj270UsmpuVdmKnSBALBMAhRLThlCUY8vHD4\nP9h2/KFMl3JK0Oup7o1MM+tzMOqshGU/wag7U6UNFNXaavKFY19N3p+YxWIsneoeUa11lJNNfBd9\nLG9uYskf5sx0p+PRSXqMOisKCqGor89trVqX2joDnTT23PFUMpioPtT2DwAqXOeNelulQCBIH0JU\nC05Z3KF6InKAZu9BZGX8K59TQVQOE5XDmS4jKfSmf+TGfqbG6mU+ASQ++aPTG+Tdw03odRIrTk9e\nwoI97mP9qBzh8MkOHnv1ALI8vIj1xG1TTAUmvR2jzkZUCRGMdrOnppUH/vYur3x4fETnx9s/sgGt\nWx0I932j1mv9yD4/tUZ/UR2MuDnWuR2AmQWXZqwugUAwPEJUC05ZtM6prIRjG9ayiYgc5B/Vd7Op\n+k4i8vhWUWcDg3WqodcnnMms6vhO9ba9dURlhaWnlZJrMyXtPvQ6ExaDC4Uo/nAHN/14E3f+YTsH\nTiRe9KGh2T8+OBga8TKV0RLfrX73cCO/eG4nG9+tGfY8RVF6tymOYUV5KtCyqgORvqI61qm2f3RE\ndXXHP4kqYSY45qckQ10gECQPIaoFpyyaxxegM3Aig5UMzsHWF3GH6vGEmjne9WamyxkXiqLELX/p\n7VQHQpE+68ozVVt8nF67O0CuzcQF85OfA6xZQHyRVs6ZowrQHQcahj3PHVRF9X2PHx5RZ3ssOOIS\nQBZq68qPDD9A6o90EJEDSIoNOWpNSW2jJRarF9epDkf9dAaOIaGnIIsXp2gLYLzhNqJyhCPtmwHG\nvb5dIBCkHiGqBacsgXBn7OtsE9W+cBsHW1+MfX+47eWMDvKNl7DsQ1bCGHQWDDoLiqLw6w27WHnn\neiRF7cx5gpn5tCAQ6SIs+zDqbFgMTj538Rz2/OZmPj/O1eSDEZ+yce5stev45v76Ic8JRwOEZTfh\niMT8KRXYLcak1wW9nWpPqIW5UwowG/Ucqe+kyxsc8jxtSLH6pIHzb/9bykT/aNA61cG4TnWbvwoF\nhTzrFAw6S6ZKGxatU+2PtHOi+20CkU6c5kmU2OdluDKBQDAcQlQLTlkCcZ3qrsDIvKPpYlfT405r\npAAAIABJREFUX4kqIcpyFmMxOOkKnqDFdzDTZY2Z/taPcFRmw9s11DZ1878vnAQyZ//oDvVaP7SY\nOoNehy0F4lXLqvaGWzi3p1P91oEGonLi7YVanF57p4VLF6cu+zk+q9pk0DOvQhV3O6uHHqzs7rF+\ntLRZOX9eGTpd5peSxDzVcaK6Ncuj9DSshnxAwh9u51DbS4DqpRbLXgSC7EeIasEpiz8S16kOnsxg\nJX1p8R3meNcO9JKRhaWfZVreRQAc7kkA+CgS6JdRbTLo+d9/v5g8h5l/vKsKH0+oKSPd+P7JH6mk\n17fcSnlRDuVFDrp8IQ4cT+yrbvOqorW9y8KqRclLI0lcmyqiF2kWkKqhLSBap7q53cYVSzOz8KU/\nZq1THWf/aPGpS1+KsnhIEUCvM2AxOFFQ6Awcw6zPYYrz3EyXJRAIRoAQ1YJTlvhOtS/cOiB+KxMo\nisyHDY8DcFrB5dhNRUzPX4lO0lPn/iDjS1LGipb80dQu8ZkfbeTl949RVujg4bUX4fUZCQT1hGVf\nwoUdqcSdTlHdb3PhTRfN5mufPAOn3ZzwnN3HjgCgV/IpdtnSUJuao33V2dNY96/LuOqcof3HTW7V\nOuXx5HL+vLKU1TcaegcV1eeTrERo81UDUGibkbG6RopmAQGYnr8SvS55A7MCgSB1CFEtOGXRhJ65\nZ61xVxb4qms7t9MRqMFqyGN20ScAdVlKee7ZgMKR9lcyW+AY0YZC61pg69462tx+AFbMn8Tt15xJ\na4c64NYVHH5oL9lkpFPdI1y/etUZ3PnpJZQXJc4enlikRiourEytbcFuUq0pvnArsiKzaHoxn7t4\nDtMmuIY8r8OnriU/bcJ0zMbsyH7uP6jY4T9GVAmRYyrts3woW9GGFXWSgen5F2e4GoFAMFKEqBac\nkiiKHEujKHGoA0BdwcyK6nDUz+7mvwEwv+T6PsNUWj5tTccWwtFARuobD9qK8pp6NQ/8zBklsdu+\n/smFuCxqVrVvjBv9xoMmqhuarfzl9UM0dnhTdl82Yz4SUiyreiQEZTVa7YyK1HZYDTozFoMTWYkS\niHSM6JyIHERvcCPLEpeccUZK6xsNvZ1q9f/4R8VPreEwqtabyc5zPhJvAgQCgYoQ1YJTkmDUg0IU\nk95OvkX1gWY6AeRA6/MEIl0UWKczxXlOn9vyrZUU2mYSln3Udm3PUIVjR+tUN7SCy27u0/3U6SSW\nTJ8DkPa88HDUjz/SgU4y8twbrXzr/7byyOb9Kbs/nWTAaswHlD4b84bCG9a2KaZm8Us8sXXlI9z6\n6A41gqTgtJSy8oyKFFY2OnoHFVX7h7b0Jdv91BozCi5hduFVnFHymUyXIhAIRoEQ1YJTkt7tfi6c\nlnIgs6LaE2riUNsmABaW3oQkDfyvOTP/EgCOtL2MoiROi8hGNP96t8fE4hnFAxIiHD1Z1elOAIlt\nUjSV8vpu9etU5FPH099X3Z+9ta2caFFtC4oixwYHtfNSWptp8NqisjxoB9/dE4OYLZsUNUxxg4qK\notDaM6T4UelU24z5zC+5TqwkFwg+YghRLTgl6Y14c+LqEdVdwRMZy4Le2fgXZCVChfM8CmzTBj2m\nLPdMrIZ83KEGGj1701zh+NB+326viTNnlgy4fbAFMLKsEImm9s2DFqdnpJjqhi5yrEYWTR9YXzLR\nvMveQbrBH1Q186n7NnDjAy/R1u0nEOkiqoQx63Mw6lO/WCUm+PvV9s9dJ1n69Sf54s9eYfu+utj/\nEy35I1s2KWrEPNURN13+OoJRNxaDMy3dfoFAcOoiRLXglMQfi3hzYTE4sRicROQAvp4BsnTS5NlH\nnfs9DDoz80s+nfA4naRnRs/Q0uH27IjXa/Ed5lDbpmHfjGifDDx825Vcs2ygN9jRT1QrisI9j73J\nl3/xCoEUreWG3uSPpjZVsJ43twyjIbUvi/1TNuKZPtHFlOIcjjZ0cdW9z3O8Tf30ROsgp5r+sXoa\nh06qkX8b363h+nUbueDbf+f3m/bS5lOjKLO1Ux0Iu6nv2gdAoW2myHoWCAQpZVx/PSKRCN/+9rc5\n77zzOPPMM1mzZg1VVVUAhMNh7rrrLhYtWsSFF17ISy+91OfcRx99lGXLlrF06VIeeuih8ZQhEIwa\nbZuiNgTkNGfOAlLV8SoAswo+gdWYN+SxU/MuQC+ZaPTsjlkXMoWsRHnzxC/Z2fgErf4jQxwnxzbb\nLayspKzQMeAYi8GJQWchFPUSjHiob/fy9PYqNr13jJt+vIluXyglj0H7He6rVsXWBQtSa/0AsPd0\nSwezf+TaTDz+7dWUFzmoberm2398HugdXEs1jgTWlLVXnsE7v/gM3/rUIkrzbFTVd3LPYzto6FSX\nJuVmmajW6wzq5k5kjne8B6iiWiAQCFLJuES1LMtMmTKF9evX895773HRRRexdu1aAP70pz9RVVXF\n1q1beeCBB7jrrrtobFT9d7t27eLhhx/m0Ucf5YUXXuDFF18cILoFglTS66nuEdWarzqY/s2K3pDa\nsSx1DL+G2GzIYYpLXQRxpH1zSusajibP3tjvsd1/NOFxoagbBRmT3oFeZxj0GEmS4rrVjZQVOFj/\n3SspcdnYcaCBa+/fQEtX8nPENVF90fxFfP6SuVw4vzzp99Gf2FbFBMOAJXk2nvjP1ZgMOvJdatKL\nPU22hfhV5f0pzbPzzWsW89bPPsP//cfFXHbmZPQmNSUkJ8vsH9BrATne/j7w0RlSFAgEH13GJapN\nJhNr166lpET9Y/ipT32KY8eO0d7ezqZNm7j55ptxOBwsXbqUhQsXsnmzKgI2bdrEJZdcwrRp0ygp\nKeG6665j48aN4380AsEI8ccNKgK9vupA+jcrapYTW4/YGorWLj91J2cDUNu5jVA0dfFvw1HTuS32\ndYe/NuFx8f71odD8rtqw4uzJ+Tz7vSupKMll37E2rv7+C7EBvmQQlSN4Qs1ISFwwZz73fe7cQbvo\nycaRYBgwnmkTXPzzx9dxxTmuPuekGi3yzx/pICqHBz3GaNBx+ZJKfvnVJUSVAGZ9TlYO1GkWkIgc\nwKAz47JMyXBFAoHg487gbaMx8uGHH1JSUkJeXh61tbVUVlZy++23c9FFFzFt2jRqamoAqK2tZcmS\nJTzyyCM0NjayePFiNmzYkMxSBIIhCcR5qgFcGbJ/ROQQwagbnaTHYsgdcLvbF2Lbvjre3F/Pm/sb\nOHRS7Qx+77aJOF31HO14nVmFV6S1ZoBQ1Eud+4PY9x2BmoTHjlRUDzasOLk4l2e/dyU3/XgTwVAU\nu8U44LyxDpd6Qo0oyDhMxWndWGcx5KGT9AQiXUTkEIYE911Rkku1z0+rL32dajXyrwBfuBVfuI0c\nc2nCY7UhxWzzU2tonWqAAut0dFJ2LKYRCAQfX5Imqt1uN+vWrePOO+9EkiT8fj82m40jR44wb948\n7HZ7zP6h3VZVVUV9fT3Lly/H5xv8o92CgoJBfy44NTEaVVE13udF+KiaX1taWEG+vQCnnIN0VIcn\n1IjT5cCgT7w2Opl09gx6OcxFFBYO7EZe+8PH2bG/t3tuNRs4Z84k8k1TiPIY+1ufY075heTZ1DcF\nr35Qy5LTJpA7xNrrZLCv4R1kJUyOaQbu4FG6gw3kumyDJlQ09wwaOm3FQ/67lYanc6AVQlJnn+MK\nCgp47cE1eAIhJhYM7Iiu33qQ7z3yND9dewmrFlWM+DF0thxQr++oSPvrjMNcTHegAZM9Qp4tsSj1\nH1GzrMuLZ5JjSU+NLttEfF2t6CxBCvIT32dDUF2sUpiT/t/fSMhpyqe554OcyYVnZGWNgsyQrL8j\ngo8P2nNivCRFVIdCIdauXcsVV1zB6tWrAbBarfj9fp577jkA7r//fux2e+w2n8/H3XffDcDmzZux\n2WyDXvu+++6Lfb18+XJWrFiRjJIFpzi+kJpmYDOpg4EGnQmXrYwO3wk6fCcoypmeljrcQdUC4DAP\n3onc/N838tsXPqDTG2DFgiksmTkBs8mAoihsPnicqpYtbNr/Q65d+FNaO6Nc+/2/YzMbueP6s1n7\nyTMxGlLTnTvUpK5L/9PzRs46w8qkUg+tnqNMcM4dcOyxFnWN9Ys7Glk1O/E1nRZVXHb7Bw5g5trN\nCd8ofFjVSFVdO5//8fMc+ONXcFhH1nXu8KmfSmhvSNJJrqWE7kAD3YHGhPcfiQbxhtrQSXrs5uGt\nQcmsrb4L3MGhM8PbvMcAyLOlfrhzLMRbUibkDnxeCgSCU5stW7awdetWAPR6PcuXLx/3NcctqqPR\nKN/85jepqKjg61//euznFRUVVFdXM3eu+mJWXV3NypUrY7cdPdo72FRVVcXUqVMHvf5tt93W5/u2\ntpFtIRN8PNE6C+N5HkTkIKGoD51kwNMVxCupyRIOw0Q6OMGxpj3oQkOncCSLxg71/4GJ3ISP6Ybz\nK2Nfe9xdeHq+nl9wE83dR+jwHecfe39CofQZTq8o4J1DTdz5f//knf0n+PlXLhiwaGW8uIONNHYf\nQIeJd/fkUVbSzqRSD0cbd2KKDLQLHKmrQW8HPY4h/93ksNrl7vDVjerf96tXzGXb7uO8fbCenzy5\nja99cmTrshs71aQio5yX9tcVE6rtqLHtKA5l8Ne+7qD6ZsRmLKCjvTNttRlk1YbU3FFDqSnx7+VE\n+4cAWCnLytdlJaK+oZTQYQgXZWWNgsyQjL8jgo8+8+bNY948NSCgoKCA7dvHv6143IGs99xzDzqd\njnvvvbfPz1evXs1jjz2G2+3m7bffZufOnaxatSp22+bNm6mqqqKpqYn169fHOtwCQaqJ9/jG59a6\nLJMB6Aymz1etraq2GUf/MaRRb2FZ+dcx6Mwc79oBlvd4+rtX8sdvXYLdYuTpN6q494m3kr7QprZT\nfeGZ7FrKlh/fSFd3PgC7T+wZ9Ph2r/oYJ+Un9ueCOjSql0yEoh6CEc+Qx8ZjNOi4Z43aYfjNi7tH\nHL+nJX/86ImjfFDVPOL7SwaJ8qDj8cQ2KaZ3YclQCSAa/nAn3cF6DDoz+ZbB3xRkGm1QsdAxDaPe\nkuFqBALBqcC4RHVdXR3r169n27ZtLF68mIULF7Jw4ULef/99brnlFmbMmMGKFSu48847WbduXSwl\nZP78+axdu5Y1a9Zw5ZVXcvnllwtRLUgb/eP0NJwW9WPsrjQOK3rHIaoBcs1lLJn4BQB2Nj1Bu7+a\nSxZN4XffWIXJoOOJ1w5Q29Q97HVkJcLOxic50fXOkMcpikxtlyqqK1znM7k4l0sXnA1Aq/fooBsQ\ntd/3jAllQ147PlavtnMbshIdtu5gxM0HDY9z1P8tPn91N53eIL97aXBxH09EDsVE9WsfBLBbkjqz\nPSyxWL0hlg1pgjvdWwATrSqPp8mrLlQpsp2WMCYx0+RbVbE/rei8DFciEAhOFcb1alhWVsbBgwcT\n3r5u3TrWrVs36G1r1qxhzZo147l7gWBM9E/+0HCZezrVaRTVWqdaW109FiY7z6HVd4Qj7Zt58+T/\ncMnU+1g+r4yHv3oRxS4blaVDp24A1Ha+yaG2jUjosRkLEq5Kb/YdxBduw2YspNg2C4Crl57D0wf/\nSIHLi0II6O0Ktnb5MRr9AMycMLz3tsg+i67gCXY2/Znqjn8yr/hfKM89C0nq+/4/Igc53PYPDrZu\nICyr11847wTLjlzMivnD30+r7zCyEuZkowOXzcnMsvTYfTRG0g32hJv7HJsuhsvRBmj27geg2D4n\nLTWNhWL7bG45+3GsRhft7R2ZLkcgEJwCiDXlglMOf7hvRrWGzViAUWclGO2OCe9UM5j9o6nDx+83\n7aW1yz/i6ywouZEC63R84TbeOvlrZEXm8iWVnDmjZMjz2t0Bdh1t4lCbmhOvEGXHyYcJRX0EQpE+\n1pH3jzRR25NNXeFcFhO6ZqOFfNtkkJQBy3OaOn24ctW8Y7t5eOG6sPQmlpZ9GbuxGHeogR0nf8U/\nqu/mZPd7KIqCrESp7nidjUfuYE/zU4RlP6WO0zEbHITlNn7/rSUsHuYxAzT3dFoP17i4cMGktK+v\ntifYXBiPJ6imJaVrm6KG1eBCJxkJRt2Eo4EBtyuKQlOPqC6xZ/cAoM2UP+ANmUA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hBCCCHakKxUi0ZdGFQDBOqjKKw6RVnNOfx1IXXu9wbby+ZeQ0RgdIP9Dgy/lbjgyQQamr55MMgQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75179e6a0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JBYv59IwqT3+QqCk9m4Wzxh4I2s0ekkkFlzNBY8fwddX13S/S2PsGLx39HnVd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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751b83b38>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is clear that as $g$ is larger we more closely follow the measurement instead of the prediction. When $g=0.9$ we follow the signal almost exactly, and reject almost none of the noise. One might naively conclude that $g$ should always be very small to maximize noise rejection. However, that means that we are mostly ignoring the measurements in favor of our prediction. What happens when the signal changes not due to noise, but an actual state change? Let's look. I will create data that has $\\dot{x}=1$ for 9 steps before changing to $\\dot{x}=0$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = [5,6,7,8,9,10,11,12,13,14]\n",
      "\n",
      "for i in range(100):\n",
      "    zs.append(14)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.1, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.1')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.5, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.5')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=0.9, h=0.01)\n",
      "plot_g_h_results(zs, data, 'g = 0.9')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Sytn7mbIyCnXBKKf2nfyH0XF6TXBd05bXNTWt/yCDZ+upsauoceh7s8uVW3hK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\nDx+WyWRSdna2LrzwQl1++eXKzs5u93m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r1q1UVlYSEhLC5MmTiY2NVX5e6OTJk+Tn53Pp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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75161f1d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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14ytWrNBVV12lsWPHat68efroo4/atdC2VlJ7vtjr6m5sIQAAAAgJEReaEB8f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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75175b7b8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0MroUAAAAmFSHaAl9IPd7SdLR3BCDKwEAAIBZdYhg7Op4F0XHOwAAADSP6YMx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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751900eb8>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see the effects of ignoring the signal. We not only filter out noise, but legitimate changes in the signal as well. \n",
      "\n",
      "Maybe we need a 'Godilocks' filter, where is not too large, not too small, but just right? Well, not exactly. As alluded to earlier, different filters choose g and h in different ways depending on the mathematical properties of the problem. For example, the Benedict-Bordner filter was invented to minimize the transient error in this example, where $\\dot{x}$ makes a step jump. We will not discuss this filter in this book, but here are two plots chosen with different allowable pairs of g and h. This filter design minimizes transient errors for step jumps in $\\dot{x}$ at the cost of not being optimal for other types of changes in $\\dot{x}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,15,16,16,16,16,16,16,16,16,16,16,16]\n",
      "    \n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=.302, h=0.054)\n",
      "plot_g_h_results(zs, data, 'g = 0.302, h = 0.054')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=4., dx=1., dt=1.,g=.546, h=0.205)\n",
      "plot_g_h_results(zs, data, 'g = 0.546, h = 0.205')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h1Gn7NJGGpA8wqYnGhdRE40JqonEhDUVBWERERERaJQVhEREREWmVFIRFREREpFVSEBYR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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7517fb6d8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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twoP9XaaISK0pCIuIyAlVuEtYmzmPfPsegizhjEi6g1Zh3QBY8rcLiQoN0nQI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\n/w+6emMa/OCwjAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc75174fb70>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Varying h"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's leave g unchanged and investigate the effect of modifying h. We know that h affects how much of we favor the measurement of $\\dot{x}$ vs our prediction. But what does this *mean*? If our signal is changing a lot (quickly relative to the time step of our filter), then a large $h$ will cause us to react to those transient changes rapidly. A smaller $h$ will cause us to react more slowly.\n",
      "\n",
      "We will look at three examples. We have a noiseless measurement that slowly goes from 0 to 1 in 50 steps. Our first filter uses a nearly correct initial value for $\\dot{x}$ and a small $h$. You can see from the output that the filter output is very close to the signal. The second filter uses the very incorrect guess of $\\dot{x}=2$. Here we see the filter 'ringing' until it settles down and finds the signal. The third filter uses the same conditions but it now sets $h=0.5$. If you look at the amplitude of the ringing you can see that it is much smaller than in the second chart, but the frequency is greater. It also settles down a bit quicker than the second filter, though not by much."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zs = np.linspace(0,1,50)\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=0., dt=1.,g=.2, h=0.05)\n",
      "plot_g_h_results(zs, data, 'dx=0, h = 0.05')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=2., dt=1.,g=.2, h=0.05)\n",
      "plt.ylim([-1,5])\n",
      "plot_g_h_results(zs, data, 'dx=2, h = 0.05')\n",
      "\n",
      "data = g_h_filter(data=zs, x0=0, dx=2., dt=1.,g=.2, h=0.5)\n",
      "plt.ylim([-1,5])\n",
      "plot_g_h_results(zs, data, 'dx=2, h = 0.5')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OoyvYc3w5MbamR0tbTDb6J00kO3UmKXH9md7yM8pEOjQVZREREWmTqoZSNu5/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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7504ae6d8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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InAbDMDWaOct2o9uzy7Dl8AWpSyEiIiICwDBMjchPo4LBJOCfa/ZIXQoRERER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\nNcMiIiIi4rDUDIuIiIiIw/o/thc/+kEygY8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc7504436d8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xV57iY92Krw64CW6t3Ps/bSr3yuUrldNbIv+ButvTTw19Drf2ye06+LndEhd0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\nl7QEfqMHIOwMF4YH9qi6GWM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oVK9OyXruznGtaptoAGgqHo9HhYWFx/yb4MLCQkmS1+sN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\nREQ8lpphEREREfFY/wfDxA4J1UKdiQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc751658588>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Final Thoughts"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Near the beginning of the chapter I used `numpy.polyfit()` to fit a straight line to the weight measurements. It fits a n-th degree polynomial to the data using a 'least squared fit'. How does this differ from the g-h filter?\n",
      "\n",
      "Well, it depends. We will eventually learn that the Kalman filter is optimal from a least squared fit perspective. However, `polyfit()` fits a polynomial to the data, not an arbitrary curve, by minimizing the value of this formula:\n",
      "$$E = \\sum_{j=0}^k |p(x_j) - y_j|^2$$\n",
      "\n",
      "I assumed that my weight gain was constant at 1 lb/day, and so when I tried to fit a polynomial of $n=1$, which is a line, the result very closely matched the actual weight gain. But, of course, no one consistently only gains or loses weight. We fluctuate. Using 'polyfit()' for a longer series of data would yield poor results. In contrast, the g-h filter reacts to changes in the rate - the $h$ term controls how quickly  the filter reacts to these changes. If we gain weight, hold steady for awhile, then lose weight, the filter will track that change automatically. 'polyfit()' would not be able to do that unless the gain and loss could be well represented by a polynomial.\n",
      "\n",
      "Another advantage of this form of filter, even if the data fits a *n*-degree polynomial, is that it is *recursive*. That is, we can compute the estimate for this time period knowing nothing more than the estimate and rate from the last time period. In contrast, if you dig into the implementation for `polyfit()` you will see that it needs all of the data before it can produce an answer. Therefore algorithms like `polyfit()` are not well suited for real-time data filtering. In the 60's when the Kalman filter was developed computers were very slow and had extremely limited memory. They were utterly unable to store, for example, thousands of readings from an aircraft's inertial navigation system, nor could they process all of that data in the short period of time needed to provide accurate and up-to-date navigation information. \n",
      "\n",
      "\n",
      "Up until the mid 20th century various forms of Least Squares Estimation was used for this type of filtering. For example, for NASA's Apollo program had a ground network for tracking the Command and Service Model (CSM) and the Lunar Module (LM). They took measurements over many minutes, batched the data together, and slowly computed an answer. In 1960 Stanley Schmidt at NASA Ames recognized the utility of Rudolf Kalman's seminal paper and invited him to Ames. Schmidt applied Kalman's work to the onboard navigation systems on the CSM and LM, and called it the \"Kalman filter\".[1] Soon after, the world moved to this faster, recursive filter.\n",
      "\n",
      "The Kalman filter only needs to store the last estimate and a few related parameters, and requires only a relatively small number of computations to generate the next estimate. Today we have so much memory and processing power that this advantage is somewhat less important, but at the time the Kalman filter was a major breakthrough not just because of the mathematical properties, but because it could (barely) run on the hardware of the day. \n",
      "\n",
      "This subject is much deeper than this short discussion suggests. We will consider these topics many more times throughout the book."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I encourage you to experiment with this filter to develop your understanding of how it reacts. It shouldn't take too many attempts to come to the realization that ad-hoc choices for $g$ and $h$ do not perform very well. A particular choice might perform well in one situation, but very poorly in another. Even when you understand the effect of $g$ and $h$ it can be difficult to choose proper values. In fact, it is extremely unlikely that you will choose values for $g$ and $h$ that is optimal for any given problem. Filters are *designed*, not selected *ad hoc*. \n",
      "\n",
      "In some ways I do not want to end the chapter here, as there is a significant amount that we can say about selecting $g$ and $h$. But the g-h filter in this form is not the purpose of this book. Designing the Kalman filter requires you to specify a number of parameters - indirectly they do relate to choosing $g$ and $h$, but you will never refer to them direcly when designing Kalman filters. Furthermore, $g$ and $h$ will vary at every time step in a very non-obvious manner. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is another feature of these filters we have barely touched upon - Bayesian statistics. You will note that the term 'Bayesian' is in the title of this book; this is not a coincidence! For the time being we will leave $g$ and $h$ behind, largely unexplored, and develop a very powerful form of probabilistic reasoning about filtering. Yet suddenly this same g-h filter algorithm will appear, this time with a formal mathematical edifice that allows us to create filters from multiple sensors, to accurately estimate the amount of error in our solution, and to control robots."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*  [1] NASA Kalman Filtering Presentation<p> http://nescacademy.nasa.gov/review/downloadfile.php?file=FundamentalsofKalmanFiltering_Presentation.pdf&amp;id=199&amp;distr=Public\n",
      "\n",
      "\n"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}