fixed use of term 'innovation'.
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389660de0c
@ -730,7 +730,7 @@
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"\n",
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" new_belief = prior_belief * measurement * sensor_error\n",
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" \n",
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"The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. Here *prior* carries the both the colloquial sense of *previoius*, but also the Bayesian meaning. In Bayesian terms the *prior* is the probability after the innovation (prediction) and before the measurements have been incorporated.\n",
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"The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. Here *prior* carries the both the colloquial sense of *previoius*, but also the Bayesian meaning. In Bayesian terms the *prior* is the probability after the prediction and before the measurements have been incorporated.\n",
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" \n",
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"If we are implementing this with Gaussians, we might expect it to be implemented as:\n",
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"\n",
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@ -1942,7 +1942,7 @@
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"source": [
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"For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
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"\n",
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"The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)."
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"The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement."
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]
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},
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{
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