Changed "unobserved" variable to "hidden"

Not sure how I ended up calling hidden variables unobserved,
but it is fixed now.

Author: rlabbe

07_Designing_Kalman_Filters.ipynb

@@ -391,7 +391,7 @@
     "\n",
     "There is nothing special about this organization. I could have listed the (xy) coordinates first followed by the velocities. I just need to be consistent in the rest of the matrices.\n",
     "\n",
-    "It might be a good time to pause and address how you identify the unobserved variables. This particular example is somewhat obvious because we already worked through the 1D case in the previous chapters. Would it be so obvious if we were filtering market data, population data from a biology experiment, and so on? Probably not. There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n",
+    "It might be a good time to pause and address how you identify the hidden variables. This particular example is somewhat obvious because we already worked through the 1D case in the previous chapters. Would it be so obvious if we were filtering market data, population data from a biology experiment, and so on? Probably not. There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n",
     "\n",
     "Beyond this you can start looking at how you might combine the data from two or more different sensors to produce more information. This opens up the field of *sensor fusion*, and we will be covering examples of this in later sections. For now, recognize that choosing the appropriate state variables is paramount to getting the best possible performance from your filter."
    ]

12_Smoothing.ipynb

@@ -634,7 +634,8 @@
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
@@ -663,7 +664,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The improvement in the velocity, which is an unobserved variable, is even more dramatic. \n",
+    "The improvement in the velocity, which is an hidden variable, is even more dramatic. \n",
     "\n",
     "Since we are plotting velocities let's look at what the the 'raw' velocity is, which we can compute by subtracting subsequent measurements. We see below that the noise swamps the signal, causing the computed values to be essentially worthless. I show this to reiterate the importance of using Kalman filters to compute velocities, accelerations, and even higher order values. I use a Kalman filter even when my measurements are so accurate that I am willing to use them unfiltered if I am also interested in the velocities and/or accelerations. Even a very small error in a measurement gets magnified when computing velocities. "
    ]

13_Adaptive_Filtering.ipynb

@@ -1269,7 +1269,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "As the standard deviation limit gets smaller the computation of the velocity gets worse. Think about why this is so. If we start varying the filter so that it prefers the measurement over the prediction as soon as the residual deviates even slightly from the prediction we very quickly be giving almost all the weight towards the measurement. With no weight for the prediction we have no information from which to create the unobserved variables. So, when the limit is 0.1 std you can see that the velocity is swamped by the noise in the measurement. On the other hand, because we are favoring the measurements so much the position follows the maneuver almost perfectly.\n",
+    "As the standard deviation limit gets smaller the computation of the velocity gets worse. Think about why this is so. If we start varying the filter so that it prefers the measurement over the prediction as soon as the residual deviates even slightly from the prediction we very quickly be giving almost all the weight towards the measurement. With no weight for the prediction we have no information from which to create the hidden variables. So, when the limit is 0.1 std you can see that the velocity is swamped by the noise in the measurement. On the other hand, because we are favoring the measurements so much the position follows the maneuver almost perfectly.\n",
     "\n",
     "Now let's look at the effect of various increments for the process noise. Here I have held the standard deviation limit to 2 std, and varied the increment from 1 to 10,000."
    ]