Cleaned up equations for UKF.

I was using a bunch of variable names that weren't consistent
with the rest of the book (but perhaps are more consistent with
the literature). It just made everything more challenging than
it needed to be, so instead of \mu and \sigma (e.g.) I use
\bar x and \bar P.

I also am in the middle of rewriting some sections for clarity,
but that work is not completed.

code/nonlinear_plots.py

@@ -246,7 +246,7 @@ def plot_monte_carlo_mean(xs, ys, f, mean_fx, label, plot_colormap=True):
     plt.scatter(mean_fx[0], mean_fx[1],
                 marker='v', s=300, c='r', label=label)
     plt.scatter(computed_mean_x, computed_mean_y,
-                marker='*',s=120, c='r', label='Computed Mean')
+                marker='*',s=120, c='b', label='Computed Mean')
 
     plot_bivariate_colormap(fxs, fys)
     plt.ylim([-10, 200])

code/ukf_internal.py

@@ -279,7 +279,7 @@ def plot_radar(xs, t, plot_x=True, plot_vel=True, plot_alt=True):
         plt.ylabel('altitude')
     plt.show()
 
-    
+
 def plot_altitude(xs, t, track):
     xs = np.asarray(xs)
 
@@ -289,7 +289,7 @@ def plot_altitude(xs, t, track):
     plt.ylabel('altitude')
     plt.legend(loc=4)
 
-    
+
 def print_sigmas(n=1, mean=5, cov=3, alpha=.1, beta=2., kappa=2):
     points = MerweScaledSigmaPoints(n, alpha, beta, kappa)
     print('sigmas: ', points.sigma_points(mean,  cov).T[0])
@@ -404,20 +404,24 @@ def _plot_iscts(pos, sa, sb, N=4):
             xs_b.append(db*math.cos(a_b) + sb[0])
             ys_b.append(db*math.sin(a_b) + sb[1])
 
-        plt.scatter(xs, ys, c='r', marker='.')
-        plt.scatter(xs_a, ys_a)
-        plt.scatter(xs_b, ys_b)
+        plt.scatter(xs, ys, c='r', marker='.', alpha=0.5)
+        plt.scatter(xs_a, ys_a, c='k', edgecolor='k')
+        plt.scatter(xs_b, ys_b, marker='v', edgecolor=None)
     plt.gca().set_aspect('equal')
 
 
 def plot_iscts_two_sensors():
+    plt.subplot(121)
     pos = np.array([4., 4,])
     sa = [0., 2.]
     sb = [8., 2.]
 
-    plt.scatter(*sa, s=100)
-    plt.scatter(*sb, s=100)
+    plt.scatter(*sa, s=200, c='k', marker='v')
+    plt.scatter(*sb, s=200, marker='s')
     _plot_iscts(pos, sa, sb, N=4)
+    plt.subplot(122)
+    plot_iscts_two_sensors_changed_sensors()
+
 
 
 def plot_iscts_two_sensors_changed_sensors():
@@ -425,8 +429,8 @@ def plot_iscts_two_sensors_changed_sensors():
     sb = [3, 7]
     pos= np.array([3., 3.])
 
-    plt.scatter(*sa, s=100)
-    plt.scatter(*sb, s=100)
+    plt.scatter(*sa, s=200, c='k', marker='v')
+    plt.scatter(*sb, s=200, marker='s')
     _plot_iscts(pos, sa, sb, N=5)
     plt.ylim(3.8, 8.5)