Minor typo fixes.

05_Kalman_Filters/Kalman_Filters.ipynb

@@ -1002,7 +1002,7 @@
       "movement = 1\n",
       "movement_variance = 2\n",
       "sensor_variance = 10\n",
-      "pos = (0, 500)   # gaussian N(0,50)\n",
+      "pos = (0, 500)   # gaussian N(0,500)\n",
       "\n",
       "dog = DogSensor(pos[0], velocity=movement, variance=sensor_variance)\n",
       "\n",
@@ -1153,7 +1153,7 @@
       "movement = 1\n",
       "movement_variance = 2\n",
       "sensor_variance = 4.5\n",
-      "pos = (0, 100)   # gaussian N(0,50)\n",
+      "pos = (0, 100)   # gaussian N(0,100)\n",
       "\n",
       "dog = DogSensor(pos[0], velocity=movement, variance=sensor_variance)\n",
       "\n",

08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb

@@ -1317,7 +1317,7 @@
       "We might think to use the same state variables as used for tracking the dog. However, this will not work. Recall that the Kalman filter state transition must be written as $\\mathbf{x}' = \\mathbf{F x}$, which means we must calculate the current state from the previous state. Our assumption is that the ball is traveling in a vacuum, so the velocity in x is a constant, and the acceleration in y is solely due to the gravitational constant $g$. We can discretize the Newtonian equations using the well known Euler method in terms of $\\Delta t$ are:\n",
       "\n",
       "$$\\begin{aligned}\n",
-      "x_t &=  v_{x(t-1)} {\\Delta t} \\\\\n",
+      "x_t &=  x_{t-1} + v_{x(t-1)} {\\Delta t} \\\\\n",
       "v_{xt} &= vx_{t-1}\n",
       "\\\\\n",
       "y_t &= -\\frac{g}{2} {\\Delta t}^2 + vy_{t-1} {\\Delta t} + y_{t-1} \\\\\n",