@@ -565,7 +565,8 @@ In the simulation, take $\theta = 10$, $\hat x_0 = 8$ and $\Sigma_0 = 1$.

565565566566Your figure should -- modulo randomness -- look something like this567567568-```{figure} /_static/lecture_specific/kalman/kl_ex1_fig.png568+```{image} /_static/lecture_specific/kalman/kl_ex1_fig.png569+:align: center569570```570571571572```{exercise-end}

@@ -629,7 +630,8 @@ Plot $z_t$ against $T$, setting $\epsilon = 0.1$ and $T = 600$.

629630630631Your figure should show error erratically declining something like this631632632-```{figure} /_static/lecture_specific/kalman/kl_ex2_fig.png633+```{image} /_static/lecture_specific/kalman/kl_ex2_fig.png634+:align: center633635```634636635637```{exercise-end}

@@ -732,7 +734,8 @@ Finally, set $x_0 = (0, 0)$.

732734733735You should end up with a figure similar to the following (modulo randomness)734736735-```{figure} /_static/lecture_specific/kalman/kalman_ex3.png737+```{image} /_static/lecture_specific/kalman/kalman_ex3.png738+:align: center736739```737740738741

Observe how, after an initial learning period, the Kalman filter performs quite well, even relative to the competitor who predicts optimally with knowledge of the latent state.