diff --git a/markdown/15-Probabilistic-Reasoning-Over-Time/exercises/ex_12/question.md b/markdown/15-Probabilistic-Reasoning-Over-Time/exercises/ex_12/question.md index 47b8f21c06..ca0530676f 100644 --- a/markdown/15-Probabilistic-Reasoning-Over-Time/exercises/ex_12/question.md +++ b/markdown/15-Probabilistic-Reasoning-Over-Time/exercises/ex_12/question.md @@ -5,8 +5,18 @@ system whose behavior switches unpredictably among a set of $k$ distinct “modes.” For example, an aircraft trying to evade a missile can execute a series of distinct maneuvers that the missile may attempt to track. A Bayesian network representation of such a switching Kalman -filter model is shown in -Figure switching-kf-figure.

+filter model is shown in the figure below. The follow-up questions will be based on this diagram. + +
+ switching-kf-figure +
A Bayesian network representation of a switching Kalman filter. The switching variable $S_t$ is a discrete state variable whose value determines + the transition model for the continuous state variables $\textbf{X}_t$. + For any discrete state $\textit{i}$, the transition model + $\textbf{P}(\textbf{X}_{t+1}|\textbf{X}_t,S_t= i)$ is a linear Gaussian model, just as in a + regular Kalman filter. The transition model for the discrete state, + $\textbf{P}(S_{t+1}|S_t)$, can be thought of as a matrix, as in a hidden + Markov model.
+
1. Suppose that the discrete state $S_t$ has $k$ possible values and that the prior continuous state estimate