CH4 1.(a) why the covariance matrix is not allowed to update?

[howardchina]

I think the covariance matrix $\Sigma_{t-1}$ should be updated at each time $t$.

$$ \begin{equation} p(x_t | u_t, x_{t-1}) \sim N(A_t x_{t-1}, A_t\Sigma_{t-1} A_t^T+R) \end{equation} $$

But your update is doing like below:

$$ \begin{equation} p(x_t | u_t, x_{t-1}) \sim N(A_t x_{t-1}, A_t\Sigma_0 A_t^T+R) \end{equation} $$

[Yu-Xiaoxian]

I think the covariance matrix Σt−1 should be updated at each time t.

p(xt|ut,xt−1)∼N(Atxt−1,AtΣt−1AtT+R)

But your update is doing like below:

p(xt|ut,xt−1)∼N(Atxt−1,AtΣ0AtT+R)

Sorry my fault, you're right