Table 1.

The complete EM algorithm.

Algorithm EM Algorithm for MR. SID
1.	Initialize θ = {A, C, R, π0} with SVD
2.	While convergence criteria are unmet E Step
3.	Update the expectations in Eq. (5) with the KFS M Step
4.	$R^{\text{new}}=\text{diag}\left\{\frac{1}{T}{\displaystyle \sum _{t=1}^T({\mathit{y}}_t{\mathit{y}}_t^{\top }-C^{\text{old}}{\widehat{\mathit{x}}}_t{\mathit{y}}_t^{\top })}\right\}$, as in Eq. 6
5.	${\pi }_0^{\text{new}}={\widehat{\mathit{x}}}_0$
6.	Update Cnew, as in Eq. (7)
7.	Update Anew with FISTA, as in Eq. (8)