System Identification: smoothing in E-step of EM algorithm
The result of the $M$-step is expressed in terms of the matrices $\mathbf{P}_n^2$ and the vectors $\mathbf{x}_n^s$. These quantities are defined as expectations. Smoothing is used to compute these expectations, because in practice expectations are usually approximated by time averages (hence 'smoothing'). If you have another method for computing these expectations, the results of the $M$-step will of course be different, but the expressions for the results of the $M$-step remain valid, you just plug in different values for the respective matrices and vectors.