In this technical report, some derivations for the smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes smoother for linear state-space models with unknownprocess and measurement noise covariances in [1] are presented. Further, the variational iterations are compared with iterations of the Expectation Maximization (EM) algorithm for smoothing linear state-space models with unknown noise covariances.

[1] T. Ardeshiri, E. Özkan, U. Orguner, and F. Gustafsson, ApproximateBayesian smoothing with unknown process and measurement noise covariances, submitted to Signal Processing Letters, 2015.