Covariance factorization algorithms for fixed-interval smoothing of linear discrete dynamic systems

Efficient factorized covariance smoothers designed to work with factorized covariance filters are derived for linear discrete dynamic systems. The approach to factorized covariance smoothers (either U -D or square root) uses outputs from factorized covariance filters and is closely derived from the G.J. Bierman´s earlier algorithm (1974), the Dyer-McReynolds covariance smoother. These algorithms are more efficient than the Bierman´s newer smoother (1983) based upon rank 1 process noise updates. The efficiency of the new algorithms increases significantly as the order of process noise increases. For full process noise, they can be implemented in a way that avoids the inverse of the transition matrix