Covariance factorization algorithms for fixed-interval smoothing of linear discrete dynamic systems
Stephen R. McReynolds · IEEE Transactions on Automatic Control · 1990
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.>