A new forward-pass fixed-interval smoother using the U-D information matrix factorization

A new U-D factorized smoothing algorithm that is numerically stable and reliable is developed by using a forward-pass fixed-interval smoother recursion. Introducing a gain for a backward-pass information filter and the notion of an input to the smoother and decomposing the system noises into each element, it is shown that three famous U-D algorithms can be naturally applied to construct such a smoother. The new result does not necessitate two burdensome matrix inversions, or any algebraic computations equivalent to them, for the transition matrix and the predicted error covariance, which are at present necessary for the Bierman's U-D smoother. Consequently, compared with the result of Bierman, the present algorithm can deal with a broader system, which may cover a time-delay system, and provide an improvement in computation speed and computer storage.