A New Computationally Efficient Fixed-Interval Discrete-Time Smoother

Abstract

The Rauch-Tung-Streibel (R-T-S) smoother recursion is used to derive a new smoother algorithm based upon a decomposition of the linear model dynamical equation and maximizing use of rank-1 matrix modification. This new algorithm, it turns out, parallels Bierman's (1982) forward recursive square-root information filter (SRIF)/backward recursive U-D factorized covariance algorithm. The new result features computational efficiency, reliance on numerically stable matrix modification algorithms, and reduced computer storage.