A new computationally efficient fixed-interval, discrete-time smoother

Abstract

The Rauch-Tung-Streibel 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 forward recursive square-root information filter/ backward recursive U-D factorized covariance algorithm [5]. The new result features computational efficiency, reliance on numerically stable matrix modification algorithms, and reduced computer storage.