The square-root fixed-interval discrete-time smoother has been used extensively in discrete recursive estimation since it was first developed by Rauch, Tung and Streibel . Various people, for example Bierman , , have recognized the inherent instability in employing this kind of smoother in its original form; they have investigated implementing the recursion more stably. Bierman's paper  is one such contribution. In this paper we plan to present a more comprehensive development of Bierman's approach, and to show that this algorithm can be implemented more stably as a square-root smoother. Throughout this paper the fixed-interval discrete-time smoother will be referred to as the RTS smoother. Numerical results are given for the usual form of the RTS smoother, Bierman's algorithm and our square-root formulation of his algorithm. These confirm that the square-root formulation is more desirable than Bierman's algorithm, which performs better than the usual implementation of the RTS smoother.
|Number of pages||12|
|Journal||Journal of the Australian Mathematical Society Series B-Applied Mathematics|
|Publication status||Published - Jul 1988|
PRVAN, T., & Osborne, M. R. (1988). A square-root fixed-interval discrete-time smoother. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 30(1), 57-68. https://doi.org/10.1017/S0334270000006032