New square-root smoothing algorithms

Abstract

This paper presents new square-root smoothing algorithms for the three best-known smoothing formulas: 1) Rauch-Tung-Striebel (RTS) formulas, 2) Desai-Weinert-Yusypchuk (DWY) formulas, called backward RTS formulas, and 3) Mayne-Fraser (MF) formulas, called two-filter formulas. The main feature of the new algorithms is that they use unitary rotations to replace all matrix inversion and backsubstitution steps common in earlier algorithms with unitary operations; this feature enables more efficient systolic array and parallel implementations and leads to algorithms with better numerical stability and conditioning properties.