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.
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