New square-root smoothing algorithms
PooGyeon Park, T. Kailath · 2002
New square-root smoothing algorithms are suggested for the four kinds of smoothing formulas: (1) Bryson-Frazier (BF) formulas, (2) Rauch-Tung-Striebel (RTS) formulas, (3) backward RTS formulas and (4) two-filter formulas. These algorithms are compared on the basis of constraints, speed in real-time or batch processing, array size, memory size, and so on. The main features of the new algorithms are to implement all the formulas with square-root arrays composed of the filtered or smoothed estimates and their error covariances, and to avoid inversion or backwards substitution in all the formulas: these features provide many advantages over the conventional algorithms with respect to systolic array and parallel implementations as well as numerical stability and conditioning.>