New square-root smoothing algorithms

Author

Park, PooGyeon ; Kailath, Thomas

Author_Institution

Inf. Syst. Lab., Stanford Univ., CA, USA

Volume

41

Issue

5

fYear

1996

fDate

5/1/1996 12:00:00 AM

Firstpage

727

Lastpage

732

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

Keywords

Kalman filters; least squares approximations; numerical stability; smoothing methods; state estimation; Desai-Weinert-Yusypchuk formulas; Mayne-Fraser formulas; Rauch-Tung-Striebel formulas; conditioning properties; numerical stability; square-root smoothing algorithms; two-filter formulas; unitary rotations; Control system synthesis; Feedback; Information filtering; Information filters; Linear matrix inequalities; Numerical stability; Robust stability; Smoothing methods; Stability analysis; Stability criteria;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.489212

Filename

489212