The solution to the Lyapunov equation in constant gain filtering and some of its applications

Author

Gray, John E. ; Smith-Carroll, A. Sunshine ; Jordan, Leon A.

Author_Institution

Dept. of Syst. Res. & Technol., Naval Surface Warfare Center Dahlgren Div., VA, USA

fYear

2004

fDate

2004

Firstpage

21

Lastpage

25

Abstract

Presented in this paper is a solution to the Lyapunov equation in constant gain filtering. A specific method for deriving the noise reduction ratios for the alpha-beta and alpha-beta-gamma filters are explored using the Lyapunov equation. This enables us to simplify the computation drastically. For a 2 × 2 matrix, one has to solve for one unknown instead of two. For a 3 × 3 matrix, one has to solve for three unknowns instead of six and so on. Thus reduction in the number of variables has considerable advantage for higher dimensional filters such as the alpha-beta-gamma filter.

Keywords

Lyapunov matrix equations; tracking filters; Lyapunov equation; alpha-beta filter; alpha-beta-gamma filter; constant gain filtering; noise reduction ratios; tracking filters; Covariance matrix; Equations; Filtering; Filters; Noise reduction; Performance analysis; Q measurement; Radar tracking; Smoothing methods; Steady-state;

fLanguage

English

Publisher

ieee

Conference_Titel

System Theory, 2004. Proceedings of the Thirty-Sixth Southeastern Symposium on

ISSN

0094-2898

Print_ISBN

0-7803-8281-1

Type

conf

DOI

10.1109/SSST.2004.1295612

Filename

1295612