Title :
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
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;
Conference_Titel :
System Theory, 2004. Proceedings of the Thirty-Sixth Southeastern Symposium on
Print_ISBN :
0-7803-8281-1
DOI :
10.1109/SSST.2004.1295612
