Title :
A note on uniform observability
Author_Institution :
IRMAR, Rennes I Univ., France
fDate :
8/1/2001 12:00:00 AM
Abstract :
We prove that the classical inequality Pt⩽𝒪 t-1Ct relating the variance of the Kalman filter estimate, the observability matrix, and the controllability matrix is not true. This inequality is the cornerstone of the asymptotic stability theory of the Kalman filter for time-varying systems. We provide another inequality of the same type
Keywords :
Kalman filters; asymptotic stability; controllability; filtering theory; observability; state estimation; time-varying systems; Kalman filter estimate; asymptotic stability theory; controllability matrix; observability matrix; time-varying systems; uniform observability; variance; Asymptotic stability; Controllability; Estimation error; Gaussian distribution; Kalman filters; Linear matrix inequalities; Observability; Symmetric matrices; Time varying systems;
Journal_Title :
Automatic Control, IEEE Transactions on
