Title :
Asymptotic convergence of Riccati equation and smoother solutions
Author :
Einicke, Garry A.
Author_Institution :
Commonwealth Sci. & Ind. Res. Organ., Pullenvale
Abstract :
This paper describes sufficient conditions for the monotonic convergence of discrete-time and continuous-time Riccati equations. It is shown that when the Riccati equation solutions converge, the time-varying, minimum-variance, fixed-interval smoothers provide optimal performance. That is, the energy of the estimation errors asymptotically approach a lower bound and attain I2/L2 stability.
Keywords :
Riccati equations; continuous time systems; discrete time systems; error analysis; smoothing methods; stability; time-varying systems; asymptotic convergence; continuous-time Riccati equations; discrete-time equations; error estimation; fixed-interval smoothers; minimum-variance systems; monotonic convergence; time-varying systems; Asymptotic stability; Difference equations; Differential equations; Estimation error; Filtering; Mercury (metals); Noise measurement; Riccati equations; Sufficient conditions; USA Councils; Kalman filtering; Riccati equations; Smoothing; non-causal filtering; stability;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4434151
