This chapter discusses the estimation of the state of continuous‐time linear dynamic systems based on observations which are made also in continuous time. The linear minimum mean square error (LMMSE) filter for this continuous‐time problem, known as the Kalman‐Bucy filter, is obtained in this chapter from a limiting process of the discrete time problem. The properties of the innovation process are derived. The asymptotic properties of the estimated state covariance equation—the continuous‐time Riccati equation—which yields a steady‐state filter, are also presented. The prediction of the state of a continuous‐time system is also presented. The duality of the LMMSE estimation with the linear‐quadratic (LQ) control problem is discussed. The chapter concludes with a brief discussion of the Wiener‐Hopf problem, which consists of the estimation of a stochastic process based on another observed process using their auto‐ and cross‐covariances. A problem solving section appears at the end of the chapter.
Continuous‐Time Linear State Estimation
04.01.2002
29 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch