Continuous-Time Set-Valued State Estimation and Model Validation

Abstract

In the previous chapters, the problem of robust state estimation was addressed by extending the standard steady state Kalman Filter to the case in which the underlying signal model is an uncertain system. The uncertain systems being considered were uncertain systems with norm bounded uncertainty and subject to stochastic white noise disturbances. In particular, the robust Kalman Filters of Chapters 2 and 3 are concerned with constructing a state estimator which bounds the mean square estimation error. However, these results may be conservative in that only an upperbound is obtained for the mean square estimation error. Also, these results do not extend in a straightforward way to the case of finite time horizon state estimation problems or robust state estimation problems with structured uncertainty.