Robust State Estimation with Discrete and Continuous Measurements

Abstract

In many filtering and state estimation problems, the process being considered has a continuous-time model but the measured output data are available only at discrete sampling instants. Hence, we are motivated to consider“hybrid” problems of problems of state estimation and model validation in which the underlying process model is continuous but the available measured data are available at discrete sampling times. Furthermore, we extend this problem to allow for the case when some of the outputs can be measured continuously and other outputs can only be measured at discrete sampling instants. Such a situation may arise in complex hybrid processes involving both digital and analog blocks. Also, there may arise situations in which some of the sensors supply data at a very fast rate (which can be approximated as a continuous-time signal) whereas other sensors supply data at a slower sample rate. In this case, it is important that the signal processing algorithm be able to simultaneously handle both types of measured data. The main results of this chapter extend the setvalued state estimation and model validation results of Chapters 4 and 5 to allow for hybrid discrete-continuous data. The results of this chapter originally appeared in the papers [125,128,138].