Robust Estimation of Uncertain Dynamical Systems

In many signal processing applications, such as radar and ultrasonic signal processing, communications, speech recognition, seismology, remote sensing, etc., mathematical models are used to investigate the behaviour of systems. However, uncertainties in these models are usually unavoidable due to modelling errors, parameter drifting and changes in the system structure throughout time, nonlinearities, environmental disturbances and measurement noises.

The ability to cope with uncertainties and achieve desired performance is referred to as robustness. The central problem in signal estimation is concerned with the recovery of unmeasurable signals from the measured ones which are usually distorted or corrupted with some unknown noise and disturbances. There is need for deriving robust techniques especially for applications requiring high precision and reliability such as air surveillance.

The aim of this research is to investigate various estimation problems in dynamical systems with uncertain parameters and disturbances. We will concentrate our research on the development of robust estimators which take into account the existence of parameter uncertainty in the design. We shall consider estimation problems using both H-2 and H-infinity performance indices. The former will yield a minimum mean square for the estimation error, and the latter, a minimum peak for the error spectrum. Our techniques will be different from current adaptive schemes because we will employ simple estimators without adaptation mechanisms for the sake of robustness and cheap computation and implementation. More importantly, the preliminary work has laid down a good foundation for the development of this proposed research. Based on this preliminary work, we will try to develop a systematic design methodology for solving the problems of robust H-2 and H-infinity signal filtering in the presence of parameter uncertainty in the signal generating system.

For more information please contact Peng Shi.