Parameter and derivative estimation for nonlinear continuous-time system identification

Abstract

In this note we investigate parameter identification for nonlinear continuous-time SISO systems, based on input/output data, where the output is assumed to be noise corrupted. Continuous-time identification requires (i) the estimation of derivatives of the output (which is nontrivial due to the influence of noise), a suitable measure thereof or a way to avoid them and (ii) methods for parameter estimation based on the measured data. Problem (i) is addressed by reviewing modulating functions and the concept of delayed state variable filters; furthermore a high-gain observer is introduced as an approach to provide the necessary derivative information. Its performance is investigated with respect to the modulating function and the delayed state variable filter approaches. Least-squares methods are assessed for continuous-time nonlinear identification (problem (ii)). It is shown that parameter identification based in modulating functions and a standard least-squares method does not guarantee bias-free estimates for some systems. Whereas ordinary (or weighted) least-squares is sufficient for parameter identification by means of modulating functions it is not for the delayed state variable filter and the high-gain observer approaches (due to dependencies between error terms). Requirements on least-squares methods for nonlinear continuous-time system identification are discusses and a solution for bilinear systems is given. The importance of an appropriate least-squares method is underlined by parameter identification for a simulated bilinear example system.