Identification of non-linear stochastic systems by state dependent parameter estimation

Abstract

The paper outlines how improved estimates of time variable parameters in models of stochastic dynamic systems can be obtained using recursive filtering and fixed interval smoothing techniques, with the associated hyper-parameters optimized by maximum likelihood based on prediction error decomposition. It then shows how, by exploiting special data re-ordering and back-fitting procedures, similar recursive parameter estimation techniques can be utilized to estimate much more rapid State Dependent Parameter (SDP) variations. In this manner, it is possible to identify and estimate a widely applicable class of nonlinear stochastic systems, as illustrated by several examples that include simulated and real data from chaotic processes. Finally, the paper points out that such SDP models can form the basis for new methods of signal processing, automatic control and state estimation for nonlinear stochastic systems.