Nonlinear Autoregressive Modeling and Estimation in the Presence of Noise

Abstract

Nonlinear autoregressive processes constitute a potentially important class of nonlinear signal models for a wide range of signal processing applications involving both natural and man-made phenomena. A state-space characterization is used to develop algorithms for modeling and estimating signals as nonlinear autoregressive processes from noise-corrupted measurements. Special attention is given to chaotic processes, which form an important subclass of nonlinear autoregressive processes. The modeling algorithms are based on the method of total least-squares, and exploit the local structure of the signals in state space. The recursive estimation algorithms for addressing problems of filtering, prediction, and smoothing, are based on extended Kalman estimators, and jointly exploit aspects of both the temporal and state-space structure in these processes. The resulting algorithms are practical both in terms of computation and storage requirements, and their effectiveness is verified through simulations involving noisy nonlinear autoregressive data.