Blind identification of an autoregressive system using a nonlinear dynamical approach

Abstract

The problem of identifying an autoregressive (AR) system with arbitrary driven noise is considered here. Using an abstract dynamical system to represent both chaotic and stochastic processes in a unified framework, a dynamic-based complexity measure called phase space volume (PSV), which has its origins in chaos theory, can be applied to identify an AR model in chaotic as well as stochastic noise environments. It is shown that the PSV of the output signal of an inverse filter applied to identify an AR model is always larger than the PSV of the input signal of the AR model. Therefore, by minimizing the PSV of the inverse filter output, one can estimate the coefficients and the order of the AR system. A major advantage of this minimum-phase space volume (MPSV) identification technique is that it works like a universal estimator that does not require precise statistical information about the AR input signal. Because the theoretical PSV is so difficult to compute, two approximations of PSV are also considered: the e-PSV and nearest neighbor PSV. Both approximations are shown to approach the ideal PSV asymptotically. The identification performance based on these two approximations are evaluated using Monte Carlo simulations. Both approximations are found to generate relatively good results in identifying an AR system in various noise environments, including chaotic, non-Gaussian, and colored noise.