A robust time-varying identification algorithm using basis functions

We extend a recently developed time invariant (TIV) model order search criterion named the optimal parameter search algorithm (OPS) for identification of time varying (TV) autoregressive (AR) and autoregressive moving average (ARMA) models. Using the TV algorithm is facilitated by the fact that expanding each TV coefficient onto a finite set of basis sequences permits TV parameters to become TIV. Taking advantage of this TIV feature of expansion parameters exploits the features of the OPS, which has been shown to provide accurate model order selection as well as extraction of only the significant model terms. Another advantage of the new algorithm is its ability to discriminate insignificant basis sequences thereby reducing the number of expansion parameters to be estimated. Due to these features, the resulting algorithm can accurately estimate TV AR or ARMA models and determine their orders. Indeed, comparison via computer simulations of AR models between the proposed method and one of the well-known iterative methods, recursive least squares, shows the greater capability of the new method to track TV parameters. Furthermore, application of the new method to experimentally obtained renal blood flow signals shows that the new method provides higher-resolution time-varying spectral capability than does the short-time Fourier transform (STFT), concomitant with fewer spurious frequency peaks than obtained with the STFT spectrogram.