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. © 2003 Biomedical Engineering Society.
 PAC2003: 8710+e, 8719Uv, 8780Tq

http://www.bme.sunysb.edu/people/faculty/docs/kchon/4zou.pdf

A robust time-varying identification algorithm using basis functions.

The Gauss-Newton variable forgetting factor recursive least squares (GN-VFF-RLS) algorithm is presented, which can be used to improve the tracking capability in time varying parameter estimation. Compared to the existing algorithm, the exponentially windowed recursive least squares (EW-RLS) algorithm with optimal forgetting factor, the presented method leads to a significant improvement in fast time varying parameter estimation. The effects of signal to noise ratio and nonstationarity have been tested using computer simulations with the given parameter model. An assessment of the performance of each algorithm is presented in terms of the mean-square-deviation (MSD).

Gauss Newton variable forgetting factor recursive least squares for time varying parameter tracking

A time varying coefficient vector AR modeling of nonstationary covariance time series

We introduce a new method to estimate reliable time-varying (TV) transfer functions (TFs) and TV impulse response functions. The method is based on TV autoregressive moving average models in which the TV parameters are accurately obtained using the optimal parameter search method which we have previously developed. The new method is more accurate than the recursive least-squares (RLS), and remains robust even in the case of significant noise contamination. Furthermore, the new method is able to track dynamics that change abruptly, which is certainly a deficiency of the RLS. Application of the new method to renal blood pressure and flow revealed that hypertensive rats undergo more complex and TV autoregulation in maintaining stable blood flow than do normotensive rats. This observation has not been previously revealed using time-invariant TF analyses. The newly developed approach may promote the broader use of TV system identification in studies of physiological systems and makes linear and nonlinear TV modeling possible in certain cases previously thought intractable.

Robust algorithm for estimation of time-varying transfer functions

A new method for on-line spectral estimation of nonstationary time series via autoregressive (AR) model construction is proposed. The method consists of on-line parameter estimation based on the recursive least squares ladder estimation algorithm with a forgetting factor and on-line order determination based on AIC with some modifications. The effectiveness of the proposed method is demonstrated by computer simulation study and applying to the actual data of electroencephalogram (EEG). >

On-line spectral estimation of nonstationary time series based on AR model parameter estimation and order selection with a forgetting factor

A method of estimating time-varying spectra of nonstationary signals using recursive least squares (RLS) with variable forgetting factors (VFFs) is described. The VFF is adapted to a nonstationary signal by an extended prediction error criterion which accounts for the nonstationarity of the signal. This method has better adaptability than the conventional algorithm with high fixed forgetting factor (FFF) in the nonstationary situation, and has lower variance than the conventional one with low FFF in the stationary situation. The extra computation time for the forgetting adaptation is almost negligible. >

Y.S. Cho

Papers

Time-varying spectral estimation using AR models with variable forgetting factors