A Robust Time-Varying Identification Algorithm Using Basis Functions

Abstract

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.

Intracranial pressure waves: characterization of a pulsation absorber with notch filter properties using systems analysis

“…The new computational techniques make the notch easier to see and study, R. Zou et al allowing future application to animal models of pathophysiological conditions and human clinical data. The effectiveness of algorithms of TVTF involved in the study has been confirmed by both simulation signals and real signals 32,48,50 (see Appendix F). …”

“…32,[46][47][48][49][50] The technical advantage of TVTF derived from ARMA modeling introduced in the study is 3-fold: 1) a parametric method to derive the transfer function from ARMA, which allows characterization of system dynamics with only a few parameters; 2) the OPS algorithm ensures an accurate estimation of transfer function, with estimated ICPs following the measured data well and prediction error consistently low (Fig. 10); and 3) with the sliding window approach a 3D TVTF (consisting of time, frequency, and gain [or phase]) can be used to visualize the dynamic response of the intracranial system to changes in mean ICP.…”

Respiratory Rate Extraction Via an Autoregressive Model Using the Optimal Parameter Search Criterion

“…6,14 Adopting the robust OPS method, the aforementioned limitations of the previously used AR method for extraction of respiratory rate can be mitigated. Thus, the goal of this work was to investigate the efficiency gained by using the OPS instead of the AIC for extraction of respiratory rates from pulse oximeter recordings of 23 human subjects.…”

A new SSI algorithm for LPTV systems: Application to a hinged-bladed helicopter

“…Recursive algorithms such as recursive least squares (RLS), recursive instrumental variable and recursive predictive error [3,4] have also been widely investigated. For the class of rapidly time-varying systems, the functional expansion techniques have been suggested in manifold works [5][6][7][8].…”

“…Recursive algorithms such as recursive least squares (RLS), recursive instrumental variable and recursive predictive error [3,4] have also been widely investigated. For the class of rapidly time-varying systems, the functional expansion techniques have been suggested in manifold works [5][6][7][8].In [9][10][11][12], efforts have been undertaken to extend the subspace identification approach [13] to the LTV case by introducing the idea of repeated experiments. As pointed in [14], most subspace-based results developed thus far, even if significant, give state space realizations that are topologically equivalent from an input and output standpoint, but are not n Corresponding author.…”