A Variable Regularized Recursive Subspace Model Identification Algorithm With Extended Instrumental Variable and Variable Forgetting Factor

Abstract

This paper proposes a new smoothly clipped absolute deviation (SCAD) regularized recursive subspace model identification algorithm with square root(SR) extended instrumental variable (EIV) and locally optimal variable forgetting factor (LOFF). The proposed algorithm is based on a new local polynomial modeling (LPM)-based variable FF EIV projection approximation subspace tracking (PAST) and multivariate recursive least squares algorithms for estimating respectively the subspace of the extended observability matrix, and the input matrix and feedthrough matrix. The SREIV-PAST algorithm offers improved resilience to additive noise over the PAST algorithm and it is implemented using the more stable square-root form. The asymptotic mean square error of the corresponding LPM-based model is derived and minimized at each time instant to obtain the proposed LOFF for improving the convergence speed and steady state error. A recursive bi-iteration singular value decomposition (SVD) algorithm is also proposed for recursive computation of the pseudo-inverse of the state transition matrix and its eigenvalues. This facilitates online estimation of its model order using classical model selection criteria. Moreover, a new criterion based on the percentage of explained variance is also proposed with improved performance. The SCAD regularization is proposed for automatic model selection of the input and feedthrough matrices, as it is asymptotically unbiased. Efficient techniques for incorporating SCAD and estimating other required quantities are also developed. The proposed algorithms are evaluated using computer simulations under stationary and nonstationary environments and a real dataset on wing flutter data. Results show that the proposed algorithms offer improved convergence speed and steady state performance over the conventional algorithms and it also provides an online estimate of the system model order. INDEX TERMS Recursive subspace model identification (RSI), variable forgetting factor (VFF), SCAD regularization, extended instrumental variable (EIV), local polynomial modeling (LPM), model order estimation.