A New Variable Forgetting Factor-Based Bias-Compensation Algorithm for Recursive Identification of Time-Varying Multi-Input Single-Output Systems With Measurement Noise

Abstract

This article proposes a new variable forgetting factor (VFF) bias-compensated recursive least-squares (BCRLS) algorithm for the recursive identification of complex time-varying multi-input single-output (MISO) systems with measurement noise. It extends a previously developed real-valued BCRLS algorithm to complex signals and introduces new self-calibrated VFF and noise variance estimation schemes for tracking time-varying systems. The proposed VFF scheme offers faster tracking speed, especially for sudden system changes, while achieving a low steady-state (SS) mean square error (MSE) in a stationary environment. Moreover, the mean and mean square deviation of the complex RLS algorithm under zero-mean white Gaussian output additive noise are performed, from which the variance of the additive noise can be estimated. To mitigate the effect of finite-sample number, a self-calibration scheme is proposed to refine the FF at the SS and hence MSE. Simulations show that the proposed self-calibrated VFF-BCRLS algorithm offers improved tracking speed in sudden system changes and offers smaller MSE over the conventional BCRLS algorithm. Applications to real-world data for pH value prediction of a pH neutralization process and temperature prediction of a glass furnace also demonstrate the effectiveness of the proposed algorithm. The good performance and efficient implementation make it an attractive alternative to other conventional methods for system identification in control and optimization processes and other possible applications.