Singular value decomposition based learning identification for linear time-varying systems: From recursion to iteration

System identification is a critical task in various engineering applications such as motion control, signal processing and robotics. In this article, the identification of linear time-varying (LTV) systems that perform tasks repetitively over a finite-time interval is investigated. Traditional LTV system identification typically adopts recursive algorithms in the time domain, which are incapable of tracking drastic-varying parameters and are subject to estimation lag and numerical instability. To address these issues, this article proposes the utilization of an iteration axis in addition to the time axis for estimating repetitive time-varying parameters. Specifically, the proposed approach involves an estimation algorithm for the time-varying parameters based on a recursive least squares (RLS) method along the iteration axis, as well as an update algorithm for the covariance matrix based on singular value decomposition (SVD) to enhance numerical stability. Additionally, a bias compensation method based on noise variance estimation is introduced for the sake of eliminating estimation error induced by measurement noise. Numerical comparisons with existing methods are conducted to demonstrate the effectiveness and superiority of the proposed method.