Enhancing Accuracy and Numerical Stability for Repetitive Time-Varying System Identification: An Iterative Learning Approach

Abstract

Time-varying system identification is an appealing but challenging research area. Existing identification algorithms are usually subject to either low estimation accuracy or bad numerical stability. These deficiencies motivate the development of an iterative learning identification algorithm in this paper. Three distinguished features of the proposed method result in the achievement of high estimation accuracy and high numerical stability: i) recursion along the iteration axis, ii) bias compensation, and iii) singular value decomposition (SVD). Firstly, an extra iteration axis associated with the original time axis is introduced in the parameter estimation process. A norm-optimal identification approach with the balance between convergence speed and noise robustness is then proposed along the iteration axis, followed by further analysis on the accuracy and the numerical stability. Secondly, in order to eliminate the estimation bias in the presence of noise and thus to improve the accuracy, a bias compensation algorithm along the iteration axis is proposed. Thirdly, a SVD-based update algorithm for the covariance matrix is developed to avoid the possible numerical instability during iterations. Numerical examples are finally provided to validate the algorithm and confirm its effectiveness.