Sliding window identification with linear-equality constraints

In this paper, we present a new algorithm of sliding window identification with linear-equality constraints. This algorithm consists in firstly deleting the oldest set of data and in secondly adding the last set of data. The method developed in this paper allows to consider at every step a set of new data by an extension of their result. The proposed algorithm is based on the recursive calculus of the pseudo-inverse matrix from the forms of Albert and Sittler. A simple and easily implementable initialization of the constrained algorithm is proposed. An improvement is obtained by removing the influence of oldest set of data and by satisfying the linear-equality constraints. It is shown that the solutions of the sliding window identification algorithm converge to the true parameter that satisfies the equality constraints. Numerical example is provided to show the effectiveness of the proposed method.