A matrix gradient algorithm for identification of parameterized time‐varying parameters

This paper considers the problem of estimating time‐varying parameters which can be parameterized by a series of arbitrary known basis functions. It is shown that this problem is equivalent to the observer design problem for a “matrix” dynamic system. A “matrix” gradient algorithm, which mimics the well‐known “vector” gradient algorithm, is proposed to estimate the unknown matrix. The contribution of this paper is to show that convergence of the proposed matrix algorithm is guaranteed by the persistent excitations of both the regressor and the basis functions.