Regularized Local Basis Function Approach to Identification of Nonstationary Processes

The problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis, the paper addresses and solves all major problems associated with implementation of the new class of estimators, such as optimization of the regularization matrix, adaptive selection of the number of basis functions and the width of the local analysis interval, and reduction of complexity of the computational algorithms.