Based On Matrix Factorization Delta Operator Filter

The matrix decomposition such as singular value decomposition (SVD) and UD factorization is of great significance in the filed of signal processing and state estimation. Matrix decomposition approach can not only improve the numerical stability and the accuracy of computations, but also can obtain the estimations of model order and parameters. In addition, delta operator method can avoid the numerical instability problems caused by the conventional shift operator when fast sampling, and also can improve the performance of adaptive algorithms.The thesis is supported in part by the Natural Science Foundation of Henan Province entitled "Robust design for adaptive inverse control systems using delta operator" and Foundation for University Key Teacher by Henan Province entitled "Delta operator approach to adaptive inverse control design and performance analysis". The developments of the matrix decomposition and the adaptive filter are firstly reviewed. Then problems of the Delta operator formulated adaptive filtering by matrix decomposition are studied. The main results are as follows:(1) The filtering problem of the SVD decomposition based LMS algorithm using delta operator (Delta-SVD-LMS) is studied. The recursive Delta-SVD-LMS algorithm is developed, and both the convergence and the traceability of this algorithm are analyzed. Simulation results show Delta-SVD-LMS algorithm has the advantages compared with the other LMS algorithm.(2) The filtering problem of the UD factorization formulated RLS algorithm with the delta operator (Delta-UD-RLS) is considered. First, the recursive formulae of the Delta-RLS algorithm are obtained. Then the UD factorization is applied to the Delta-RLS algorithm. The analysis of convergence property and the traceability of the algorithm are also given. Simulations indicate Delta-UD-RLS algorithm has the better performance.