Variable Explicit Regularization in Affine Projection Algorithm: Robustness Issues and Optimal Choice

HERNÁN REY; LEONARDO REY VEGA; SARA TRESSENS; JACOB BENESTY

IEEE TRANSACTIONS ON SIGNAL PROCESSING

IEEE

Lugar: New York; Año: 2007 vol. 55 p. 2096 - 2109

1053-587X

A variable regularized affine projection algorithm (VR-APA) is introduced, without requiring the   classical step size. Its use is supported from different points of view. First, it has the property of being H$^infty$ optimal and it satisfies certain error energy bounds. Second, the time-varying  regularization parameter is obtained by maximizing the speed of convergence of the algorithm.  Although we first derive the VR-APA for a linear time invariant (LTI) system, we show that the  same expression holds if we consider a time-varying system following a first-order Markov  model. We also find expressions for the power of the steady-state error vector for the VR-APA  and the standard APA with no regularization parameter. Particularly, we obtain quite different  results with and without using the independence assumption between the a priori error vector and  the measurement noise vector. Simulation results are presented to test the performance of  the proposed algorithm and to compare it with other schemes under different situations. An  important conclusion is that the former independence assumption can lead to very inaccurate  steady-state results, especially when high values of the projection order are used.