Adaptive weighted least squares algorithm for volterra signal modeling. Circuits and Systems I: Fundamental Theory and Applications

Abstract—This paper presents a novel algorithm for least squares (LS) estimation of both stationary and nonstationary signals which arise from Volterra models. The algorithm concerns the recursive implementations of the method of LS which usually have a weighting factor in the cost function. This weighting factor enables nonstationary signal models to be tracked. In particular, the behavior of the weighting factor is known to influence the performance of the LS estimation. However, there are certain constraints on the weighting factor. In this paper, we have refor-mulated the LS estimation with the commonly used exponential weighting factor as a constrained optimization problem. Specif-ically, we have addressed this constrained optimization using the Lagrange programming neural networks (LPNN’s) thereby enabling the weighting factor to be adapted. The utility of our adaptive weighted least squares (AWLS) algorithm is demon-strated in the context of Volterra signal modeling in stationary and nonstationary environments. By using the Kuhn–Tucker conditions, all the LS estimated parameters may be shown to be optimal. Index Terms—Least square estimation, neural networks, non-linear signal modeling, Volterra system. I