A NEURAL APPROACH TO THE UNDERDETERMINED-ORDER RECURSIVE LEAST-SQUARES ADAPTIVE FILTERING

The incorporation of the neural architectures in adaptive filtering ap plications has been addressed in detail. In particular, the Underdeter mined-Order Recursive Least-Squares (URLS) algorithm, which lies betwe en the well-known Normalized Least Mean Square and Recursive Least Squ ares algorithms, is reformulated via a neural architecture. The respon se of the neural network is seen to be identical to that of the algori thmic approach. Together with the advantage of simple circuit realizat ion, this neural network avoids the drawbacks of digital computation s uch as error propagation and matrix inversion, which is ill-conditione d in most cases. It is numerically attractive because the quadratic op timization problem performs an implicit matrix inversion. Also, the ne ural network offers the flexibility of easy alteration of the predicti on order of the URLS algorithm which may be crucial in some applicatio ns. It is rather difficult to achieve in the digital implementation, a s one would have to use Levinson recursions. The neural network can ea sily be integrated into a digital system through appropriate digital-t o-analog and analog-to-digital converters. (C) 1997 Elsevier Science L td.