Globally convergent adaptive IIR filters based on fixed pole locations

A new class of adaptive filters, dubbed fixed pole adaptive filters (FPAF's), is introduced. These adaptive filters have infinite impulse responses, yet their adaptation exhibits provable global convergence. Good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure, thus reducing the computational burden needed to implement adaptive filters. The implementation and computational complexity of the FPAF is described, and its modeling capabilities are determined. Excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms. Some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter. The FPAF is tailored to applications by such a procedure, enabling improved performance. In examples, the FPAF is shown to achieve a smaller minimum mean square error, given an equal number of adapted parameters, in comparison with adaptive FIR filters and adaptive filters based on Laguerre and Kautz models.