Derivation of the Fast Pole - Zero ( ARMA ) Recursive Least Squares Algorithm Using Geometric Projections

The Fast Pole-Zero (ARMA) Recursive Least Squares Algorithm is derived using geometric projections. The new algorithm has a reduced number of computations compared to the algorithm obtained using matrix methods. In particular two inner products are eliminated. This is particularly important in multiprocessor implementations of the algorithm. The geometric approach provides insight and useful interpretations of the various filters and residuals that form the algorithm. Such insights are absent in the matrix derivation. Simulations verifying the performance of the algorithm are presented where the poles and zeroes of an IIR filter are estimated. The algorithm finds application in echo cancellation and system identification.