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 pole-zero fast Kalman algorithm. In particular, four vector inner products and scalar-times-vector operations 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. Simulations verifying the performance of the algorithm are presented where the poles and zeroes of an IIR filter are estimated.