A fast ARMA transversal RLS filter algorithm

A fast pole-zero (ARMA) transversal RLS (recursive least squares) algorithm is derived, using a geometric formulation and the concept of projection onto a vector subspace to derive a recursive solution. The algorithm estimates a parameter vector that contains both numerator and denominator coefficients of an unknown system transfer function, i.e. models an ARMA (pole-zero) process. The algorithm has a transversal filter structure, but is distinguished from previous multichannel transversal algorithms, wherein each input channel is constrained to have the same order; here the pole and zero orders can be independently and arbitrarily specified. The derivation of the algorithm uses permutation matrices similar to those in the ARMA fast Kalman algorithm, but achieves a significant reduction in computations when compared to that algorithm. It is shown that when the pole and zero orders of the ARMA process are correctly specified, the algorithm generates an extremely good estimate. Furthermore, if the poles and zeros are overspecified, it is shown that a spectral match is still achieved by mutual cancellation of superfluous poles and zeros