QR based iterative unbiased equation error filtering

A QR decomposition-based algorithm is presented for unbiased, equation error adaptive IIR filtering. The algorithm is based on casting the adaptive IIR filtering in a mixed least squares-total least squares (LS-TLS) framework. This formulation is shown to be equivalent to the minimization of the mean-square equation error subject to a unit norm constraint on the denominator parameter vector. An efficient implementation of the mixed LS-TLS solution is achieved through the use of back substitution and inverse iteration. Unbiasedness of the system parameter estimates is established for the mixed LS-TLS solution in the case of uncorrelated output noise, and the algorithm is shown to converge to this solution