An observer-based algorithm for adaptive IIR filters

The output error approach to adaptive IIR filtering is considered from a state observation perspective, and a new algorithm termed the observer-based regressor filtering (OBRF) algorithm is developed. The convergence requirements of the OBRF are established as a persistent excitation condition on a strict positive reality condition on an operator arising in the algorithm. The OBRF is shown to compare favorably to the equation error with respect to parameter bias in the presence of output measurement noise, and is shown to offer more flexibility in comparison to standard output error approaches with regard to the choice of algorithm filter parameters for stable algorithm behavior.