An adaptive IIR filter algorithm based on observers

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 the regressor and a strict positive reality (SPR) condition on an operator arising in the algorithm. Speed of convergence experiments show that the OBRF algorithm converges more quickly than the related output error algorithm for the hyperstable adaptive recursive filter (HARF), although the OBRF algorithm converges as quickly as typical equation error schemes. The OBRF is shown to compare favorably with equation error with respect to parameter bias in the presence of output measurement noise. Thus, OBRF is a compromise between the equation error and output error approaches. In addition, algorithm parameter selection to satisfy the SPR condition for OBRF is explored and compared with the related conditions for HARF.