The composite regressor algorithm for IIR adaptive systems

An adaptive IIR algorithm called the composite regressor algorithm (CRA) is developed. The algorithm is a generalization of the common equation error, a priori output error, and a posteriori output error adaptive IIR algorithms. The CRA is analyzed for convergence in a noiseless environment and for bias in a stochastic setting. It is determined that, by using a parameter called the regressor composition parameter, a tradeoff can be obtained between the automatic convergence but large bias results of the equation error algorithm and the difficult convergence condition but small bias results of the output error algorithms. In proving results for the CRA, it is shown that the a posteriori output error algorithm produces estimates with nonzero bias when the adaptive gain is small but bounded away from zero. A convergence condition for the a priori output error algorithm is derived for the first time