Convergence analysis of a combined output error-equation error algorithm

An investigation of the convergence of adaptive infinite impulse response (IIR) filters is conducted by analyzing a general system that includes as special cases the well-known equation error and output error algorithms. This general system is called the composite regressor algorithm (CRA). As with the output error algorithm, the principal constraint in the CRA convergence result is a passivity condition on a time-varying operator. However, the CRA passivity constraint is shown to be more easily satisfied than the corresponding output error condition. This advantage of CRA is illustrated by simulations