Extension of the equation error scheme for alternative realizations of adaptive IIR filters

The extension of the equation error (EE) adaptive algorithm to others than the direct-form realization is investigated. Implementing the EE algorithm with nondirect-form realizations is justified by the existence of EE-based adaptive algorithms that require continuous pole monitoring to avoid instability of the adaptive filter during the convergence process. Due to their respective importance, focus is given to the parallel, cascade, and lattice realizations. It is concluded that while the parallel and cascade structures present serious problems for a straightforward extension, the lattice realization is shown to be extremely suitable for efficient implementation of the EE algorithm.