An overview is presented of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering. Both the equation-error and output-error formulations are described, although the focus is on the adaptive algorithms and properties of the output-error configuration. These parameter-update algorithms have the same generic form, and they are based on a prediction-error performance criterion. A direct-form implementation of the adaptive filters is emphasized, but alternative realizations such as the parallel and lattice forms are briefly discussed. Several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence, are addressed. >

Adaptive IIR filtering

Conventional derivative based learning rule poses stability problem when used in adaptive identification of infinite impulse response (IIR) systems. In addition the performance of these methods substantially deteriorates when reduced order adaptive models are used for such identification. In this paper the IIR system identification task is formulated as an optimization problem and a recently introduced cat swarm optimization (CSO) is used to develop a new population based learning rule for the model. Both actual and reduced order identification of few benchmarked IIR plants is carried out through simulation study. The results demonstrate superior identification performance of the new method compared to that achieved by genetic algorithm (GA) and particle swarm optimization (PSO) based identification.

IIR system identification using cat swarm optimization

The convergence and accuracy properties of the Steiglitz and McBride identification method are examined. The analysis is valid for a sufficiently large number of data. It is shown that the method can converge to the true parameter vector only when the additive output noise is white. In that case the method is proved to be locally convergent to the true parameters. The global convergence properties are also investigated. It is pointed out that the method is not always globally convergent. Some sufficient conditions guaranteeing global convergence are given. Assuming convergence takes place the estimates are shown to be asymptotically Gaussian distributed. An explicit expression is given for their asymptotic covariance matrix.

The Steiglitz-McBride identification algorithm revisited--Convergence analysis and accuracy aspects

A family of stochastic approximation variants of the Steiglitz-McBride identification scheme [1]-[3] is developed for adaptive IIR filtering. Parameter convergence is shown by computer simulation. An interesting phenomenon, global convergence regardless of local minima, is observed.

T Söderström

Papers

Brief paper: On the uniqueness of maximum likelihood identification