An informational approach to the convergence of output error adaptive IIR filter structures

The convergence of previously described output error identification procedures is examined. The convergence analysis uses the eigeninformation of the parameter correlation matrix (really its inverse, the Fisher information matrix) for the identified structure. Convergence rates are important in digital adaptive equalizer design, for example. The eigeninformation of the parameter information matrix related the system sensitivity and numerical conditioning in a manner which provides insight into the identification process. An interesting sideline of this work is that balanced-coordinate state-space structures appear to consistently have good information properties. The relevant eigeninformation is combined in a proposed scalar convergence time constant. An important result is that identification of the usually identified direct form II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter convergence for the system being identified