Some Effects of Parametrization Change in System Identification

The effect of linear parametrization changes on least mean square adaptation of finite impulse response models is examined. Adaptation in different parametrizations is compared given a fixed value for the steady state mean square error. It is noted that orthogonal transformations of the parameters change no aspects of performance. Orthogonalization of convergence modes, followed by normalization of convergence rates, attains the maximal minimum convergence rate, but changes the frequency distribution of the asymptotic frequency response variance. Relations between change of input correlation and change of parametrization are described.