Title: Pseudo-linear regression identification based on generalized orthonormal transfer functions: Convergence conditions and bias distribution,
Abstract: In this paper we generalize three identification recursive algorithms
belonging to the pseudo-linear class, by introducing a predictor established on
a generalized orthonormal function basis. Contrary to the existing
identification schemes that use such functions, no constraint on the model
poles is imposed. Not only this predictor parameterization offers the
opportunity to relax the convergence conditions of the associated recursive
schemes, but it entails a modification of the bias distribution linked to the
basis poles. This result is specific to pseudo-linear regression properties,
and cannot be transposed to most of prediction error method algorithms. A
detailed bias distribution is provided, using the concept of equivalent
prediction error, which reveals strong analogies between the three proposed
schemes, corresponding to ARMAX, Output Error and a generalization of ARX
models. That leads to introduce an indicator of the basis poles location effect
on the bias distribution in the frequency domain. As shown by the simulations,
the said basis poles play the role of tuning parameters, allowing to manage the
model fit in the frequency domain, and allowing efficient identification of
fast sampled or stiff discrete-time systems.