On adaptive estimation and pole assignment of overparametrized systems

In this paper, a first step is taken to avoid ill-conditioning in adaptive estimation and pole assignment schemes for the case when there is a signal model overparametrization. Such a situation can occur in practice when an unknown model order is guessed too high so as to be on the "safe" side. The methods proposed in the paper are relatively simple compared to on-line order determination, being based on introducing suitable excitation in the "regression" vectors of the parameter estimation algorithms to ensure parameter convergence. For the case when the models are nonunique in that pole-zero cancellations can occur,the algorithms seek to estimate the unique model where the cancellations occur at the origin. Applying estimates of this (unique) model turns out to avoid ill-conditioning in central tendency adaptive pole assignment. For the case of one pole-zero cancellation the convergence theory of the algorithm is complete. For the more general case, algorithms are readily devised which appear to work well but for which a complete theory is not available.