On the accuracy of least squares algorithms for estimating zeros

We investigate the accuracy of least-squares-based algorithms for estimating system zeros in the presence of known or unknown order and known or unknown relative degree. Specifically, we use least-squares to estimate the parameters of ARX and μ-Markov models from which zero estimates are calculated directly using the numerator polynomial as well as indirectly using the truncated Laurent expansion or the eigensystem realization algorithm (ERA). To employ the truncated Laurent expansion or ERA, we consider the Markov parameters estimated from the μ-Markov model. Lastly, we investigate the spurious zeros of the μ-Markov model and truncated Laurent expansion to determine to what extent these zeros behave in a predictable manner.