Parameter identification with derivative shift operator parametrization (Q1301457)

Using a combined \(d\)-operator which generalizes the shift operator \((q)\) and the delta operator \((\delta)\) in the form \(d^\ell_k= q^\ell\delta^k\) (where \(\ell\) and \(k\) are the number of \(q\) and \(\delta\) operations, respectively) one proposes a new parametrization of linear systems. One shows that it improves the parameter identification process. The condition number of the information matrix is significantly lower than the one using the \(q\)- or the \(\delta\)-operator. Accurate and fast converging parameter identification can be achieved at fast sampling rates, especially for systems with relatively wide bandwidth. Three simulation examples illustrate the proposed approach.