Recursive Extended Compensated Least Squares based Algorithm for Errors-in-Variables Identification

An algorithm for the recursive identification of single-input single-output linear discrete-time time-invariant errors-in-variables system models in the case of white input and coloured output noise is presented. The approach is based on a bilinear parametrisation technique which allows the model parameters to be estimated together with the auto-correlation elements of the input/output noise sequences. In order to compensate for the bias in the recursively obtained least squares estimates, the extended bias compensated least squares method is used. An alternative for the online update of the associated pseudo-inverse of the extended observation covariance matrix is investigated, namely an approach based on the matrix pseudo-inverse lemma and an approach based on the recursive extended instrumental variables technique. A Monte-Carlo simulation study demonstrates the appropriateness and the robustness against noise of the proposed scheme.