Identification algorithms based on H∞ state-space filtering techinques

An identification algorithm is proposed based on an extension of the results of H_∞ filtering and Kalman filtering theory. The objective is to minimize the H_∞ norm of the map from exogenous inputs (noise) to the estimation error of the parameters of an autoregressive moving average with external variable (ARMAX) model. The technique can provide an improved fit of a low-order estimated model to be obtained, relative to the usual least squares based algorithms. The function γ which arises in H_∞ filtering problems can be found by iteration, starting with a high initial value and then computing γ online until it converges to the optimal value. An online check on the a posteriori covariance matrix is necessary to make sure the solution remains valid. The proposed algorithm is straightforward to implement and has the potential to improve the robustness of self-tuning filtering and control algorithms