An optimal algorithm for the parameter identification of MIMO linear systems using bounding ellipsoids

This contribution proposes a recursive and easily implementable online algorithm for the parameters estimation of linear multi-output systems using ellipsoidal bounds on the unknown observation noises. A simple approach based on parameters bounding techniques is presented. A particular ω-parameterization of the algorithm is used, first to characterize, at each step, the set containing all possible values of the true parameters consistent with input/output data and the noises´ bounds and also to guaranty the convergence of the estimated parameters to some neighborhood of their true values. A rigorous convergence analysis is performed and a number of algorithm´s properties are highlighted such as the decrease of the normed estimation error, the shrinkage of the parameters outer-bounding set and the acceptability of the output error. Finally, the theoretical results are illustrated by a numerical simulation on a simple example.