Large Sample Efficiency for Adaptx Subspace System Identification with Unknown Feedback

Over the last two decades, the canonical variate analysis method for subspace system identification has been widely applied. A number of these applications have demonstrated near maximum likelihood accuracy of the adaptx CVA subspace algorithm in large samples with unknown feedback. The critical step in the algorithm is the use of an ARX model estimated by conditional maximum likelihood to remove the effects of future inputs on future outputs. It is shown that the subspace estimates can be considered as restrictions on the ML ARX estimates to a subspace of the parameters obtained by projection methods. As a result, the errors between the models are orthogonal to the subspace model, and the subspace parameter estimates are asymptotically ML. A critical step in showing this orthogonality is use of the multistep form of the likelihood function. Copyright c ©2004 IFAC