MAXIMUM-LIKELIHOOD IDENTIFICATION AND REALIZATION OF STOCHASTIC-SYSTEMS

A new maximum likelihood (ML) realization/identification technique is presented. The method utilizes the recently introduced eigensystem realization algorithm (ERA) in combination with a stochastic adaptive filter/fixed-interval smoother. The resulting algorithm, called ML/ERA, is thus capable of estimating a minimal, internally balanced realization for a stochastic system whose process and/or measurement noise covariances are not necessarily known. Belonging to the ML class of algorithms, the new method is consistent and asymptotically efficient under reasonable conditions. Moreover, by using standard statistical testing techniques, the user is able to assess the quality of the resulting estimates during the iterative estimation process. A numerical investigation of the performance of the new algorithm has shown a vast improvement over the performance of the original, unaugmented ERA. In cases where the ERA could not determine the system order because the data was completely masked by noise, the ML/ERA algorithm was able to identify the order and realize an accurate mathematical model of the system. Numerical examples, demonstrating the performance of the new algorithm, are included in the paper.