A transfer function approach to MIMO system identification

The introduction of the state-space (SS) approach based on instrumental variables and subspace approximations has created a large interest in the identification of multi-input multi-output (MIMO) linear systems. The SS approach has gained popularity since it only requires the determination of one structural parameter. It has also empirically been found to provide models with good accuracy in many cases. However, SS has some drawbacks: there is no well established method tied to this approach for determining the structural parameter and, perhaps more importantly, the SS parameter estimates depend on the data in a rather complicated way, which renders almost futile any attempt to analyze and optimize the performance of the estimator. We propose an alternative to the SS approach based on a transfer function (TF) model and instrumental variables (IVs). The simplest canonical parameterization of the TF is used; the denominator consists of a scalar polynomial times the identity matrix. The analysis and performance optimization of the TF approach is shown to be relatively straightforward. A statistical test for estimating the single structural parameter needed is also presented. Simulations show that TF can provide more accurate models than SS at a lower computational cost.