Residual Models and Stochastic Realization in State-Space System Identification

This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem