Stochastic Theory of Continuous-Time State-Space Identification

This paper presents theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. 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.