Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations

A numerically stable and general algorithm for identification and realization of a complete dynamic linear state space model, including the system order, for combined deterministic and stochastic systems from time series is presented. A special property of this algorithm is that the innovations covariance matrix and the Markov parameters for the stochastic sub-system are determined directly from a projection of known data matrices, without e.g. recursions of non-linear matrix Riccatti equations. A realization of the Kalman filter gain matrix is determined from the estimated extended observability matrix and the Markov parameters. Monte Carlo simulations are used to analyze the statistical properties of the algorithm as well as comparing with existing algorithms.