Two subspace algorithms for the identification of combined deterministic-stochastic systems

Two new subspace algorithms for identifying mixed deterministic-stochastic systems are derived. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of nonsteady-state Kalman filter banks. From these it is easy to determine the state space system matrices. The algorithms are always convergent (noninterative) and numerically stable since they only make use of QR and singular value decompositions. The two algorithms are similar, but the second one trades off accuracy for simplicity. An example involving a glass oven is considered.< >