A novel subspace identification approach with enforced causal models

Subspace identi cation methods (SIMs) for estimating state-space models have been proven to be very useful and numerically e cient. They exist in several variants, but have one feature in common: as a rst step, a collection of high-order ARX models are estimated from vectorized inputoutput data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coe cients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A,B,C,D) and the Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants, such as poles.