Structure and order estimation of multivariable stochastic processes

An easy-to-implement, numerically efficient algorithm which estimates the Kronecker invariants is presented. A procedure allowing estimation of the structure of a state-space representation for a multivariable stationary stochastic process from measured output data is presented. It is assumed that the observed vector time series is a realization of a process with rational spectrum or the output of a stable, time-invariant, linear system driven by white noise. An algorithm is proposed which selects a maximal set of linearly independent rows of the Hankel matrix built upon the estimated covariance sequence, and thus yields estimates of the Kronecker invariants. When applied to simulated examples, it systematically yielded the good structure without any ambiguity, i.e. with a surprising robustness with respect to the choice of the probability of false alarm. The numerical efficiency of the procedure is remarkable, and no exhaustive search over the set of all possible Kronecker indexes has to be performed