Subspace identification of (AR)ARMAX, Box-Jenkins, and generalized model structures

An algorithm is proposed for the subspace identification of a generalized discrete linear time invariant model structure, composing of a deterministic and a stochastic subsystem that are only partially coupled. In a first step, the impulse response of the deterministic subsystem and the correlation function of the stochastic subsystem are estimated in a statistically consistent way. The second step consists of system realization, where a specific choice of the state-space basis, that reveals the deterministic and the stochastic dynamics and their coupling, is imposed. A simulation example illustrates the identification of a system that is excited by a known input and by colored noise.