MIMO State Space Models given in Innovations Form from Input-Output Data*

input-output data can under the presence of process- and measurement noise be solved in a non-iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output-error state space model class of subspace model identification schemes. Key Words--State space; system identification; linear systems; linear algebra. Abstract--In this paper we describe two algorithms to identify a linear, time-invariant, finite dimensional state space model from input-output data. The system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise. Both noise sequences are discrete zero-mean white noise, The first algorithm gives consistent estimates only for the case where the input also is zero-mean white noise, while the same result is obtained with the second algorithm without his constraint. For the special case where the input signal is discrete zero-mean white noise, it is explicitly shown that this second algorithm is a special case of the recently developed Multivariable Output-Error State Space (MOESP) class of algorithms based on instrumental variables. The usefulness of the presented schemes is highlighted in a realistic simulation study. I