A subspace method for frequency selective identification of stochastic systems

Abstract

A parametric method for the estimation of vector valued discrete-time stochastic systems or equivalently the spectrum of a stochastic process is presented. The key feature is that the method can be used to frequency selectively fit the model to the data. This means that parts of the spectrum can be modeled with a lower model order than otherwise would be necessary if the entire spectrum would be modeled. The method is based on a frequency domain subspace method which delivers a state-space model. It explicitly takes into account that the frequency domain data is derived from finite data and hence suppresses the leakage effects. Furthermore the method employs convex optimization to guarantee that the estimated parametric model represents a non-negative spectrum.