Subspace-based closed-loop system identification using polyspectral analysis

The problem of closed-loop system identification given noisy input-output measurements is considered. The various noise processes affecting the system are zero-mean stationary Gaussian, whereas the closed-loop system operates under an external non-Gaussian input which is not measured. First the open-loop transfer function is estimated using the integrated polyspectrum and cross-polyspectrum of the time-domain input-output measurements. Then an existing subspace-based technique for parametric system identification given noisy measurements of the underlying transfer function, is adapted to apply to the problem under consideration. We show that the resultant parametric transfer function estimator is strongly consistent. A simulation example is presented.