Closed-loop linear model validation and order estimation using cyclic-spectral analysis

Suppose that we perform closed-loop linear system identification using cyclic-spectral analysis given noisy time-domain input-output measurements. In this set-up it is assumed that various disturbances affecting the system are zero-mean stationary whereas the closed-loop system operates under an external (possibly noisy) cyclostationary input. The closed-loop system must be stable but it is allowed to be unstable in open-loop. Recently various techniques have been proposed for system identification using cyclic spectral analysis. Having obtained a model, how do we know if the fitted model is “good?” This paper is devoted to the problem of model validation using cyclic spectral analysis. We propose a simple statistical test based upon the estimated cyclic spectrum of an output error signal. Model order estimation is a by-product of the model validation procedure. Computer simulation examples are presented in support of the proposed approaches