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This paper proposes a methodology to easily extract some valuable nonparametric information on linear slowly time-varying systems, which have been excited by multisines. More specifically, it is first explained how time-varying systems behave when excited by multisines and how a rough nonparametric idea of the speed of variation of the instantaneous frequency response function is estimated. Second, a nonparametric model of the disturbing colored noise on the measured input and output signals is estimated. The methodology circumvents the need for repeated experiments, which are, for time-varying systems, usually difficult to perform. The estimation of the disturbing noise is mandatory when identifying dynamic systems within an errors-in-variables framework. The estimated noise model is intended for system identification performed in the frequency domain, where a nonparametric noise model is easily implemented. The noise model is estimated independently of the parameters of the time-varying system under consideration. The estimate of the speed of variation of the instantaneous frequency response function gives some insight into the measured system. It might actually provide an idea of which poles or zeros are actually moving and which are not.

The identification of SISO linear dynamic systems in the presence of output noise disturbances is considered. A 'nonparametric' Box-Jenkins approach is studied: the parametric noise model is replaced by a nonparametric model that is obtained in a preprocessing step, and this without any user interaction. The major advantage for the user is that i) one method can be used to replace the classical ARX, ARMAX, OE, and Box-Jenkins models; ii) no noise model order should be selected. This makes the identification much easier to use for a wider public; iii) a bias on the plant model does not create a bias on the noise model; iv) Improved convergence for the numerical optimization procedure. The disadvantage of the proposed nonparametric approach is a small loss in efficiency with respect to the optimal parametric choice. These results are illustrated on a series of well selected problems.

This paper presents a method to estimate a nonparametric noise model for multiple input, multiple output systems excited by arbitrary inputs. It is an extension of the method described in [1] for single input, single output systems. It is shown that the proposed procedure is more robust than the classical spectral analysis based on correlation techniques. The theory is supported by simulations and a real measurement example.

Identification of parametric transfer function models from noisy input/output observations is an important task in many engineering applications. Aside from the parametric model, the estimation algorithm used should also provide accurate confidence bounds. In addition it is important to know whether the proposed estimation algorithm has the lowest possible uncertainty within the class of consistent estimators. This paper handles these issues for the frequency domain Gaussian maximum likelihood estimator of rational transfer function models within an errors-in-variables framework.