Nonparametric identification of linear dynamic errors-in-variables systems

The present work handles the nonparametric identification of linear dynamic systems within an errors-in-variables framework, where the input is arbitrary, and both the input and output disturbing noises are white with unknown variances. Using the property that the frequency response function and the system leakage term can be locally approximated very well by a low-order degree polynomial, a frequency domain estimator is developed, which gives consistent estimates for the frequency response function and the input-output noise variances. The consistency and uniqueness of the estimator are theoretically analyzed under mild conditions, and uncertainty bounds are also provided. The proposed method is finally validated on a simulated linear dynamic system.

Figures 1 and 2 show the results. 

Contour plot

Figure 1: Contour plot for the cost function evaluated on a dense grid

FRF measurement

Figure 2: Nonparametric estimate of the FRF. Blue solid line: true FRF, black solid dashed line: sample standard deviation, red+: predicted standard deviation, green thin dash-dotted line: residual error from the local polynomial method that neglects the inputs noise, black thin dotted line: residual error from the present method.

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