Frequency domain weighted nonlinear least squares estimation of parameter-varying differential equations

This paper presents a frequency domain identification technique for estimation of Linear Parameter-Varying (LPV) differential equations. In a band-limited setting, it is shown that the time derivatives of the input and output signals can be computed exactly in the frequency domain, even for non-periodic inputs and parameter variations. The method operates in an errors-in-variables framework (noisy input and output), but the scheduling signal is assumed to be known. Under these conditions, the proposed estimator is proven to be consistent.