Frequency-domain weighted non-linear least-squares estimation of continuous-time, time-varying systems

A frequency-domain least-squares estimator is presented for identifying linear, continuous-time, time-varying dynamical systems. The model considered is a linear, ordinary differential equation whose coefficients vary as polynomials in time. A frequency-domain approach is used, thus allowing the user to determine easily the frequency band(s) of interest. It is shown that the bias errors because of windowing and sampling the continuous-time signals can be modelled by a polynomial function of the frequency. The regression matrices of the estimators are shown to be very efficiently computed using the fast Fourier transform algorithm and its inverse. The total least-squares, generalised total least-squares and weighted, non-linear least-squares estimators are constructed. The latter two are shown to be consistent. The estimators are illustrated on simulation and measurement data.