Summary: This paper considers the problem of identifying continuous-time fractional systems from noisy input/output measurements. Firstly, the differentiation orders are fixed and the differential equation coefficients are estimated using an estimator based on higher-order statistics: fractional fourth-order cumulants based least squares (ffocls). Then, the commensurate order is estimated along with the differential equation coefficients. Under some assumptions on the distributional properties of additive noises and the noise-free input signals, the developed estimator gives consistent results. Hence, the noise-free input signal is assumed to be non Gaussian, whereas the additive noises are assumed to be Gaussian. The performances of the developed algorithm are assessed through a numerical example.
For the entire collection see [Zbl 1417.93035].