Continuous-time model identification from noisy input/output measurements using fourth-order cumulants

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to be non-Gaussian, whereas the noises contaminating the data are assumed to be Gaussian. The fourth-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Two estimators based on this noise-cancellation property are proposed. The performance of the proposed algorithms are assessed through a numerical simulation.