Stochastic system identification with noisy input using cumulant statistics

The author addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise-contaminated. It is assumed that the input is non-Gaussian and the noises are Gaussian. Magnitude of the fourth cumulant of a generalized error signal, and its square root, are proposed as performance criteria for parameter estimation. An optimization algorithm is presented. Strong consistency of the proposed parameter estimators is proved under certain sufficient conditions. Both single input single output and multiple input multiple output cases are investigated. Finally, simulation results are presented to illustrate the proposed approach