Stochastic system identification with noisy input using cumulant statistics

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. The square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion 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.<>