A cumulant based algorithm for the identification of input output quadratic systems

A parameter estimation algorithm is developed for the identification of an input output quadratic model. The excitation is a zero mean white Gaussian input and the output is corrupted by additive measurement noise. Input output crosscumulants up to fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of succesive linear systems of equations that are solved iteratively. Simulation results are provided for different SNR's illustrating the performance of the algorithm and confirming the theoretical set up.