New approaches without postprocessing to FIR system identification using selected order cumulants

In this paper, we address the problem of identifying the parameters of the nonminimum-phase FIR system from the cumulants of noisy output samples. The system is driven by an unobservable, zero-mean, independent and identically distributed (i.i.d) non-Gaussian signal. The measurement noise may be white Gaussian, colored MA, ARMA Gaussian processes, or even real noises. For this problem, two novel methods are proposed. The methods are designed by using higher order cumulants with the following advantages. i) Flexibility: Method 1 employs two arbitrary adjacent order cumulants of output, whereas Method 2 uses three cumulants of output: two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one. Because of this flexibility, we can select cumulants with appropriate orders to accommodate different applications. ii) Linearity: Both the formulations in Method 1 and Method 2 are linear with respect to the unknowns, unlike the existing cumulant-based algorithms. The post-processing is thus avoided. Extensive experiments with ARMA Gaussian and three real noises show that the new algorithms, especially Algorithm 1, perform the FIR system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature.