Extending HOC-based methods for identifying the diagonal parameters of quadratic systems

In this paper, methods developed for the linear case of identifying the diagonal parameters of quadratic systems are extended to nonlinear case. Firstly, nonlinear relationships between model kernels and output cumulants are presented. Secondly, the relationship linking output cumulants and the coefficients of systems presented in the linear case, is extended to the general case of nonlinear quadratic systems identification. According to this concept, two nonlinear approaches are developed, the first use the fourth-order cumulants, and the second combined the third- and fourth-order cumulants. The numerical simulation results, for various signal to noise ratio (SNR) and 200 Monte Carlo runs, show that the proposed approaches achieve better accuracy, as compared with the related algorithm in the literature. Furthermore, the second algorithm is more precise in high noise environment (smallest $$\mathrm{SNR}=0$$SNR=0 dB), but the first algorithm more efficient in the weak noise environment case (highest SNR $$\ge $$≥ 8 dB) comparing to using others methods.