Two dimensional cubic nonlinear coupling estimation in zero mean independent multiplicative noise

According to the correlation and the statistic characteristic of the noise incorporated with the harmonic signal, a new special fourth order time average moment was defined in this paper. The statistic characteristic of the multiplicative and additive noise included in the sampled data was changed by a special signal preprocessing method, i.e., squaring the sampled data, and subsequently two dimensional cubic nonlinear coupling problem in zero mean independent noise was studied by using this special fourth order time average moment spectrum. The theory analysis and the proof for the method were developed in details. Because the method can also be applied to the situation where the mean of the noise is nonzero, no matter how the correlation characteristic between the noises is correlative or independent, the method proposed in this paper doesn't need any constrain on the mean, distribution, and the color of the noise. The simulation result illustrated the validity and correctness of the proposed method. The computational efficiency of the method was analyzed when the method was applied to the situations where the mean of the noise was nonzero or the correlation characteristic between the noise was correlative, and some improvement measures were put forward.