零均值独立复杂噪声背景下二维谐波估计的时间平均矩方法  

Two Dimensional Cubic Nonlinear Coupling Estimation in Zero Mean Independent Multiplicative Noises

作　　者：张政伟[1] 樊养余[1] 赵炯[1] 李龙[1] 

机构地区：[1]西北工业大学电子信息学院,西安710072

出　　处：《信号处理》2009年第5期702-707,共6页Journal of Signal Processing

基　　金：航空科学基金(批准号:04F53035);陕西省自然科学基金(批准号:2003F40)

摘　　要：对于零均值独立乘性噪声背景下二维谐波的三次非线性耦合估计问题,由于缺乏理论支持及有效的计算方法,至今尚无有效的解决办法。本文首先分析了不同的噪声模型对谐波耦合分析所产生的影响,通过对原始采样数据进行平方预处理,改变了采样信号的信噪模型,利用新模型下噪声的统计特性及噪声间的相关特性,通过定义一种特殊四阶时间平均矩,首次解决了零均值独立噪声背景下谐波频率的二维三次非线性耦合问题。数学推导了该特殊四阶时间平均矩的矩多谱,理论证明了相应估计子渐进无偏性和一致性。理论分析和试验结果表明,该方法用于二维谐波的三次耦合分析时,不再需要对噪声的统计特性及噪声间的相关特性作任何限制。The cubic nonlinear coupling problem of two dimensional harmonics under zero-mean independent muhiplicative noises is an open problem for some theoretical and computational reasons. This paper studies the effects caused by different noises on the eou- piing problem firstly, and then subtly changes the signal-noise model by squaring the sample data. Based on the correlative and the statis- tic characteristics of this changed model, a special fourth-order time average moment is defined. A method is proposed for two dimension- al cubic coupling problem applying the pre-defined special fourth-order moment. The poly-spectral of the special fourth-order time aver- age moment is deduced mathematically, and the theoretical proof is given that the estimator is asymptotically unbiased and consistent. Further, both the theoretical and experimental results show that it is also successful for all the other two dimensional cubic coupling prob- lem no matter what the correlative and the statistic characteristics of noises are like. Namely, the method lowers the requirement of the noises to the most.

关 键 词：零均值独立 特殊四阶时间平均矩 二维谐波三次耦合 乘性噪声 

分 类 号：TN911.23[电子电信—通信与信息系统]