四元数和超复数在加性高斯噪声背景下二维谐波频率估计中的应用

针对二维谐波频率估计中的分维配对问题,首先对一般二维谐波信号模型进行变换, 构造了符合四元数结构的新的信号模型。并根据该模型利用特殊的四阶累积量切片分析了加性高斯有色噪声中二维谐波频率估计及联合Hamilton四元数和超复数在二维谐波频率估计中的应用前景。此方法避免了在复数模型的二维谐波频率估计中构造复杂的增广矩阵问题, 并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对以及有可能产生的两维频率估计精度的不平衡性这两大难题。仿真实验验证了该算法的有效性。

Two-dimensional harmonics frequency estimation in additive gaussian noise background based on quaternion and hypercomplex

The pairing steps were always needed to estimate the frequency pairs of harmonics which was described by the complex signals. The quaternion signal model was constructed through the separated signal and its Hilbert transform. The corresponding four order cumulant was defined to restrain the additive Gauss noise and the frequency was extracted using the properties of Hamilton quaternion and hypercomplex. Using this method there is no need to construct the complicated extended matrix, and the error frequency pairs and the imbalance of the two frequencies of the frequency pairs may be accounted for. The algorithm was verified by simulations.