水声信号稀疏重构的高阶累积量波达方向估计

Direction of arrival estimation based on high-order cumulant by sparse reconstruction of underwater acoustic signals

高阶累积量具有高斯噪声抑制和阵元扩展特性,将高阶累积量引入水声信号的方位估计中,提出了离格稀疏贝叶斯学习重构的高阶累积量测向算法。该方法利用高阶累积量对高斯噪声的自然盲性,计算阵列信号四阶累积量来滤除高斯噪声,使阵元在原来的结构上扩展了一倍;并构造出选择矩阵剔除了四阶累积量中的冗余项,能再一次的扩展阵元,得到的新观测模型具有更好的统计性能;最后利用空域稀疏性,推导出四阶累积量下的离格稀疏表示模型,采用贝叶斯学习解算出源信号的最大后验概率,实现了目标方位估计。数值仿真和海试实验数据表明,该方法在相邻声源方位间隔为4°的情况下分辨概率可达到95%以上,在信噪比大于-5 dB时目标方位估计的均方根误差在1°以内,可显著抑制背景噪声干扰,在多声源密集分布条件下也能准确、稳健的对水声目标方位进行估计。

The high-order cumulant has the characteristics of Gaussian noise suppression and array elements expansion,introduced it into the Direction Of Arrival(DOA)estimation of the underwater acoustic signals,an algorithm of DOA estimation based on high-order cumulant by off-grid sparse Bayesian learning reconstruction is proposed.This method uses the natural blindness of the high-order cumulant to Gaussian noise,and calculates the fourth-order cumulant of the array signal to filter out the Gaussian noise,then the array elements doubles the original structure.The selection matrix is constructed to eliminate the redundant items in the fourth-order cumulant,the array elements can be expanded again,and the new observation model obtained has better statistical performance.Then,using the sparsity of the spatial domain,the off-grid sparse representation model under the fourth-order cumulant is derived,the maximum posterior probability of the source signal is calculated by Bayesian learning,and the target azimuth estimation is realized.Numerical simulation and sea measured data show that,this method can achieve a resolution probability of more than95%when the azimuth interval between adjacent sound sources is 40,the root mean square error of the target azimuth estimation is within 1°when the signal-to-noise ratio is greater than-5 dB.This method can significantly suppress background noise interference,it can accurately and robustly estimate the azimuth of the underwater acoustic target even under the condition of densely distributed multiple sound sources.