水下宽带源方位估计的克拉美-罗界研究

推导了水下宽带源方位估计的克拉美-罗界(CRB)解析式。它揭示了宽带CRB的特点和影响方位估计性能的因素:(1)单源的宽带CRB可分为两部分:与阵列相关的部分包括阵列结构、目标方位及基阵参考点等因素;与信号相关的部分包括信号频率二阶矩及信噪比等。(2)相互独立的两个目标源,每个源的CRB与单源时相应目标源得到的结果相等。(3)两个相关源之间的夹角大于一个波束宽度时,每个源的CRB与单源结果也很接近。(4)由于信源数估计错误,单源误以为是双源,将使CRB值趋于无穷大。仿真结果验证了理论分析的正确性。因此,宽带CRB除给出宽带方位估计算法的最佳估计性能外,还能从方位估计的角度,为宽带阵列及信号波形设计等提供有益的指导。 

The CRB of direction estimation for underwater wideband sources

The Cramer-Rao Bound (CRB) expression of direction estimation for underwater wideband sources is deduced. According to the expression,the characteristics of wideband CRB and the factors relating to the performance of direction estimation are shown:the wideband CRB of single source can be divided into two items,and one depends on signal characteristics,which include the second moment in frequency and SNR etc.The other one lies on the array geometry composed of array manifold,the source direction,the position of reference point and so on.As for two mutually independent sources,the CRB of each source is equaled to the one of single source.When the included angle of two mutually dependent sources is larger than beam-width,the CRB of each source is approximate to the one of single source.Because of mistaken estimation of sources number,one source is mistaken for two sources,and then the CRB of each source close to infinity.According to the wideband CRB expression,not only the best performance of the wideband direction estimation algorithms is presented,but also useful guidance is provided from the point to improve the performance of direction estimation.