中文摘要：

给出了海洋波导中位置未知简谐声源的广义似然比检测器及其理论检测性能．通过对检测器中模态相关矩阵进行特征值分解，将该检测器分解为与各阶特征值相对应的谱成分．推导了各阶谱成分的统计特性并以此获得了谱成分对输入信号的空间处理增益，该增益与谱成分对应的特征值成正比．当模态信息采样不完备时，模态相关矩阵存在部分接近于0的小特征值，相应的谱成分对输入信号的空间处理增益与其余谱成分相比非常小．通过舍去这部分谱成分，提出了有效谱检测器．该检测器在保持其输出中目标信号成分与广义似然比检测器相同的基础上，有效减少了其中的噪声成分，因此，具有比广义似然比检测器更好的检测性能．在典型的浅海环境下进行仿真实验，仿真结果验证了理论分析、推导以及有效谱检测器的有效性，并且表明非完备采样程度越严重，有效谱检测器相对于广义似然比检测器的检测性能提高越显著．此外，有效谱检测器具有比广义似然比检测器更好的数值计算稳健性．

英文摘要：

The generalized likelihood ratio test （GLRT） detector and its theoretical detection performance for an underwater narrowband source with an unknown position are both given in this paper. Via the eigenvlue decomposition of the mode correlation matrix （MCM）, the GLRT detector is decomposed into different spectrum components corresponding to the eigenvalues of the MCM. Based on the derived statistical property of each component, the spatial processing gain of each spectrum component with respect to the input signal is obtained, which is proportional to the corresponding eigenvalue. As there are several eigenvalues of the MCM approaching to zero when the modal information is incompletely sampled, the components corresponding to these small eigenvalues contribute much less spatial processing gain to the input signal than other components. By discarding the components corresponding to these small eigenvalues, the effective spectrum detector （ESD） is proposed, of which the target signal component in the output is approximately identical to that of the GLRT detector, and the noise in the ESD output is much less. Therefore, a much more robust detection performance is obtained by ESD than by the GLRT detector. Numerical simulations in a typical shallow water environment demonstrate that 1） the theoretical analyses, derivations and the effectiveness of the proposed ESD are verified; 2） the more incomplete the modal information sampling is, the more significant performance improvement of ESD over the GLRT detector can be acquired; 3） the numerical stability of the ESD is better than that of the GLRT detector.