AI 中文总结
本文针对线谱估计与检测问题，在多快照牛顿化正交匹配追踪算法（MNOMP）基础上，通过分析GLRT统计量分布开发增强型EMNOMP。它在连续频域求解GLRT，推导虚警概率和阈值，分析SNR增益，经数值模拟验证了其有效性。
AI 中文摘要
多快照牛顿化正交匹配追踪算法（MNOMP）将牛顿方法融入正交匹配追踪算法，以避免离网格问题，通过多测量向量实现高精度、高分辨率和快速线谱估计。它采用具有恒虚警率（CFAR）准则的广义似然比检验（GLRT）来确定正弦波数量。本文通过分析精确GLRT统计量的统计分布，开发了一种增强型MNOMP（EMNOMP）。与MNOMP不同，EMNOMP在连续频域上求解GLRT，而非在离散傅里叶变换（DFT）网格频率上近似GLRT。关键技术创新在于利用卡方随机场理论推导连续域GLRT的虚警概率，并通过兰伯特W函数得到封闭形式的阈值。深入推导并分析了EMNOMP相对于MNOMP的信噪比（SNR）增益。数值模拟验证了理论分析以及EMNOMP相对于MNOMP的有效性。
英文摘要
Multisnapshot Newtonized orthogonal matching pursuit (MNOMP) incorporates Newton's method into OMP to avoid the off-grid issues, achieve high accuracy, high resolution and fast line spectrum estimation with multiple measurement vectors. It employs the generalized likelihood ratio test (GLRT) with a constant false alarm rate (CFAR) criterion to determine the number of sinusoids. In this paper, we develop an enhanced MNOMP (EMNOMP) by analyzing the statistical distribution of the exact GLRT statistic. In contrast to MNOMP, which approximates the GLRT by restricting the search to discrete Fourier transform (DFT) grid frequencies, EMNOMP instead solves the GLRT over the continuous frequency domain. The key technical novelty is the derivation of the false alarm probability for this continuous-domain GLRT using chi-squared random field theory and the resulting closed-form threshold via the Lambert W function. The signal-to-noise ratio (SNR) gain of EMNOMP relative to MNOMP is derived and analyzed in depth. Numerical simulations validate the theoretical analysis and the effectiveness of EMNOMP compared to MNOMP.
