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针对在辐射源个数未知的条件下嵌套阵列难以估计多个辐射源角度的问题,提出了基于最大似然估计(MLE)的嵌套阵列角度估计算法。算法在嵌套阵列模型的基础上,首先通过推导阵列截获多辐射源信号的最大似然函数及其梯度,利用最速下降法估计出空域中所有潜在辐射源的角度;然后,通过多元假设检验,利用最大似然比与门限进行比较,确定出空域中所有潜在辐射源中某一时刻发射信号的活跃辐射源角度,排除其余噪声形成的虚假辐射源角度,解决了在辐射源个数未知条件下嵌套阵列对多个辐射源角度估计问题。仿真结果表明:与传统多重信号分类(MUSIC)算法相比,该算法在辐射源数目未知、存在相干信号、低信噪比(SNR)、低快拍数条件下,均具有较好的角度估计精度,并且算法形成的虚拟阵列自由度是空间平滑MUSIC算法的2倍;多元假设检验法比传统信源数目估计算法在低信噪比条件下和处理相干信号方面具有明显优势。
Aiming at the problem that it is difficult to estimate the angle of multiple radiation sources in the nested array under the condition that the number of radiation sources is unknown, a nested array angle estimation algorithm based on Maximum Likelihood Estimation (MLE) is proposed. Based on the nested array model, firstly, the maximum likelihood function and its gradient of the multi-radiation source signal are intercepted by the derivation array and the steepest descent method is used to estimate the angles of all the potential radiation sources in the spatial domain. Then, By comparing the maximum likelihood ratio with the threshold, the angle of the active radiation source transmitting signals at a certain moment in all the potential radiation sources in the airspace is determined, and the angle of the false radiation source formed by the remaining noise is eliminated. In the case that the number of the radiation sources is unknown Nested Arrays Estimate the Angle of Multiple Radiation Sources. The simulation results show that the proposed algorithm has a better angle estimation than the traditional multiple signal classification (MUSIC) algorithm under the condition of unknown number of sources, coherent signals, low signal-to-noise ratio (SNR) Accuracy, and the degree of freedom of the virtual array formed by the algorithm is twice that of the space-smoothing MUSIC algorithm. The multivariate hypothesis test has obvious advantages over traditional signal source estimation algorithms in low signal-to-noise ratio and coherent signal processing.