圆与非圆信号混合入射下的低复杂度分布式信源DOA估计算法
A Low-Complexity DOA Estimation Algorithm for Distributed Sources Under the Coexistence of Circular and Non-circular Sources
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摘要: 传统的波达方向(Direction-of-Arrival,DOA)估计算法通常基于理想的点信源模型进行理论推导和算法设计,而随着社会的发展,越来越多的测向定位需求以密集的城市环境为背景,比如针对城区低空无人机的定位工作,一般的点信源模型已经无法准确描述这样的环境,这种情况应当采用分布式信源的建模方法。同时,许多传统的算法仅考虑空间中所有信源发射相同类型信号的情况,比如仅针对圆信源或非圆信源设计的算法,这些算法不能有效处理两类信源并存的情况。为了解决上述问题,本文提出了一种在圆和非圆信号混合背景下的低复杂度相干分布式(Coherently Distributed, CD)信源DOA估计方法。首先,本文采用相干分布式信源进行建模,推导了圆信号和严格非圆信号同时入射到均匀线阵的信号模型,充分利用了空间中非圆信号的非圆相位信息构造增广输出信号模型;接着,基于广义旋转不变性降秩的原理,我们推导并设计了在混合源场景下的代价函数;最后通过一维谱峰搜索,完成信源的中心DOA估计。本文通过数值仿真分析全面对比所提算法以及其他算法之间的性能,表明了所提算法在复杂度和参数估计精度之间达到了更好的平衡,充分考虑到非圆相位的所包含的信息,同时有着更加广泛的适用性,有着良好的应用前景。Abstract: Traditionally, researchers use the ideal point source model when designing Direction-of-Arrival (DOA) estimation algorithms. With the development of modern society, the demand for source localization in dense urban areas is growing. Applications such as the direction-finding of low-altitude unmanned aerial vehicles (UAVs) are becoming increasingly important. Signals from the source are reflected and scattered by surrounding objects before they reach the sensor array. The traditional point source model is no longer capable of accurately describing such a complex environment. Methods based on the ideal mathematical model may suffer from severe performance deterioration and need to be reconsidered under the distributed source model. Moreover, many studies focus on either circular or non-circular signals independently, without considering the coexistence of both signal types in real-world scenarios. Given the limitations of current approaches, we propose a low-complexity DOA estimation algorithm to address the challenges associated with estimating the DOAs of sources in complex urban areas with a mixture of circular and non-circular signals. First, we choose to employ the coherently distributed source model in this study. We derive the received signal model for a mixture of both circular and strictly non-circular signals. Then, we use the observed signal vector and its complex conjugate counterpart to construct an extended signal vector, leveraging the additional information provided by the non-circular phases. This approach enhances the accuracy and robustness of DOA estimation in the presence of both circular and non-circular signals. Next, we analyze the Generalized Estimation of Signal Parameters via Rotational Invariance Techniques (GESPRIT) algorithm and derive the cost function for our proposed algorithm. Through a one-dimensional peak searching procedure, we obtain the nominal DOAs of the sources. Several numerical simulations are conducted to illustrate the proposed algorithm in detail. Comparisons with several competing methods demonstrate the reliability and advantages of our approach. Results show that MIX-GESPRIT not only achieves an optimal balance between computational cost and direction-finding accuracy but also exhibits strong robustness and practicality.