广义B样条−压缩感知波达方位估计
Direction-of-arrival estimation based on generalized B-splines and compressed sensing
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摘要: 针对基于压缩感知的波达方位估计方法在低信噪比下方位估计性能下降且计算量较大的问题, 提出了一种基于广义B样条控制顶点表示的多测量向量迭代聚焦波达方位估计方法。建立了基于广义B样条控制顶点表示的阵列接收信号模型, 在此基础上建立正则化的多测量向量迭代聚焦算法, 用广义B样条控制顶点的能量谱密度表示空间方位谱; 根据完备字典中每个原子对阵列信号控制顶点的贡献度大小调整聚焦值, 使算法更关注贡献度大的原子, 波达方位估计值尽可能接近最优解。研究表明, 当广义B样条拟合的控制顶点数取信号长度所包含的信号周期的2~3倍时, 能够有效抑制背景噪声, 提高算法在低信噪比下的波达方位估计性能, 并大幅降低计算量; 根据贡献度大小调整聚焦值后, 正则化多测量向量迭代聚焦算法更易于收敛到最优解, 提高波达方位估计精度和算法效率; 信噪比为−16 dB时, 波达方位估计性能相比于基本的正则化多测量向量迭代聚焦算法, 提高41倍; 算法计算量平均降低51.2%。Abstract: To address the issues of degraded direction-of-arrival estimation performance and high computational complexity based on compressed sensing under low signal-to-noise ratio conditions, a multi-measurement vector iterative focusing direction-of-arrival estimation method based on generalized B-spline control point representation is proposed. An array signal based on generalized B-spline control points is established. Then, a regularized multi-measurement vector iterative focusing algorithm is developed. The spatial direction-of-arrival spectrum is represented by the energy spectral density of the generalized B-spline control points. The focusing value is adjusted according to the contribution of each atom in the complete dictionary to the array signal control points, thereby enabling the algorithm to focus more on atoms with greater contributions. This improvement ensures that the estimated direction-of-arrival value approaches the optimal solution as closely as possible. Research shows that when the number of control points fitted by the generalized B-spline is 2 to 3 times the number of signal periods contained in the signal length, it effectively suppresses background noise, improves the direction-of-arrival estimation performance under low signal-to-noise ratio conditions, and significantly reduces computational time. Furthermore, adjusting the focusing value based on the contribution ensures that the regularized multi-measurement vector iterative focusing algorithm converges more easily to the optimal solution, raises direction-of-arrival estimation precision and computational efficiency. At a signal-to-noise ratio of −16 dB, the performance of direction-of-arrival estimation is 41 times higher than that of the basic regularized multi-measurement vector iterative focusing algorithm, while the algorithm’s computational complexity is reduced by an average of 51.2%.