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基于降维与半谱搜索的低复杂度矢量水听器DOA估计方法

Low-Complexity DOA Estimation for Acoustic Vector Sensors Based on Dimensionality Reduction and Semi-Spectrum Search

  • 摘要: 针对矢量水听器阵列高分辨波达方向(Direction Of Arrival,DOA)估计中全空间谱峰搜索计算量过大的问题,提出一种基于降维与半谱搜索的低复杂度方位估计方法。首先,通过声压−振速联合降维处理,将复数域的高维接收数据变换为低维实值数据。降维后的等效导向矢量退化为实数形式,且其空间相位差仅依赖于目标方位的正弦值。由于正弦函数在−180°,180°内的非单调性,不同方位可产生相同的正弦值,即引入正弦模糊,使降维空间谱呈现关于0°和90°的对称性。利用该对称性,仅在0°~90°区间内进行降维谱峰搜索,再由正弦模糊关系将每个谱峰扩展为全空间域中的4个候选方位。随后,分别构造这4个候选方位的全维矢量导向矢量,利用全维噪声子空间进行谱值计算,借助子空间正交性消除正弦模糊,仅真实目标方位的导向矢量与噪声子空间满足正交性而获得最大谱值,其余伪峰均被有效剔除。蒙特卡洛仿真结果表明:该方法在保持无模糊超分辨测向性能的同时,单次方位估计的总运算时间较传统全维全空间搜索方法降低约75%。

     

    Abstract: To alleviate the heavy computational burden of full-space spectral peak search in high-resolution direction-of-arrival (DOA) estimation with acoustic vector sensors, this paper presents a low-complexity approach that couples dimensionality reduction with a semi-spectrum search strategy. First, a joint pressure-velocity transformation converts the high-dimensional complex-valued measurements into low-dimensional real-valued data. The resulting equivalent steering vector becomes real, and its spatial phase difference depends solely on the sine of the target azimuth. Because the sine function is not monotonic over −180°, 180°, distinct azimuth angles can produce the same sine value. This sine ambiguity causes the reduced-dimensional spatial spectrum to be symmetric about 0° and 90°. By exploiting this symmetry, the spectral peak search needs to be conducted only within 0°, 90°. Each detected peak is subsequently expanded via the sine ambiguity relation into four candidate azimuths that cover the full angular space. For each candidate, the corresponding full-dimensional steering vector is reconstructed, and its spectral value is evaluated against the noise subspace of the original data. Subspace orthogonality then resolves the ambiguity: only the steering vector of the true azimuth is orthogonal to the noise subspace and hence yields the maximum spectral value, whereas the three spurious candidates are strongly suppressed. Monte Carlo simulation results indicate that the proposed method preserves unambiguous super-resolution direction-finding capability while cutting the computation time per DOA estimate by approximately 75% compared with conventional full-dimensional search methods.

     

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