低仰角目标高精度波束空间DOA估计方法

刘旗; 郭瑞; 王佳佳; 徐世友; 陈曾平

doi:10.12000/JR25173

低仰角目标高精度波束空间DOA估计方法

DOI: 10.12000/JR25173 CSTR: 32380.14.JR25173

中山大学电子与通信工程学院深圳 518107

基金项目: 国家自然科学基金(U2133216)，深圳市科技计划资助(KQTD20190929172704911)，广东省科技技术项目(2019ZT08X751)，广东省科技厅先进智能感知技术重点实验室科技规划项目(2023B1212060024)

详细信息

作者简介:
刘　旗，博士生，主要研究方向为阵列信号处理

郭　瑞，博士，副教授，主要研究方向为数字阵列雷达技术、阵列信号处理技术等

王佳佳，硕士生，主要研究方向为阵列信号处理

徐世友，博士，教授，主要研究方向为宽带雷达成像、自动目标识别、信息融合、多功能数字阵列雷达等

陈曾平，博士，教授，主要研究方向为空间态势感知、软件化雷达探测、宽带成像识别等

通讯作者:
郭瑞 guor29@mail.sysu.edu.cn

责任主编：陈小龙 Corresponding Editor: CHEN Xiaolong

中图分类号: TN958
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出版历程
- 收稿日期: 2025-09-10
- 修回日期: 2025-12-13
- 网络出版日期: 2025-12-31

A High-accuracy Beamspace DOA Estimation Method for Low-elevation Angle Targets

School of Electronics and Communication Engineering, Sun Yat-sen University, Shenzhen 518107, China

Funds: The National Natural Science Foundation of China (U2133216), Shenzhen Science and Technology Program (KQTD20190929172704911), Guangdong Provincial Science and Technology Program (2019ZT08X751), Science and Technology Planning Project of Key Laboratory of Advanced Intellisense Technology, Guangdong Science and Technology Department (2023B1212060024)

More Information

Corresponding author: GUO Rui, guor29@mail.sysu.edu.cn

摘要

摘要: 低仰角目标波达方向(DOA)估计是米波雷达与全息凝视雷达中的关键问题，其估计误差直接影响目标的测高精度。传统波束空间方法通过构建波束形成器，将高维阵元空间数据映射至低维波束空间以降低计算复杂度。然而，该类方法的有损映射会造成部分目标信息丢失，使目标仰角估计精度显著低于阵元空间方法。为解决这一问题，该文提出了一种低仰角目标高精度波束空间DOA估计方法。首先，推导了阵元空间与波束空间中DOA估计的克拉美罗界(CRB)，并分析了两者相等所需满足的充分条件。由于该条件在实际应用中难以严格满足，该文进一步提出一种基于近似条件的波束形成器设计方法。该方法在降低数据维度的同时，最大限度保留目标的有效信息。最后，基于最大似然准则实现了目标仰角的精确估计。仿真与实测结果表明，所提方法在显著降低处理数据维度的同时，能够在低仰角观测区域内保持与阵元空间方法相近的估计精度，并优于现有波束空间算法。
- 低仰角目标 /
- 波达方向(DOA)估计 /
- 波束空间处理 /
- 克拉美罗界(CRB) /
- 多径效应 /
- 最大似然
Abstract: Direction of Arrival (DOA) estimation for low-elevation angle targets is a critical challenge in meter-wave and holographic staring radar systems, as its accuracy directly affects target height measurement performance. Traditional beamspace methods reduce computational complexity by projecting high-dimensional element-space data onto a low-dimensional beamspace using a beamformer. However, this lossy mapping leads to partial information loss, resulting in degraded elevation-angle estimation accuracy compared to that of element-space methods. To address this issue, this study proposes a high-accuracy beamspace DOA estimation method for low-elevation angle targets. First, the Cramér-Rao Bound (CRB) for both element-space and beamspace DOA estimation is derived, and the conditions under which these bounds are equal are analyzed. Since these conditions are difficult to satisfy in practical scenarios, an approximate-condition-based beamformer design strategy is developed to reduce data dimensionality while preserving effective target information. Finally, precise elevation-angle estimation is achieved using the maximum likelihood criterion. Simulation and experimental results show that the proposed method significantly reduces data dimensionality while maintaining estimation accuracy comparable to that of element-space methods at low-elevation angles, clearly outperforming existing beamspace algorithms.
- Low-elevation angle target /
- Direction of Arrival (DOA) estimation /
- Beamspace processing /
- Cramér-Rao Bound (CRB) /
- Multipath effect /
- Maximum likelihood

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图 1 低仰角目标多径传播几何模型

Figure 1. Geometric model of low-elevation target multipath propagation

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图 2 不同算法波束形成器增益随测试角度的变化

Figure 2. Beamformer gain versus test angle for different algorithms

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图 3 目标仰角估计的RMSE随目标仰角的变化

Figure 3. RMSE of target elevation angle estimation versus target elevation angle

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图 4 目标仰角估计的RMSE随信噪比的变化

Figure 4. RMSE of target elevation angle estimation versus SNR

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图 5 不同算法的目标仰角估计CRB随信噪比的变化

Figure 5. CRB of target elevation angle estimation versus SNR for different algorithms

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图 6 目标仰角估计的RMSE随快拍数的变化

Figure 6. RMSE of target elevation angle estimation versus number of snapshots

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图 7 不同$ \gamma $下目标仰角估计的RMSE随目标仰角的变化

Figure 7. RMSE of target elevation angle estimation versus target elevation angle for different $ \gamma $

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图 8 不同$ \gamma $下目标仰角估计的CRB随目标仰角的变化

Figure 8. CRB of target elevation angle estimation versus target elevation angle for different $ \gamma $

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图 9 目标仰角估计的RMSE随$ \left| \rho \right| $的变化

Figure 9. RMSE of target elevation angle estimation versus $ \left| \rho \right| $

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图 10 目标仰角估计的RMSE随阵元数的变化

Figure 10. RMSE of target elevation angle estimation versus number of array elements

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图 11 不同算法平均运行时间随阵元数的变化

Figure 11. Average runtime versus number of array elements for different algorithms

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图 12 实验场景

Figure 12. Experimental scene

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图 13 无人机飞行轨迹示意图

Figure 13. Schematic diagram of the UAV flight trajectory

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图 14 不同算法对目标仰角的估算结果

Figure 14. Estimation results of target elevation angle using different algorithms

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图 15 不同算法对目标仰角的估计误差

Figure 15. Estimation errors of target elevation angle using different algorithms

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表 1 不同波束空间DOA估计算法波束形成器的波束指向角设置

Table 1. Beam steering angle configurations of beamformers in different beamspace DOA estimation algorithms

算法	波束指向角集合
3D-BML	$ {\boldsymbol{\theta }}_{B}=\left[-{7.18}^{ \circ},{0}^{\circ},{7.18}^{ \circ}\right] $
RML-SDB	$ {\boldsymbol{\theta }}_{B}=\left[-{7.18}^{ \circ},{7.18}^{ \circ}\right] $
本文方法	$ {\boldsymbol{\theta }}_{B}=\left[-{6.73}^{ \circ},-{5.41}^{\circ},-{2.08}^{\circ},{5.06}^{ \circ},{5.78}^{ \circ}\right] $

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表 2 不同算法的计算复杂度

Table 2. Computational complexity of different algorithms

算法	在线计算复杂度	离线计算复杂度
3D-BML	$ O\left(\overline{Q}{B}_{\text{3D}}M+\overline{Q}{({{B}_{\text{3D}}})}^{3}\right) $	$ O\left({B}_{\text{3D}}ML\right) $
RML-SDB	$ O\left(\overline{Q}{B}_{\text{SDB}}M+\overline{Q}{({{B}_{\text{SDB}}})}^{3}\right) $	$ O\left({B}_{\text{SDB}}ML\right) $
本文方法	$ O\left(\overline{Q}{B}_{\text{PM}}M+\overline{Q}{({{B}_{\text{PM}}})}^{3}\right) $	$ O \left( NKM{({{B}_{\text{PM}}})}^{2} \right) $
AP-Newton	$ O \left({M}^{3} + \overline{Q}{M}^{2} + L{M}^{2} + {I}_{\text{AP}}M\right) $	—
RML	$ O\left(\overline{Q}{M}^{3}\right) $	—

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表 3 L波段全息凝视雷达关键参数

Table 3. Key parameters of the L-Band holographic staring radar

参数	数值
带宽	2～16 MHz
接收通道数	8×8
方位覆盖范围	90°
俯仰覆盖范围	22.5°, 30.0°, 45.0°, 60.0° (可设定)
脉冲重复频率	～5 kHz
更新频率	～1 s
探测距离	10 km (@RCS 0.01 m²)

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表 4 不同算法对目标仰角估计的RMSE

Table 4. RMSE of target elevation angle estimation using different algorithms

算法	RMSE (°)
3D-BML	0.4587
RML-SDB	0.1998
AP-Newton	0.1688
RML	0.1279
本文方法	0.1537

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