基于移动虚拟插值阵列协方差矩阵快速补全的多目标直接定位方法

王鸿帧; 王鼎; 聂福全; 唐涛

doi:10.12000/JR26006

基于移动虚拟插值阵列协方差矩阵快速补全的多目标直接定位方法

DOI: 10.12000/JR26006 CSTR: 32380.14.JR26006

王鸿帧^{1, 4},
王鼎^{1, 2, ,},
聂福全³,
唐涛¹

1.
信息工程大学信息系统工程学院郑州 450001
2.
国家数字交换系统工程技术研究中心郑州 450002
3.
河南科技学院新乡 453000
4.
解放军93575部队承德 067000

基金项目: 国家自然科学基金(62171469, 62071029)

详细信息

作者简介:
王鸿帧，博士研究生，工程师，主要研究方向为无源定位、阵列信号处理等

王　鼎，教授，主要研究方向为无源定位、阵列信号处理等

聂福全，教授，主要研究方向为工程机械设计、目标定位等

唐　涛，教授，主要研究方向为无线电智能测向定位、阵列信号处理等

通讯作者:
王鼎 wang_ding814@aliyun.com

责任主编：郭福成 Corresponding Editor: GUO Fucheng

中图分类号: TN97
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出版历程
- 收稿日期: 2026-01-05

A Multi-Target Direct Localization Method Based on Fast Completion of the Covariance Matrix of the Mobile Virtual Interpolation Array

WANG Hongzhen^{1, 4},
WANG Ding^{1, 2
, ,},
NIE Fuquan³,
TANG Tao¹

1.
School of Information System Engineering, Information Engineering University, Zhengzhou 450001, China
2.
National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China
3.
Henan Institute of Science and Technology, Xinxiang 453000, China
4.
Unit 93575 of the People's Liberation Army, Chengde 067000, China

Funds: The National Natural Science Foundation of China (62171469, 62071029)

More Information

Corresponding author: WANG Ding, wang_ding814@aliyun.com

摘要

摘要: 该文基于互质差分共性阵列研究运动单站的多目标直接定位问题。针对现有基于矩阵范数最小化的运动单站直接定位方法存在虚拟阵元冗余数据利用不充分和运算复杂度高的问题，该文提出了一种融合虚拟阵元冗余数据平均和协方差矩阵缺失元素快速补全的多目标直接定位方法。该方法引入虚拟阵元冗余数据平均技术构建差分共性阵列，并结合孔洞零值填充和Toeplitz矩阵重构恢复协方差矩阵的秩，然后基于核范数与Frobenius范数比值最小化原则，设计基于自适应阈值策略和Toeplitz约束的交替投影迭代算法，以实现虚拟阵列协方差矩阵缺失元素的高效补全，最后应用数据融合算法进行定位。数值仿真表明，所提方法能够在降低运算复杂度的同时提升定位精度，尤其在低信噪比和少观测数据场景中表现优异，有效平衡了定位精度与实时性的需求。
- 互质阵列 /
- 直接定位 /
- 冗余数据平均 /
- 协方差矩阵补全 /
- 凸优化
Abstract: This paper addresses the multitarget direct localization problem for moving single stations using the coprime difference co-array. Existing methods based on matrix norm minimization often suffer from underutilization of redundant data from virtual array elements and high computational complexity. To overcome these limitations, we propose a multitarget direct localization approach that combines redundant data averaging for virtual array elements with fast completion of missing covariance matrix entries. First, redundant data averaging is applied to construct the difference co-array. Missing elements are then filled through zeroinitialization followed by Toeplitz matrix reconstruction, which restores the rank structure of the covariance matrix. An alternating projection iterative algorithm is subsequently developed to minimize the ratio of the nuclear norm to the Frobenius norm. By incorporating an adaptive threshold strategy and Toeplitz constraints, the algorithm efficiently completes the missing elements in the virtual array covariance matrix. Finally, a data fusion scheme is employed to obtain the localization results. Numerical simulations demonstrate that the proposed method reduces computational complexity while improving localization accuracy, particularly under low signal-to-noise ratios and limited observation data. The results indicate that the method effectively balances localization accuracy with real-time performance requirements.
- Coprime array /
- Direct position determination /
- Redundant data averaging /
- Covariance matrix completion /
- Convex optimization

HTML全文

图 1 基于互质阵列的移动单站直接定位示意图

Figure 1. Schematic diagram of moving single-station direct localization based on coprime array

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图 2 扩展互质阵列结构示意图

Figure 2. Schematic diagram of extended coprime array structure

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图 3 所提方法流程图

Figure 3. Flowchart of the proposed method

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图 4 虚拟阵列插值示意图

Figure 4. Schematic diagram of virtual array interpolation

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图 5 两相邻目标定位场景示意图

Figure 5. Schematic diagram of localization scenario for two adjacent targets

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图 6 各DPD方法代价函数谱(SNR=0 dB, K=30条件下)

Figure 6. Cost function spectra of DPD methods (under conditions of SNR=0 dB and K=30)

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图 7 各DPD方法代价函数谱(SNR=–3dB, K=10条件下)

Figure 7. Cost function spectra of DPD methods (under conditions of SNR=–3 dB and K=10)

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图 8 各DPD方法代价函数谱(SNR=–5 dB, K=5条件下)

Figure 8. Cost function spectra of DPD methods (under conditions of SNR=–5 dB and K=5)

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图 9 各DPD方法的PSD

Figure 9. The PSD of various DPD methods

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图 10 RMSE与$ \Delta d $关系图

Figure 10. Relationship diagram between RMSE and $ \Delta d $

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图 11 定位RMSE随SNR的变化情况

Figure 11. Variation of localization RMSE with SNR

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图 12 定位RMSE随快拍数的变化情况

Figure 12. Variation of localization RMSE with the number of snapshots

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图 13 定位RMSE随观测批次的变化情况

Figure 13. Variation of localization RMSE with observation batches

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图 15 多目标代价函数谱(14个辐射源)

Figure 15. Cost function spectrum of multi-targets (14 radiation sources)

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图 16 多目标代价函数谱(20个辐射源)

Figure 16. Cost function spectrum of multi-targets (20 radiation sources)

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图 14 多目标定位场景示意图

Figure 14. Schematic diagram of multi-target localization scenario

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图 17 矩阵补全迭代收敛曲线

Figure 17. Matrix completion iteration convergence curve

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表 1 各DPD方法计算复杂度

Table 1. Computational complexity of DPD methods

方法	运算复杂度
MCVA	$ O\left(LK{J}^{2}+L{\bar{V}}^{3}+{N}^{\mathrm{p}}L{\bar{V}}^{2}\right) $
ANM	$ O \left(LK{J}^{2} + LD({(V + 1)}^{3} + {(V + 1)}^{2} + 1) + L{V}^{3} + {N}^{\mathrm{p}}L{V}^{2}\right) $
本文	$ O\left(LK{J}^{2}+LI{V}^{3}+L{V}^{3}+{N}^{\mathrm{p}}L{V}^{2}\right) $

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表 2 各DPD方法运行时间

Table 2. Running Time of DPD Methods

算法	核心步骤	运行时间(s)
MCVA	$ {\hat{\boldsymbol{R}}}_{l} $计算+RD+选取连续部分+Toeplitz 平滑+矩阵分解+谱峰搜索	36.75
ANM	$ {\hat{\boldsymbol{R}}}_{l} $计算+RD+孔洞零插值+Toeplitz 平滑+CVX补全+矩阵分解+谱峰搜索	437.63
本文	$ {\hat{\boldsymbol{R}}}_{l} $计算+RA+孔洞零插值+Toeplitz平滑+ APIA-ATSTC补全+矩阵分解+谱峰搜索	42.49

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