Single-Channel High-Precision Sparse DOA Estimation of GNSS Signals for Deception Suppression
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摘要: 针对全球导航卫星系统(GNSS)面临的欺骗攻击威胁，传统多天线阵列欺骗检测方法存在硬件复杂度高、低信噪比下估计精度不足等问题，该文提出了一种面向欺骗抑制的单通道高精度稀疏波达方向(DOA)估计方法，旨在降低欺骗检测的硬件成本并提升极低信噪比条件下的估计性能。首先，基于参考阵元跟踪环路参数重构数字中频信号，利用不同伪随机噪声码信号间的正交性，通过重构信号与原始阵列信号的相关处理显著提升解扩前信噪比，提取“纯净”导向矢量；其次，结合GNSS空域稀疏特性构建过完备字典，将DOA估计转化为导向矢量的稀疏重构；最后，采用交替方向乘子法求解优化模型，以实现高精度二维DOA估计。仿真表明本文方法在极低信噪比下较Unitary ESPRIT和Cyclic MUSIC算法的估计精度和分辨力提高明显，基于把本文方法DOA估计的结果，LCMV波束形成器能够有效抑制欺骗信号。相较于信号载波相位检测的方法，该方法仅需处理单个阵元通道的信号，显著降低硬件复杂度，为空域欺骗检测与抑制提供了高效解决方案。
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关键词:
- 卫星导航 /
- 欺骗检测 /
- 到达方向估计 /
- 稀疏重建 /
- 交替方向乘法器(ADMM)
Abstract:Objective The proliferation of spoofing attacks poses a significant threat to the reliability and security of Global Navigation Satellite Systems (GNSS), which are critical for navigation and positioning across civilian and military applications. Traditional anti-spoofing methods relying on multi-antenna arrays incur high hardware complexity and exhibit limited estimation accuracy under low signal-to-noise ratio (SNR) conditions, compromising their effectiveness in resource-constrained or adverse environments. This research proposes a novel single-channel high-precision sparse direction-of-arrival (DOA) estimation method aimed at suppressing spoofing signals in GNSS receivers. The primary goals are to substantially reduce the hardware complexity associated with spoofing detection and to achieve superior DOA estimation performance even in extremely low SNR scenarios. By exploiting the spatial sparsity of GNSS signals and integrating advanced signal processing techniques, this approach seeks to deliver a cost-effective, robust solution for enhancing GNSS security against deceptive interference. Methods The proposed method leverages a single-channel processing framework to estimate the DOA of GNSS signals with high precision, employing a multi-step strategy tailored for spoofing suppression. The process begins with reconstructing the digital intermediate frequency signal using tracking loop parameters—such as code phase and carrier Doppler—derived from a reference array element. This reconstruction capitalizes on the orthogonality of pseudo-random noise codes inherent to GNSS signals, enabling correlation between the reconstructed signal and the original array data to enhance the SNR prior to despreading. This step isolates a clean steering vector, minimizing noise and interference contributions. The method then harnesses the spatial sparsity of GNSS signals, which arises from the limited number of authentic satellites and potential spoofing sources in the angular domain. An overcomplete dictionary is constructed, comprising steering vectors corresponding to a grid of possible azimuth and elevation angles. The DOA estimation is reformulated as a sparse reconstruction problem, where the steering vector is represented as a sparse combination of dictionary elements. To solve this efficiently, the Alternating Direction Method of Multipliers (ADMM) is employed, iteratively optimizing a regularized objective that balances data fidelity with sparsity. A two-stage grid refinement approach—starting with a coarse search followed by a finer resolution—reduces computational demands while maintaining accuracy. Once DOA estimates are obtained, spoofing signals are identified by their angular proximity to authentic signals, and a Linearly Constrained Minimum Variance (LCMV) beamformer is applied to suppress these interferers while preserving legitimate signals. Results and Discussions Simulations were conducted to assess the proposed method’s performance across various low SNR conditions, using a 4×4 uniform planar array and Beidou B3I signals as a test case. The results reveal that the single-channel sparse DOA estimation method significantly outperforms traditional algorithms like Unitary ESPRIT and Cyclic MUSIC in both accuracy and resolution. In scenarios with an SNR as low as –35 dB, the proposed approach achieves root mean square errors (RMSE) for azimuth and elevation estimates below 1 degree ( Fig.2 ), compared to errors exceeding 30 degrees for the benchmark methods (Fig. 3(a) ,Fig. 3(b) ). It also resolves signals separated by as little as 1 degree (Fig. 4(a) ,Fig. 4(b) ), highlighting its superior resolution capability. Building upon the accurate DOA estimates obtained in the proposed method, LCMV beamforming successfully suppressed spoofing signals. As shown inFig. 5(b) , the proposed method's high-fidelity DOA estimates allowed the beamformer to place deep nulls precisely at the estimated spoofing directions (e.g., (10°, 250°) and (20°, 250°)), effectively attenuating spoofers while preserving genuine signals. In contrast, the lower DOA estimation accuracy of Cyclic MUSIC (Fig. 5(a) ) resulted in misaligned nulls and compromised suppression performance. This validates the practical utility of the high-precision DOA estimates for robust spoofing mitigation.Conclusions This study introduces a pioneering single-channel high-precision sparse DOA estimation method for GNSS spoofing suppression, addressing the limitations of traditional multi-antenna approaches in terms of complexity and low-SNR performance. By integrating signal reconstruction, sparse modeling, and ADMM-based optimization, the method achieves exceptional accuracy and resolution under challenging conditions, validated through simulations showing RMSE below 1 degree at -35 dB SNR. Coupled with LCMV beamforming, it effectively mitigates spoofing threats, enhancing GNSS reliability with minimal hardware requirements. This cost-effective solution is particularly valuable for resource-limited applications, reducing dependency on complex arrays while maintaining robust security. Future work could explore its adaptability to dynamic environments, such as moving spoofers or multipath scenarios, and its integration with complementary anti-spoofing techniques. Overall, this research provides a practical, high-performance framework for securing GNSS systems, with significant implications for navigation safety and operational efficiency. -
表 1 不同方法计算复杂度对比
算法 计算复杂度 主要操作 本文方法 O(D3)+ O(TD2) ADMM迭代、矩阵求逆 UnESPRIT O(NM2)+O(M3) 实值特征值分解 Cyclic MUSIC O(NM2)+O(M3)+ O(GM(M-r)) 特征值分解、谱搜索 
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