无人蜂群可以形成柔性阵列，实现灵巧的波束形成，但其性能受蜂群节点定位精度的影响较大.传统蜂群阵列位置估计受到GPS定位精度影响，精度通常在0.1~1 m.当阵列校正载波的半波长小于定位误差时，传统阵列误差校正算法会因相位混叠难以实施.当阵列同时存在通信时延误差和相位误差时，阵列误差更加难以校正.为此，提出一种基于双频法的阵列误差联合校正算法.该算法基于双频差异构建等效低频测量，优选了频差设计方案，突破定位误差建模的半波长限制，可以得到高精度的校正性能.仿真实验结果表明，当位置误差与通信时延误差同时存在时，该算法在不同信噪比条件下均能实现高效的误差联合校正.

Drone swarms can form flexible arrays to achieve agile beamforming，but their performance relies on precise node localization. Traditional swarm array position estimation is constrained by GPS accuracy，typically within 0.1~1 m. When the half⁃wavelength of the array calibration carrier is smaller than the positioning error，conventional array error calibration algorithms fail due to phase ambiguity. The challenge is further compounded when both communication time⁃delay errors and phase errors coexist in the array. To address these issues，this paper proposes a joint array error calibration algorithm based on a dual⁃frequency method. By constructing equivalent low⁃frequency measurements from dual⁃frequency differences and optimizing the frequency difference design，the algorithm overcomes the half⁃wavelength limitation in error modeling and achieves high⁃precision calibration. Simulation results demonstrate that the proposed method enables efficient joint error correction under various signal⁃to⁃noise ratio conditions，even when both positional errors and communication time⁃delay errors are present.

基于双频法的蜂群柔性阵列位置、相位与通信时延误差联合校正算法

曹关皓, 杨吉斌, 申海霞, 汪涛, 涂宇

南京大学学报(自然科学版)››2025, Vol. 61››Issue (6): 987-998.

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南京大学学报(自然科学版) ›› 2025, Vol. 61 ›› Issue (6) : 987-998. DOI: 10.13232/j.cnki.jnju.2025.06.009

基于双频法的蜂群柔性阵列位置、相位与通信时延误差联合校正算法

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A joint calibration algorithm for position, phase and time⁃delay errors in swarm⁃based flexible arrays using the dual⁃frequency method

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收稿日期	出版日期
2025-09-15	2025-11-30
发布日期
2025-12-17

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{{article.zuoZheCn_L}}.{{article.title_cn}}[J]. {{journal.qiKanMingCheng_CN}}, 2025, 61(6): 987-998 https://doi.org/10.13232/j.cnki.jnju.2025.06.009

{{article.zuoZheEn_L}}.{{article.title_en}}[J]. {{journal.qiKanMingCheng_EN}}, 2025, 61(6): 987-998 https://doi.org/10.13232/j.cnki.jnju.2025.06.009

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