Relative Positioning Technology for Two Points Based on Cluster Cooperative Orientation

doi:10.12382/bgxb.2023.0829

Abstract

Abstract:

Precise inter-node position acquisition is the basis for coordination in unmanned vehicle clusters, but the global navigation satellite system (GNSS) struggles to provide the stable and accurate position information in complex and dynamic application environments. It is difficult to deploy the auxiliary anchor points, and most traditional relative positioning methods have limitations on the number of nodes. A new relative localization method for cluster nodes under GNSS-denied conditions is proposed to address the above three problems. Taking two nodes equipped with inertial measurement units (IMUs) and ultra-wideband sensors as an example, a relative positioning model is established, and an extended Kalman filter algorithm is used to fuse IMU and inter-node distance information for the optimal estimation of relative position. Simulation experiments show that the proposed method is used to achieve a relative positioning accuracy of about 1.3m within 200m range between unmanned aerial vehicles, improving nearly 4 times over existing multi-node relative positioning algorithms. The high-precision relative positioning between two nodes can be achieved without relying on GNSS or auxiliary anchor points, providing an effective and feasible solution for collaborative positioning of unmanned vehicle clusters in complex application environment.

Key words: relative positioning, ranging, inertial measurement unit, extended Kalman filter, GNSS-denied

CLC Number:

V249.32⁺8

DENG Tingxiang, REN Peng, CHENG Jia, WANG Jianbing, LIANG Zhenjie, XIANG Zheng. Relative Positioning Technology for Two Points Based on Cluster Cooperative Orientation[J]. Acta Armamentarii, 2023, 44(S2): 22-34.

Figures/Tables 17

Fig.1 UAV relative positioning system

Fig.2 Working process of the whole system

Table 1 Simulation experiment parameters

参数	数值
IMU采样率/s	0.005
陀螺仪常值漂/(deg·h^-1)	0.1
加速度计常值漂移/ug	100
测距误差/m	0.5
初始位置误差/m	(2,2,2)
初始速度误差/(m·s^-1)	(0.1,0.1,0.1)
UWB位置(x,y,z)/m	UWB₁(0.4,0,0) UWB₂(-0.3,0,0) UWB₃(0,0.3,0.4)
状态噪声矩阵	diag(10^-5×I_3×1;10^-2×I_3×1; 10^-8×I_6×1)

Table 2 Motion parameter setting

运动参数	数值
飞行时长/s	600
初始相对位置/m	18
初始速度/(m·s^-1)	0

Fig.3 Relative motion trajectory of UAV

Fig.4 Distance between UAVs

Fig.5 Relative position error of inertial navigation

Fig.6 Simulation of relative positioning algorithm

Fig.7 Comparison of relative positioning algorithm and inertial navigation

Fig.8 The effect of distance on relative positioning performance

Table 3 UWB sensor settings

UWB传感器编号	位置(x,y,z)/m
UWB1	(0.4,0,0)
UWB2	(-0.3,0,0)
UWB3	(0,0.3,0.4)
UWB4	(0,-0.5,0)
UWB5	(0,0,-0.5)

Fig.9 Relative positioning results of different number of UWB sensors

Fig.10 Comparison of positioning errors of two algorithms

Fig.11 Sample prototype

Fig.12 Deployment of system prototypes

Fig.13 UAV position value obtained from the test

Fig.14 Position error of UAV

References 45

[1]	陈炜军, 邹庆, 涂卫军. 空面武器智能化发展趋势与应用[J]. 直升机技术, 2021(e2): 69-72.
	CHEN W J, ZOU Q, TU W J. Research on intelligent development trend and application of air-to-surface weapons[J]. Helicopter Technique, 2021(e2): 69-72. (in Chinese)
[2]	郝菁. 基于惯导/数据链协同的无人机集群导航定位算法研究[D]. 北京: 中国电子科技集团公司电子科学研究院, 2019.
	HAO J. INS/Intra flight datalink cooperative positioning algorithm for UAVs[D]. Beijing: China Academic of Electronics and Information Technology, 2019. (in Chinese)
[3]	裴凌, 李涛, 花彤, 等. 多源融合定位算法综述[J]. 南京信息工程大学学报(自然科学版), 2022, 14(6): 635-648.
	PEI L, LI T, HUA T, et al. A survey of multi-source fusion positioning algorithms[J]. Journal of Nanjing University of Information Science & Technology(Natural Science Edition), 2022, 14(6): 635-648. (in Chinese)
[4]	ZHUANG Y, SUN X, LI Y, et al. Multi-sensor integrated navigation/positioning systems using data fusion: from analytics-based to learning-based approaches[J]. Information Fusion, 2023, 95: 62-90. doi: 10.1016/j.inffus.2023.01.025 URL
[5]	韩煜, 宋韬, 郑多, 等. 基于冲突触发避碰机制的无人飞行器集群协同制导技术[J]. 兵工学报, 2023, 44(7): 1881-1895. doi: 10.12382/bgxb.2022.0152
	HAN Y, SONG T, ZHENG D, et al. Unmanned aerial vehicle cluster cooperative guidance technology based on conflict trigger mechanism[J]. Acta Armamentarii, 2023, 44(7): 1881-1895. (in Chinese) doi: 10.12382/bgxb.2022.0152
[6]	PENG J, ZHANG P, ZHENG L X, et al. UAV positioning based on multi-sensor fusion[J]. IEEE Access, 2020, 8: 34455-34467. doi: 10.1109/Access.6287639 URL
[7]	LU S Y, ZHI Y S, ZHANG S M, et al. Semi-direct monocular SLAM with three levels of parallel optimizations[J]. IEEE Access, 2021, 9: 86801-86810. doi: 10.1109/ACCESS.2021.3071921 URL
[8]	MUNGUIA R, TRUJILLO J C, GUERRA E, et al. A hybrid visual-based SLAM architecture: local filter-based SLAM with keyframe-based global mapping[J]. Sensors, 2021, 22(1):210. doi: 10.3390/s22010210 URL
[9]	WANG H C, WANG Z, ZHANG L, et al. A highly stable fusion positioning system of smartphone under NLOS acoustic indoor environment[J]. ACM Transactions on Internet Technology, 2023, 23(2): 1-19.
[10]	XU C, HE J, LI Y Y, et al. Optimal estimation and fundamental limits for target localization using IMU/TOA fusion method[J]. IEEE Access, 2019, 7: 28124-28136. doi: 10.1109/ACCESS.2019.2902127 URL
[11]	ZOU A R, HU W W, LUO Y H, et al. An improved UWB/IMU tightly coupled positioning algorithm study[J]. Sensors, 2023, 23(13): 5918. doi: 10.3390/s23135918 URL
[12]	LI B B, HAO Z J, DANG X C. An indoor location algorithm based on kalman filter fusion of ultra-wide band and inertial measurement unit[J]. AIP Advances, 2019, 9(8):085210. doi: 10.1063/1.5117341 URL
[13]	夏楠, 邱天爽, 李景春, 等. 一种卡尔曼滤波与粒子滤波相结合的非线性滤波算法[J]. 电子学报, 2013, 41(1): 148-152. doi: 10.3969/j.issn.0372-2112.2013.01.026
	XIA N, QIU T S, LI J C, et al. A nonlinear filtering algorithm combining the kalman filter and the particle filter[J]. Acta Electronica Sinica, 2013, 41(1): 148-152. (in Chinese) doi: 10.3969/j.issn.0372-2112.2013.01.026
[14]	刘燕, 张健, 肖庆高, 等. UKF与EKF在导航定位中的对比研究[J]. 微处理机, 2023, 44(4): 30-33.
	LIU Y, ZHANG J, XIAO Q G, et al. A comparative study of UKF and EKF in navigation and positioning[J]. Microprocessors, 2023, 44(4): 30-33. (in Chinese)
[15]	刘向阳. 几种典型非线性滤波算法及性能分析[J]. 舰船电子工程, 2019, 39(7): 32-36.
	LIU X Y. Several typical nonlinear filtering algorithms and performance analysis[J]. Ship Electronic Engineering, 2019, 39(7): 32-36. (in Chinese)
[16]	HU E W, DENG Z L, XU Q Q, et al. Relative entropy-based kalman filter for seamless indoor/outdoor multi-source fusion positioning with INS/TC-OFDM/GNSS[J]. Cluster Computing, 2018, 22(S4): 8351-8361. doi: 10.1007/s10586-018-1803-1
[17]	高嵩, 宋佳鹏, 房穹, 等. 抗差自适应容积卡尔曼滤波在UWB室内定位中的应用[J]. 导航定位学报, 2023, 11(1): 142-147.
	GAO S, SONG J P, FANG Q, et al. Application of adaptively robust cubature kalman filter in UWB indoor location[J]. Journal of Navigation and Positioning, 2023, 11(1): 142-147. (in Chinese)
[18]	徐阳扬, 陈明, 赵艳, 等. 基于粒子滤波的室内机器人定位加速收敛算法[J]. 电子设计工程, 2023, 31(14): 6-11.
	XU Y Y, CHEN M, ZHAO Y, et al. Speedup convergence algorithm for robot indoor localization based on particle filter[J]. Electronic Design Engineering, 2023, 31(14): 6-11. (in Chinese)
[19]	苏佳, 杨泽超, 易卿武, 等. 基于遗传算法优化BP神经网络的GNSS干扰源定位技术[J/OL]. 无线电工程, 2023(2023-08-29)[2023-12-06]. http://kns.cnki.net/kcms/detail/13.1097.TN.20230829.1520.006.html.
	SU J, YANG Z C, YI Q W, et al. GNSS interference source localization technology based on genetic algorithm optimized BP neural network[J/OL]. Radio Engineering, 2023 (2023-08-29)[2023-12-06]. http://kns.cnki.net/kcms/detail/13.1097.TN.20230829.1520.006.html. (in Chinese)
[20]	CHU P, ZHANG H, CHEN Y R, et al. Multi-source data high-performance indoor positioning considering genetic optimization neural network algorithm[J]. Mathematical Problems in Engineering, 2022, 2022(9): 1-11.
[21]	鱼瑜, 吴明亮, 张来喜, 等. 多传感器融合定位方法探讨[J]. 导航定位学报, 2023, 11(5): 151-163.
	YU Y, WU M L, ZHANG L X, et al. Discussion on positioning methods of multi-sensor fusion[J]. Journal of Navigation and Positioning, 2023, 11(5): 151-163. (in Chinese)
[22]	冯硕. 基于UWB与深度学习融合的单基站定位算法[D]. 海口: 海南大学, 2022.
	FENG S. Single base station location algorithm based on UWB and deep learning[D]. Haikou: Hainan University, 2022. (in Chinese)
[23]	李玉柏, 孙迅. 基于迁移学习提高WiFi室内定位中信道状态信息指纹库的鲁棒性[J]. 电子与信息学报, 2023, 45(10): 3657-3666.
	LI Y B, SUN X. A highly robust indoor location algorithm using WiFi channel state information based on transfer learning reinforcement[J]. Journal of Electronics & Information Technology, 2023, 45(10): 3657-3666. (in Chinese)
[24]	CARRIO A, SAMPEDRO C, RODRIGUEZ-RAMOS A, et al. A review of deep learning methods and applications for unmanned aerial vehicles[J]. Journal of Sensors, 2017(2):1-13.
[25]	吴杰宏, 李丹阳. 无人机集群编队控制方法研究综述[J]. 无线电通信技术, 2023, 49(4): 589-596.
	WU J H, LI D Y. A review of UAV cluster formation control methods[J]. Radio Communications Technology, 2023, 49(4): 589-596. (in Chinese)
[26]	武成锋, 程进, 郭晓云, 等. 飞行器集群协同定位与导航对抗技术发展与展望[J]. 宇航学报, 2022, 43(2): 131-142.
	WU C F, CHENG J, GUO X Y, et al. Development and prospect of aircraft clusters cooperative positioning and navigation countermeasures technology[J]. Journal of Astronautics, 2022, 43(2): 131-142. (in Chinese)
[27]	ZHU X D, LAI J Z, ZHOU B C, et al. Weight factor graph co-location method for UAV formation based on navigation performance evaluation[J]. IEEE Sensors Journal, 2023, 23(12): 13037-13051. doi: 10.1109/JSEN.2023.3252019 URL
[28]	TANG C K, WANG C, ZHANG L L, et al. Geometric-manifold-assisted distributed navigation probabilistic information fusion cooperative positioning algorithm[J]. Remote Sensing, 2021, 13(24):4987. doi: 10.3390/rs13244987 URL
[29]	朱徐东, 赖际舟, 周本川, 等. 基于构型寻优的多无人机鲁棒自适应协同定位方法[J]. 中国惯性技术学报, 2023, 31(7): 650-658,64.
	ZHU X D, LAI J Z, ZHOU B C, et al. Robust adaptive cooperative localization method for multiple UAVs based on configuration optimization[J]. Journal of Chinese Inertial Technology, 2023, 31(7): 650-658,64. (in Chinese)
[30]	朱奎宝, 温紫晴, 狄世彦, 等. 多机器人系统的可观测性及协同定位精度分析[J/OL]. 电讯技术, 2023(2023-06-05)[2023-12-06].https://doi.org/10.20079/j.issn.1001-893x.230417003.
	ZHU K B, WEN Z Q, DI S Y, et al. Observability and co-positioning accuracy analysis of multi-robot systems[J/OL]. Telecommunication Engineering, 2023 (2023-06-05)[2023-12-06].https://doi.org/10.20079/j.issn.1001-893x.230417003. (in Chinese)
[31]	刘杨. 多AUV协同导航优化算法与编队构型设计[D]. 哈尔滨: 哈尔滨工程大学, 2015.
	LIU Y. Optimized algorithm of multi-AUV cooperative navigation system and design of its formation configuration[D]. Harbin:Harbin Engineering University, 2015. (in Chinese)
[32]	LIU W L, WU S T, WU X L. Relative navigation of missile formation and INS error correction methods[C]// Proceedings of the 2017 29th Chinese Control and Decision Conference. Chongqing, China: IEEE, 2017.
[33]	王小刚, 郭继峰, 崔乃刚. 基于数据链的智能导弹协同定位方法[J]. 中国惯性技术学报, 2009, 17(3):319-323.
	WANG X G, GUO J F, CUI N G. Cooperative localization approach to intelligent missile based on data link[J]. Journal of Chinese Inertial Technology, 2009, 17(3): 319-323. (in Chinese)
[34]	GONG Z, WANG M G, HE J G, et al. A robust adaptive control algorithm for multimissile cooperative formation[J]. International Journal of Aerospace Engineering, 2022, 2022: 5483667.
[35]	闵海根, 李尧, 汪建球, 等. 考虑通信时延的智能网联汽车协同定位方法[J]. 中国公路学报, 2023, 36(6): 220-234. doi: 10.19721/j.cnki.1001-7372.2023.06.019
	MIN H G, LI Y, WANG J Q, et al. Cooperative localization method for connected and autonomous vehicles considering communication delay[J]. China Journal of Highway and Transport, 2023, 36(6): 220-234. (in Chinese)
[36]	张红娟, 钱闯, 招倩莹, 等. 顾及通信延迟的车路协同高精度定位[J/OL]. 测绘学报, 2023(2023-06-08)[2023-12-06]. http://kns.cnki.net/kcms/detail/11.2089.P.20230608.0903.002.html.
	ZHANG H J, QIAN C, ZHAO Q Y, et al. Vehicle high-precision positioning considering communication delay for intelligent vehicle-infrastructure cooperation system[J/OL]. Acta Geodaetica et Cartographica Sinica, 2023(2023-06-08)[2023-12-06]. http://kns.cnki.net/kcms/detail/11.2089.P.20230608.0903.002.html. (in Chinese)
[37]	卢健, 陈旭, 罗毛欣, 等. 考虑通信延迟的多自治水下航行器协同定位算法[J]. 控制理论与应用, 2020, 37(9): 2061-2072.
	LU J, CHEN X, LUO M X, et al. Cooperative localization algorithm considering of communication delay for autonomous underwater vehicles[J]. Control Theory & Applications, 2020, 37(9): 2061-2072. (in Chinese)
[38]	刘天豪. 空中自组织网络优化分簇相对定位算法研究[D]. 北京: 中国电子科技集团公司电子科学研究院, 2019.
	LIU T H. Research on relative location algorithm of optimized clustering for FANET[D]. Beijing: China Academic of Electronics and Information Technology, 2019. (in Chinese)
[39]	彭宏泽. 无人机组合导航与多机协同定位研究[D]. 长春: 吉林大学, 2023.
	PENG H Z. Research on UAV integrated navigation and multi-UAV cooperative localization[D]. Changchun: Jilin University, 2023. (in Chinese)
[40]	严恭敏, 翁浚. 捷联惯导算法与组合导航原理[M]. 西安: 西北工业大学出版社, 2019.
	YAN G M, WENG J. Inertial navigation algorithm and principle of integrated navigation[M]. Xi’an: Northwestern Polytechnical University Press, 2019. (in Chinese)
[41]	秦永元, 张洪钺, 王叔华. 卡尔曼滤波与组合导航原理[M]. 西安: 西北工业大学出版社, 2012.
	QIN Y Y, ZHANG H Y, WANG S H. Kalman filtering and principle of integrated navigation[M]. Xi’an: Northwestern Polytechnical University Press, 2012. (in Chinese)
[42]	CHENG J, REN P, DENG T X. A novel ranging and IMU-based method for relative positioning of two-MAV formation in GNSS-denied environments[J]. Sensors (Basel), 2023, 23(9):4366. doi: 10.3390/s23094366 URL
[43]	YANG B, LI J, SHAO Z P, et al. Self-supervised deep location and ranging error correction for UWB localization[J]. IEEE Sensors Journal, 2023, 23(9): 9549-9559. doi: 10.1109/JSEN.2023.3258432 URL
[44]	GULER S, ABDELKADER M, SHAMMA J S. Peer-to-peer relative localization of aerial robots with ultrawideband sensors[J]. IEEE Transactions on Control Systems Technology, 2021, 29(5): 1981-1996. doi: 10.1109/TCST.2020.3027627 URL
[45]	杨彬. 基于MDS的无人机群协同定位算法研究[D]. 西安: 西安电子科技大学, 2021.
	YANG B. Cooperative localization algorithm of UAV swarm based on MDS[D]. Xi’an: Xidian University, 2021. (in Chinese)