一种基于位置修正和卡尔曼滤波的姿态角推算算法
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摘要
在动态载体如汽车、船舶或静态载体如桥梁、房屋的姿态推算中,使用全球导航卫星系统(global navigation satellitesystem,GNSS)进行载体测向,比起使用惯性传感器成本较低;且随时间不会累积误差。针对在多天线基线解算时存在的接收机时钟不同步造成基线解算精度下降,以及载体运动过程中多径和周跳等造成的误差问题,提出了一种基于参考天线位置修正的扩展卡尔曼滤波(extended Kalman filter,EKF)算法。根据载体移动速度和接收机之间的时钟差对每一历元载体参考天线位置矫正,提高基线解算的精度,从而提高姿态角精度。基线解算采用实时动态定位技术(real time kinematic,RTK),根据接收机给出的载波相位观测量,在参考天线和其他天线之间做双差建立观测方程,求解出基线向量。将得到的多组基线向量利用最小二乘法求解出姿态角。根据实际测试表明,该方法在基线长度不超过1. 5 m的情况下,静态航向角和俯仰角精度达到0. 2°,低动态情况下航向角精度达到0. 2°,俯仰角精度达到0. 3°。
To determing the attitude of moving platform such as vehicles and ships,or static carrier such as bridge and building,the use of global navigation satellite system( GNSS) is lower cost and the errors of attitude parameters won't accumulate with time compare with inertial sensors. This case study aims to demonstrate an antenna-position-correction algorithm based on extended Kalman filter( EKF),to solve the error caused by the synchronization of the receiver clock and multi-path effect or cycle slips during the movement of the platform. By correcting the position of reference antenna of each epoch,the accuracy of baseline and attitude angle could be improved. At the same time,using real time dynamic( RTK) positioning technique to calculate the vector of baseline. According to the observation of carrier-phase given by the receiver,the double difference between reference antenna is made to establish the observation equation. The obtained sets of baseline vectors are solved by least squares method to evaluate attitude angle. The experiment results indicate that in the static mode,the precision of the static heading and pitching angle is 0. 2 degrees under the condition which baseline length less than 1. 5 meters. And under the low dynamic mode,the precision of the heading angle is 0. 2 degrees and the pitch angle accuracy reaches 0. 3 degrees.
To determing the attitude of moving platform such as vehicles and ships,or static carrier such as bridge and building,the use of global navigation satellite system( GNSS) is lower cost and the errors of attitude parameters won't accumulate with time compare with inertial sensors. This case study aims to demonstrate an antenna-position-correction algorithm based on extended Kalman filter( EKF),to solve the error caused by the synchronization of the receiver clock and multi-path effect or cycle slips during the movement of the platform. By correcting the position of reference antenna of each epoch,the accuracy of baseline and attitude angle could be improved. At the same time,using real time dynamic( RTK) positioning technique to calculate the vector of baseline. According to the observation of carrier-phase given by the receiver,the double difference between reference antenna is made to establish the observation equation. The obtained sets of baseline vectors are solved by least squares method to evaluate attitude angle. The experiment results indicate that in the static mode,the precision of the static heading and pitching angle is 0. 2 degrees under the condition which baseline length less than 1. 5 meters. And under the low dynamic mode,the precision of the heading angle is 0. 2 degrees and the pitch angle accuracy reaches 0. 3 degrees.
引文
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13 Elmowafy A,Mohamed A.Attitude determination from GNSS using adaptive kalman filtering[J].Journal of Navigation,2005,58(1):135-148
14 Eling C,Zeimetz P,Kuhlmann H.Development of an instantaneous GNSS/MEMS attitude determination system[J].GPS Solutions,2013,17(1):129-138
2蔡艳辉,程鹏飞,李夕银.用卡尔曼滤波进行GPS动态定位[J].测绘通报,2006(7):6-8Cai Yanhui,Cheng Pengfei,Li Xiyin.Kinematic point positioning with kalman filtering[J].Bulletin of Surveying and Mapping,2006(7):6-8
3张方照,柴艳菊,柴华,等.两种多天线GNSS定姿方法的精度分析[J].中国惯性技术学报,2016,24(1):30-35Zhang Fangzhao,Chai Yanju,Chai Hua,et al.Analysis on precision of two attitude determination methods using GNSS multi-antenna data[J].Journal of Chinese Inertial Technology,2016,24(1):30-35
4王立红,郝继平,汤云.基于最小二乘法的GPS多天线测姿及精度分析[J].测试技术学报,2007,21(1):1-5Wang Lihong,Hao Jiping,Tang Yun.Attitude determination and accuracy analysis by multi-antenna GPS technology based on least square algorithm[J].Journal of Test and Measurement Techol,2007,21(1):1-5
5李跃军,阎超.飞行器姿态角解算的全角度双欧法[J].北京航空航天大学学报,2007,33(5):505-508Li Yuejun,Yan Chao.Improvement of dual-Euler method for full scale Eulerian angles solution of aircraft[J].Journal of Beijing University of Aeronautics and Astronautics,2007,33(5):505-508
6丁文利,王怀念,黄良.动态GPS(RTK)测量的精度分析[J].地矿测绘,2004,20(2):16-17Ding Wenli,Wang Huainian,Huang Liang.Precision analysis of kinematic GPS(RTK)survey[J].Surveying and Mapping of Geology and Mineral Resources,2004,20(2):16-17
7吴建军,钱峰.多信息融合的定向测姿方法的研究[J].电子测量技术,2012,35(2):41-45Wu Jianjun,Qian Feng.Research on directional attitude determination method based on multi information fusion[J].Electronic Measurement Technology,2012,35(2):41-45
8王勇,赵修斌,庞春雷,等.GNSS测姿系统天线设置及精度分析[J].计算机测量与控制,2014,22(9):3024-3027Wang Yong,Zhao Xiubin,Pang Chunlei,et al.Antenna configuration and accuracy analysis of GNSS attitude determination system[J].Computer Measurement,2014,22(9):3024-3027
9吴涛,白茹,朱礼尧,等.基于卡尔曼滤波的航姿参考系统设计[J].传感技术学报,2016,29(4):531-535Wu Tao,Bai Ru,Zhu Liyao,et al.Design of AHRS based on Kalman filter[J].Chinese Journal of Sensor and Actuators,2016,29(4):531-535
10钟林,周海渊.测姿GPS系统在测量船上的应用[J].科学技术与工程,2013,13(3):641-644Zhong Ling,Zhou Haiyuan.Measured pose GPS system on the tracking ship[J].Science Technology and Engineering,2013,13(3):641-644
11龙达峰,刘俊,张晓明,等.地磁导航中磁测姿态解算误差分析[J].科学技术与工程,2015,15(6):204-209Long Dafeng,Liu Jun,Zhang Xiaoming,et al.Error analysis of magnetic attitude measurement system on geomagnetic navigation[J].Science Technology and Engineering,2015,15(6):204-209
12王守华,邓桂辉,纪元法,等.基于组合滤波的低成本飞行器姿态解算算法[J].计算机应用,2017,37(5):1507-1511Wang Shouhua,Deng Guihui,Ji Yuanfa,et al.Attitude calculation algorithm of low-cost aircraft based on combined filter[J].Journal of Computer Applications,2017,37(5):1507-1511
13 Elmowafy A,Mohamed A.Attitude determination from GNSS using adaptive kalman filtering[J].Journal of Navigation,2005,58(1):135-148
14 Eling C,Zeimetz P,Kuhlmann H.Development of an instantaneous GNSS/MEMS attitude determination system[J].GPS Solutions,2013,17(1):129-138