逆向求解整周模糊度的姿态测量方法

1、逆向求解整周模糊度的姿态测量方法*李玉海1 夏 娜1,2 唐 媚1 钱浩伟1 (1. 合肥工业大学计算机与信息学院, 合肥 230009; 2. 安全关键工业测控技术教育部工程研究中心, 合肥 230009)摘 要: 导航卫星载体姿态测量是航空、航天、航海和陆地导航中的关键问题。该文提出了一种逆向求解整周模糊度的载体姿态测量方法。基于相位双差观测方程构造适应度函数, 采用进化算法搜索得到基线的初始姿态角, 并由此求解出双差整周模糊度N, 此后基于N实时计算基线姿态。该方法避开了直接搜索整周模糊度, 可实现性好, 同时又可以保证姿态解算的效率和稳定性。实验结果表明该方法不仅具有很高的测姿精度,

2、而且在动态条件下具有良好的稳定性和动态性能。关键词: 姿态测量；整周模糊度；进化算法；逆向求解中图分类号: V 294.32, TP391文献标识码: A国家标准学科分类代码: 510.40A method of attitude determination based on counter solved integer ambiguityLi Yuhai1 Xia Na1,2 Tang Mei1 Qian Haowei1(1. School of Computer and Information, Hefei University of Technology, Hefei 230009, C

3、hina; 2. Engineering Research Center of Safety Critical Industrial Measurement and Control Technology,Ministry of Education, Hefei 230009, China)Abstract: Attitude determination is a key problem in aviation, marine and land navigation. This paper presents a new method for carrier attitude measuremen

4、t with navigation satellites. Design a fitness function based on double difference phase observation equation, and search for the attitude angles of baseline using evolutionary algorithm. Then, counter calculate the double difference integer ambiguity N. Thereafter, calculate the baseline attitude a

5、ngles in real-time based on N. This method can avoid searching the integer ambiguity directly, and guarantee the efficiency and stability of attitude determination. The experimental results show this method achieves high precision, good stability and dynamic characteristic, so it is applicable for d

6、ynamic attitude determination. Keywords: attitude determination; integer ambiguity; evolutionary algorithm; counter solve1 引 言载体姿态测量是指利用导航卫星技术测定载体(航天器、飞机、船舶等)的姿态(航向角、俯仰角和横滚角), 它是航空、航天、航海以及陆地导航中的关键技术, 已成为导航信息处理的重要研究分 支1-2。载体姿态测量的基本思路是在载体平台上适当配置二个以上非共线的卫星天线, 利用载波相位差分测量技术, 即利用多个天线接收的载波相位差、测距码和导航电文信息, 通

7、过一定的算法实时解算天线之间确定的基线向量, 从而得到载体的姿态 信息。目前, 在基于载波相位差的载体姿态测量中, 相位双差整周模糊度的求解是重点和难点, 因此快速准确地解算整周模糊度成为了姿态测量研究的焦点。解算整周模糊度的方法主要有AFM (ambiguity function method)3、LSS (least squares search)4、FARA (fast ambiguity resolution algorithm)5、FASF (fast ambiguity search filter)6、LAMBDA (least squares ambiguity decorrel

8、ation adjustment)7, 以及文献8-11提出一些方法。由于整周模糊度的求解复杂, 实时性差, 因此限制了它在姿态测量中的应用。国内学者许江宁等12-13基于AFM 方法, 提出了一种避开整周模糊度的求解而直接解算姿态角的遗传算法, 该方法提高了姿态角解算的速度, 解决了GPS姿态测量中的实时性问题, 但由于是采用进化搜索算法, 因此不能保证对全局最优解的求解, 特别是在载体运动的情况下算法搜索的成功率不够理想。本文结合上述两类方法的优点, 提出了一种导航卫星载体姿态测量方法, 不仅避开了直接搜索整周模糊度, 而且可以保证姿态解算的效率和稳定性。2 采用进化算法搜索基线姿态角首先

9、基于相位双差观测方程构造适应度函数, 采用进化算法搜索得到基线姿态角。图1 单基线姿态测量原理示意图Fig. 1 Principle of single baseline attitude determination如图1所示, 采用2个GPS接收机和天线(天线A和天线B) 组成基线矢量b, 通过解算b的姿态角来确定载体的姿态。基线长度一般为几米或几十米, 短基线一般3米。为接收机A和B对观测卫星的相位差小数值; 为接收机A和B对观测卫星的相位差小数值; 则接收机A和B对同一时刻观测的两颗卫星i和j的载波相位双差为:(1)式中: b为基线长度, l为射频载波的波长, ai和aj分别是卫星i和j

10、对基线的载波平面的高度角, Wi和Wj分别是卫星i和j对基线的载波平面的方位角, j和b则为基线矢量的航向角和俯仰角。GPS相位双差可以消除空间相关的各种误差源, 如电离层误差、对流层误差、钟差等。Nij为相位双差整周模糊度, dij为观测噪声, 是均值为零的高斯白噪声。因此式(2)的数 学期望是整数, (2)那么, 式(3)的目标函数值为1, (3)在式(3)中, 航向角j和俯仰角b 未知。适当选取j,b 值使得等式成立, 则该j,b 值即为基线的航向角和俯仰角。这样, GPS载体姿态测量问题就转变为一个非线性组合优化问题。图2 粒子群算法搜索最优解流程图Fig. 2 Flow chart

11、of optimal solution searching basedon Particle Swarm Optimization为了保证解的唯一性, 需要用到颗卫星和个历元, 构成多约束条件, 并建立如下适应度函数: (4)针对非线性组合优化问题, 可以采用进化算法, 如粒子群算法(particle swarm optimization, PSO), 搜索其最优解, 即基线的航行角j、俯仰角b。图2给出了粒子群算法的流程。3 逆向求解双差整周模糊度3.1 由姿态角得到基线矢量已知基线的航行角j、俯仰角b 和基线长度b, 根据极坐标和直角坐标的关系可得基线在当地水平直角坐标系下的三维分量:(5

12、)进一步计算出基线在地心坐标系下的三维分量:(6)(7)式中: Bp,Lp为观测点的大地纬度和经度。基线矢量b即为。3.2 求解双差整周模糊度相位双差观测方程又可以表示为: (8)式中: F 为相位双差值矩阵, N为双差整周模糊度矩阵, b为基线矢量, e为观测噪声误差矢量(均值为0, 方差为Q), A和B分别为N和b的设计矩阵。对式(8)进行最小二乘估计, 得到实数估计值、和协方差矩阵: 若已知双差整周模糊度N, 则可由下式计算出基线矢量b: (9)那么, 在已知基线矢量b的前提下, 就可以逆向求解出双差整周模糊度N: (10)此后, 基于N, 根据式(9)实时计算基线姿态。4 实 验采用2

13、个GPS-701-GG天线组成1米的短基线, 如图3所示; GPS接收板为OEMV-1G, 可输出载波相位、天线的位置以及卫星的坐标等数据, 由天线的位置和卫星的坐标可计算出卫星的高度角和方位角, 参见文献14。接收板数据输出频率最高20 Hz, 通过RS232串口将数据送计算机。计算机运行本文算法实时解算基线姿态(航向角和俯仰角)。图3 基线及其旋转结构Fig. 3 Baseline and rotating structure本文方法的静态测姿结果如表1所示。可见该方法的测姿结果精度高, 航向角误差为0.023 5º, 俯仰角误差为0.016 442º。同时, 测量结果

14、方差小, 数据稳定性好。表1 静态测姿结果(基线1m)Table 1 Static attitude determination results航向角(°)俯仰角(°)均 值60.02350.916 442方 差0.013 6020.008 061实际值60.000.90注: 实际值采用精确指北装置和高精度陀螺仪测定。表2给出了在动态条件下本文方法的实验数据和测姿结果。在3个不同的时刻, 分别解算出基线的姿态为航向84.04°, 俯仰0.10° 航向176.30°, 俯仰表2 动态测姿的实验数据与结果(基线1m)Table 2 Experime

15、nt data and results of dynamic attitude determination序号GPS时间卫星1卫星2卫星3卫星4卫星5载波相位1,2高度角/rad方位角/rad载波相位1,2高度角/rad方位角/rad载波相位1,2高度角/rad方位角/rad载波相位1,2高度角/rad方位角/rad载波相位1,2高度角/rad方位角/rad1370970000-112378673. 672567 -115616057.7086880.8776533.607026-110538759.277598 -113776150.1452080.883050 1.904128-10583

16、3626. 678244 -109071023. 0618441.172127 3.276654-121356330.570057 -124593724.6440790.491531 1.873136-115270458.750076 -118507853.3948670.734478 5.581465370970050-112378552.429819 -115615936.4958740.8776603.607030-110538845.668904 -113776236.5932300.883045 1.904137-105833533.715860 -109070930.1325441

17、.172135 3.276654-121356263.235031 -124593657.3484380.491534 1.873129-115270344.708573 -118507739.3580900.734483 5.581467370970100-112378431.194948 -115615815.2988130.877667 3.607033-110538932.083842 -113776323.0160450.883040 1.904145-105833440.777108 -109070837.2142731.172143 3.276654-121356195.9299

18、37 -124593590.0622500.491538 1.873122-115270230.646590 -118507625.3496710.734489 5.581470370970150-112378309.974257 -115615694.0875740.877674 3.607036-110539018.487752 -113776409.4687930.883035 1.904154-105833347.832055 -109070744.3007271.172151 3.276654-121356128.620118 -124593522.7697600.491541 1.

19、873115-115270116.614539 -118507511.3239220.734495 5.581473解算结果航向角：84.044250° 俯仰角：0.106980°2370996050-112315666.041511 -115553061.9058860.881332 3.608808-110583931.218062 -113821327.5208720.880426 1.908541-105785430.429212 -109022836.4591091.176331 3.276693-121321397.383424 -124558795.89855

20、50.493303 1.869613-115211096.508565 -118448497.3794160.737475 5.582947370996100-112315545.435233 -115552941.3216640.881339 3.608811-110584018.233235 -113821414.5533740.880421 1.908549-105785338.394751 -109022744.4404021.176339 3.276693-121321330.602946 -124558729.1369810.493306 1.869606-115210982.69

21、3923 -118448383.5663490.737481 5.582950370996150-112315424.844709 -115552820.7279890.881346 3.608815-110584105.237380 -113821501.5685470.880416 1.908558-105785246.361866 -109022652.4153941.176347 3.276693-121321263.828769 -124558662.3722570.493309 1.869599-115210868.877705 -118448269.7595830.737487

22、5.582952370996200-112315304.244733 -115552700.1453420.881353 3.608818-110584192.252553 -113821588.5915970.880411 1.908566-105785154.332131 -109022560.3919611.176355 3.276693-121321197.073497 -124558595.6185610.493313 1.869593-115210755.066213 -118448155.9512420.737493 5.582955解算结果航向角：176.305115°

23、; 俯仰角：4.122766°3371035200-112221593.076850 -115458977.5525140.886862 3.611516-110652399.678626 -113889781.5001750.876471 1.915126-105713888.261212 -108951282.6314251.182651 3.276731-121269420.925130 -124506803.2213120.495950 1.864302-115122093.051688 -118359489.2088810.741989 5.585163371035250-

24、112221473.382740 -115458857.8631300.886869 3.611519-110652487.539799 -113889869.3629240.876466 1.915134-105713797.559556 -108951191.9250431.182659 3.276731-121269354.913457 -124506737.2159400.495953 1.864295-115121979.530073 -118359375.7014460.741995 5.585166371035300-112221353.694932 -115458738.176

25、8970.886876 3.611523-110652575.410425 -113889957.2351250.876461 1.915142-105713706.857900 -108951101.2202371.182667 3.276731-121269288.912811 -124506671.2074180.495956 1.864288-115121866.027364 -118359262.1845580.742000 5.585169371035350-112221234.008699-115458618.4906650.886883 3.611526-110652663.2

26、87353 -113890045.0994490.876456 1.915151-105713616.156245 -108951010.5185811.182675 3.276731-121269222.916892 -124506605.2193760.495960 1.864282-115121752.519928 -118359148.6881500.742006 5.585171解算结果航向角：268.181213° 俯仰角：9.485320°4.12° 航向268.18°, 俯仰9.48°。每次解算用到5颗卫星, 4个历元。该表的内

27、容不仅可以证明本文方法的正确性, 而且可以为读者开展载体姿态测量相关算法研究提供实验数据和验证。图4示出了在不同的动态条件下本文方法的测姿结果。可见, 在基线不同的转速情况下(24 s/圈、15 s/圈、5 s/圈), 本文方法的测姿结果均正确而稳定, 具有良好的动态性能。而基于遗传算法的搜索方法, 在基线转速较高的情况下(15 s/圈、5 s/圈)搜索出错, 如图5所示, 这是因为进化搜索算法不能保证对全局最优解的求解, 特别是在载体运动的情况下算法搜索的成功率下降。图4 本文方法的动态测姿结果(航向角)Fig. 4 Dynamic attitude determination using

28、the method of this paper 图5 基于遗传算法的搜索方法的动态测姿结果Fig. 5 Dynamic attitude determination results based on Genetic Algorithm (GA)5 结 论提出了一种逆向求解整周模糊度的载体姿态测量方法。采用进化算法(粒子群算法)搜索得到基线的初始姿态角, 并由此求解出双差整周模糊度N, 此后再基于N实时计算基线姿态。该方法避开了直接求解整周模糊度, 可实现性好, 同时基于整周模糊度的姿态计算又可以保证测姿的稳定性。实验结果表明该方法不仅具有很高的测姿精度, 而且具有良好的稳定性和动态性能, 适

29、用于动态载体姿态测量。参考文献: 1 刘基余. GPS卫星导航定位原理和方法M. 北京: 科学出版社, 2003.LIU J Y. Satellite navigation and positioning principles and methodsM. Beijing: Science Press, 2003.2 许江宁. 基于遗传算法的GPS姿态测量技术研究D. 东南大学, 2002.XU J N.Research of attitude determination technology based on genetic algorithmD. Southeast University ,

30、 2002.3 COUNSELMAN C, GOUREVITCH S. Miniature interferometer terminals for earth surveying: ambiguity and multipath with the global positioning system J. IEEE Transactions on Geoscience and Remote Sensing, 1981, 19(4): 244-252.4 HATCH R. The GPS carrier phase ambiguity resolution.5 FREI E, BEUTLER G

31、. Rapid static positioning based on the fast ambiguity resolution approach “FARA”: theory and first results J. Manuscripta Geodaetica, 15(4): 325-356.6 CHEN D. Fast ambiguity search filter (FASF): a novel concept from GPS ambiguity resolution A. Proceedings of the ION GPS-93C, 1993, 781-787.7 TEUNIS

32、SEN P. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation J. Journal of Geodesy, 1995, 70(4): 65-82.8 ZHAO Z, GAO Q, HU W. An efficient method for carrier phase ambiguity resolution in GPS attitude determination A. Proceedings of the IET Internat

33、ional Conference on Wireless Mobile and Multimedia Networks C, 2006: 376.9 LUO X, OU J, YUAN Y. Regularization approach for fast integer ambiguity resolution of medium-long baseline GPS network RTK J. Transactions of Nanjing University of Aeronautics and Astronautics, 2006, 23(3): 235-242.10 TARO K,

34、 YUJI K, KOJI O, et al. Fast ambiguity resolution by a combined system of multiple-baseline equations A. Proceedings of the 19th International Technical Meeting of the Satellite Division C, 2006: 286-291.11 蔡英杰, 向敬成. GPS接收机用于两点间精密测距方法的研究J. 电子测量与仪器学报, 1999, 13(3): 6-10.CAI Y J, XIANG J CH. On point-t

35、o-point precise ranging by using two GPS receivers J. Journal of Electronic Measurement and Instrument, 1999,13(3): 6-10.12 许江宁, 万德钧, 王庆,等. 基于遗传算法的GPS姿态测量技术J. 中国惯性技术学报, 2002, 10(4): 9-13. XU J N, WAN D J, WANG Q,et al.A new technique of GPS attitude determination based on Genetic AlgorithmJ. Journal

36、 of Chinese Inertial Technology, 2002,10(4): 9-13.13 SHEN M. GPS attitude determination technology research based on floating-coding genetic algorithm J. Journal of Projectiles, Rockets, Missiles and Guidance. 2007, 27(1): 21-24.夏 娜14 周红进, 许江宁, 李方能. GPS卫星位置计算及精度鉴定方法研究J. 计算机测量与控制, 2005, 13(11): 1177-

37、 1179.ZHOU H J, XU J N, LI F N. Research on GPS position calculation and precision checkup method computer automated measurement & controlJ. 2005, 13(11): 1177-1179.作者简介: 李玉海李玉海: 现为合肥工业大学信息安全专业学生, 研究方向为GPS导航信息处理。E-mail: LiyuhaiansinLi Yuhai: is a student in Information Security major in Hefei University of Technology. His research interest is in navigation information processing.夏 娜: