Additional nonlinear baseline length constraint is often used for GNSS dynamic relative positioning, but the LAMBDA method can only deal with linear constraint model. So, it is necessary to linearize and approximate nonlinear constraint conditions. Linearized approximate constraint usually increases the success rate of fixing integer ambiguity, but for the ultra-short baseline, the opposite results may be derived. When will the linearized approximate baseline length constraint can improve the success rate of fixing ambiguity? This article attempts to answer these questions. Firstly, the float solution's maximum influence value formula is derived when using linearized approximate baseline length constraint, based on GNSS relative positioning model; Secondly, a discriminant condition is given to determine whether baseline length constraint can be linear approximation. When the condition is met, the influence can be ignored, linearized approximate baseline length constraint can improve the accuracy of float solution and increase the success rate of fixing ambiguity,on the contrast, the influence may not be ignored, linear approximation will result in a biased float solution and the ambiguity cannot be fixed correctly; At last, the foregoing conclusions are verified with some numerical example in this paper.
NIE Zhixi
,
WANG Zhenjie
,
OU Jikun
,
JI Shengyue
. On the Effect of Linearization and Approximation of Nonlinear Baseline Length Constraint for Ambiguity Resolution[J]. Acta Geodaetica et Cartographica Sinica, 2015
, 44(2)
: 168
-173
.
DOI: 10.11947/j.AGCS.2015.20130491
[1] WANG B, MIAO L, WANG S, et al. A Constrained LAMBDA Method for GPS Attitude Determination[J]. GPS Solutions, 2009, 13(2): 97-107.
[2] TEUNISSEN P J G. Integer Least-Squares Theory for the GNSS Compass[J]. Journal of Geodesy, 2010, 84(7): 433-447.
[3] TEUNISSEN P J, GIORGI G, BUIST P J. Testing of a New Single-frequency GNSS Carrier Phase Attitude Determination Method: Land, Ship and Aircraft Experiments[J]. GPS Solutions,2011, 15(1): 15-28.
[4] CHEN W, QIN H. New Method for Single Epoch, Single Frequency Land Vehicle Attitude Determination Using Low-end GPS Receiver[J]. GPS Solutions, 2012, 16(3): 329-338.
[5] KROES R, MONTENBRUCK O, BERTIGER W, et al. Precise GRACE Baseline Determination Using GPS[J]. GPS Solutions, 2005, 9(1): 21-31.
[6] ARDAENS J S, D'AMICO S, MONTENBRUCK O. Flight Results from the PRISMA GPS-based Navigation[C]//Proceedings of the 5th ESA Workshop on Satellite Navigation Technologies. Noordwijk:[s.n.],2010:8-10.
[7] MONTENBRUCK O, WERMUTH M, KAHLE R. GPS Based Relative Navigation for the TanDEM-X Mission First Fight Results[J]. Navigation, 2011, 58(4): 293-304.
[8] HAN Baoming, OU Jikun. A GPS Single Epoch Phase Processing Algorithm with Constraints for Single-frequency Receivers[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(4):300-304. (韩保明, 欧吉坤. 一种附约束的单频单历元GPS双差相位解算方法[J]. 测绘学报, 2002, 31(4) : 300 - 304.)
[9] YU Xuexiang,XU Shaoquan,LU Weicai.The Research of Single Epoch Algorithm for GPS Deformation Monitor Information[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2): 123-127.(余学祥, 徐绍铨, 吕伟才. GPS 变形监测信息的单历元解算方法研究[J]. 测绘学报, 2002, 31(2): 123-127.)
[10] TANG Weiming,SUN Hongxing,LIU Jingnan. Ambiguity Resolution of Single Epoch Single Frequency Data with Baseline Length Constraint Using LAMBDA Algorithm[J].Geomatics and Information Science of Wuhan University, 2005, 30(5): 444-446.(唐卫明, 孙红星, 刘经南. 附有基线长度约束的单频数据单历元LAMBDA方法整周模糊度确定[J].武汉大学学报:信息科学版, 2005, 30(5): 444-446.)
[11] LI Zhenghang,LIU Wanke,LOU Yidong, et al. Heading Determination Algorithm with Single Epoch Dual-frequency GPS Data[J].Geomatics and Information Science of Wuhan University, 2007, 32(9): 753-756.(李征航, 刘万科, 楼益栋, 等. 基于双频GPS数据的单历元定向算法研究[J]. 武汉大学学报: 信息科学版, 2007, 32(9): 753-756.)
[12] LI Bofeng, SHEN Yunzhong. Fast GPS Ambiguity Resolution Constraint to Available Conditions[J]. Geomatics and Information Science of Wuhan University,2009, 34(1): 117-121.(李博峰, 沈云中. 附有约束条件的GPS模糊度快速解算[J]. 武汉大学学报: 信息科学版, 2009, 34(1): 117-121.)
[13] HOFMANN-WELLENHOF B, LICHTENEGGER H, WASLE E. GNSS: Global Navi-gation Satellite Systems: GPS, GLONASS, Galileo, and More[M]. Berlin:Springer, 2007.
[14] SU Yucai, JIANG Cuibo, ZHANG Yuehui. Matrix Theory[M]. Beijing: Science Press, 2006. (苏育才,姜翠波,张跃辉.矩阵理论[M]. 北京: 科学出版社, 2006.)
[15] TEUNISSEN P J G. The Least-squares Ambiguity Decorrelation Adjustment: A Method for Fast GPS Integer Ambiguity Estimation[J]. Journal of Geodesy, 1995, 70(2): 65-82.
[16] TEUNISSEN P J G, DE JONGE P J, TIBERIUS C C J M. Performance of the LAMBDA Method for Fast GPS Ambiguity Resolution[J]. Navigation, 1997,44(3): 373-383.
[17] TEUNISSEN P J G. An Optimality Property of the Integer Least-squares Estimator[J]. Journal of Geodesy, 1999,73(11):587-593.
[18] CHANG X W, YANG X, ZHOU T. MLAMBDA: A Modified LAMBDA Method for Integer Least-squares Estimation[J]. Journal of Geodesy, 2005, 79(9): 552-565.
[19] XU Guochang. GPS Theory,Algorithms and Application[M].LI Qiang,LIU Guangjun,YU Hailiang,et al, trans. 2nd ed. Beijing: Tsinghua University Press, 2011.(许国昌.GPS理论、算法与应用[M]. 李强, 刘广军, 于海亮, 等, 译.第2版.北京: 清华大学出版社, 2011.)
[20] WANG Songgui, WU Mixia, JIA Zhongzhen. Matric Inequalities[M]. 2nd ed.Beijing: Science Press, 2006. (王松桂, 吴密霞, 贾忠贞. 矩阵不等式[M]. 第2版.北京: 科学出版社, 2006.)
[21] SHENG Zhou, XIE Shiqian, PAN Chengyi. Probability Theory and Mathematical Statistics[M].4th ed. Hangzhou:Zhejiang University Press, 2008. (盛骤, 谢式千, 潘承毅. 概率论与数理统计[M].第4版.杭州: 浙江大学出版社, 2008.)
