一种改进型的GPS单频整周模糊度快速解算方法

doi:10.3969/j.issn.1000-1093.2012.11.018

兵工学报 ›› 2012, Vol. 33 ›› Issue (11): 1387-1392.doi: 10.3969/j.issn.1000-1093.2012.11.018

一种改进型的GPS单频整周模糊度快速解算方法

庞春雷，赵修斌，卢艳娥，余永林，严玉国

(空军工程大学信息与导航学院，陕西西安 710077)

收稿日期:2011-05-19 修回日期:2011-05-19 上线日期:2014-01-10
作者简介:庞春雷（1986—），男，博士研究生
基金资助:
国家自然科学基金项目（61071014）

An Improved Method for Rapid Ambiguity Calculation Using Single Frequency GPS Receiver

PANG Chun-lei, ZHAO Xiu-bin， LU Yan-e， YU Yong-lin， YAN Yu-guo

(Information and Navigation College, Air Force Engineering University, Xi’an 710077, Shaanxi, China)

Received:2011-05-19 Revised:2011-05-19 Online:2014-01-10

摘要/Abstract

摘要： 针对高精度的快速定位中观测矩阵存在病态性问题，研究了单频GPS整周模糊度快速解算方法。依据Tikhonov正则化原理和奇异值分解(SVD)的扰动性质，设计了SVD分解的改进算法，避免了因较小奇异值发生较大抖动而使正则化矩阵出现不稳定的情况；在分析法矩阵病态性特点的基础上，设计了正则化矩阵的构造方法，并从理论上证明了其优越性。实验结果表明，与传统方法和Tikhonov正则化-LAMBDA法相比，新算法能更有效地改善法矩阵的病态性，只利用3～5个历元即能实现模糊度浮点解的快速解算及其固定，且结果可靠，浮点值更加接近真实值。

关键词: 飞行器控制、导航技术, 整周模糊度, 浮点值, 奇异值, 改善正则化矩阵, 病态矩阵

Abstract: Aimed at ill-condition observation matrix in precise rapid positioning, a new algorithm for ambiguity resolution using single frequency GPS receiver was studied. According to the principle of Tikhonov regularized algorithm and the perturbation theory of singular value decomposition, an improved algorithm for singular value decomposition (SVD) was designed, and then the non-stabilization on regularized matrix caused by little singular values was avoided. The improved regularized matrix was educed, the construction method was established on the basis of analyzing the characteristics of ill-condition matrix, and it was proved theoretically. The experiment results indicate that the improved algorithm is more effective to improve ill-condition observation matrix, comparing with conventional LAMBDA algorithm and Tikhonov regularized-LAMBDA algorithm; the more precise floating-point and fixing-point solutions can be acquired quickly and credible.

Key words: control and navigation technology of aircraft, integer ambiguity, floating-point, singular value, improved regularized matrix, ill-condition matrix

中图分类号:

V557

庞春雷，赵修斌，卢艳娥，余永林，严玉国. 一种改进型的GPS单频整周模糊度快速解算方法[J]. 兵工学报, 2012, 33(11): 1387-1392.

PANG Chun-lei, ZHAO Xiu-bin， LU Yan-e， YU Yong-lin， YAN Yu-guo. An Improved Method for Rapid Ambiguity Calculation Using Single Frequency GPS Receiver[J]. Acta Armamentarii, 2012, 33(11): 1387-1392.

参考文献

［1］谢钢. GPS原理与接收机设计[M]. 北京: 电子工业出版社, 2009.
XIE Gang. Principles of GPS and receiver design[M]. Beijing: Publishing House of Electronics Industry, 2009. (in Chinese)
[2] Frei E, Beulter G. Rapid static positioning based on the fast ambiguity resolution approach FARA, theory and first results[J]. Manuscript Geodaetica, 1990, 15(6): 325-356.
[3] Hatch R. Instantaneous ambiguity resolution. proceedings of kinematic systems in geodesy, surveying, and remote sensing[C]∥IAG Symposium 107. Banff: International Association of Geodesy, 1990: 299-308.
[4] Euler H, Landau H. Fast GPS ambiguity resolution on-the-fly for real-time application[C]∥The 6th International Geodetic Symposium on Satellite Positioning. Columbus：Global Positioning Systems Society Inc，1992： 17-20.
[5] Kim D, Langley R. An optimized least-squares technique for improving ambiguity resolution and computational efficiency[C]∥ION GPS.Salt Lake City: Institute of Navigation, 1999: 1579-1588.
[6] Teunissen P. The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation[J]. Journal of Geodesy，1995, 70(1): 65-82.
[7] Teunissen P J G. The LAMBDA method for the GNSS compass[J]. Artificial Satellites, 2006, 41(3): 89-103.
[8] Kubo N, Pullen S. Instantaneous RTK positioning based on user velocity measurements[C]∥ION GNSS.Savannah, Georgia: Institute of Navigation, 2008: 1406-1417.
[9] Teunissen P J G, Verhagen S. GNSS ambiguity resolution: when and how to fix or not to fix?[C]∥A symposium on Theoretical and Computational Geodesy. Springer,Berlin: International Association of Geodesy Symposia, 2008: 143-148.
[10] Nobuaki Kubo. Advantage of velocity measurements on instantaneous RTK positioning[J]. GPS Solutions, 2009， 13（4）：271-280.
[11] Wang B, Miao L J, Wang S T, et al. A constrained LAMBDA method for GPS attitude determination[J]. GPS Solutions, 2009,13(2): 97-107.
[12] 李屹旭, 张俊. GPS双差基线模型的有偏估计解法研究[J]. 贵州大学学报:自然科学版, 2009, 26(4): 50-52.
LI Yi-xu, ZHANG Jun. Research on using the biased estimator to resolve GPS double-difference base-line model[J]. Journal of Guizhou University: Natural Sciences, 2009,26(4): 50-52. (in Chinese)
[13] 欧吉坤, 王振杰.单频GPS快速定位中模糊度解算的一种新方法[J]. 科学通报, 2003,48(24): 2572-2575.
OU Ji-kun, WANG Zhen-jie. A new method of ambiguity resolution in single frequency GPS quickly positioning[J]. Chinese Science Bulletin, 2003, 48(24): 2572-2575. (in Chinese)
[14] 刘立龙, 刘基余, 李光成. 单频GPS整周模糊度动态快速求解的研究[J]. 武汉大学学报:信息科学版, 2005, 30 (10): 885-887.
LIU Li-long, LIU Ji-yu, LI Guang-cheng. Rapid ambiguity resolution on-the-fly for single frequency receiver[J]. Geomantic and Information Science of Wuhan University：Information Science Edition, 2005, 30(10): 885-887. (in Chinese)
[15] 柯福阳, 王庆, 潘树国. 网络RTK参考站间模糊度动态解算中病态方程的一种解算算法[J]. 中国惯性技术学报, 2008, 16(6): 676-681.
KE Fu-yang, WANG Qing, PAN Shu-guo. A method of ill-posed equation resolution for ambiguity resolution on-the-fly in network RTK reference station[J]. Journal of Chinese Inertial Technology, 2008,16(6): 676-681. (in Chinese)
[16] Sauer T. 数值分析[M]. 王国荣, 徐兆亮，译. 北京：人民邮电出版社, 2010.
Sauer T. Numerical analysis[M]. WANG Guo-rong, XU Zhao-liang, translated. Beijing: Posts & Telecom Press, 2010.
(in Chinese)
[17] 马振华.现代应用数学手册:计算与数值分析卷[M]. 北京: 清华大学出版社, 2007.
MA Zhen-hua. Modern application mathematic manual (calculating and numerical analysis)[M]. Beijing: Tsinghua University Press, 2007. (in Chinese)

[1]	黄文宽, 钱林方, 尹强, 刘太素. 基于迁移学习的供药装置故障诊断方法[J]. 兵工学报, 2023, 44(10): 2964-2974.
[2]	陆瑶敏, 龚建伟, 王博洋, 关海杰. 基于多重示范的智能车辆运动基元表征与序列生成[J]. 兵工学报, 2021, 42(4): 851-861.
[3]	李金朋，范红波，张英堂，李志宁，尹刚. 斜磁化条件下多磁源目标的边界识别方法[J]. 兵工学报, 2020, 41(10): 2033-2044.
[4]	李金朋，张英堂，范红波，李志宁，张光. 强剩磁条件下磁性目标三维正则化聚焦反演方法[J]. 兵工学报, 2018, 39(11): 2202-2210.
[5]	潘江怀，乔慧. 多传感器空间配准的病态性及其稳健估计[J]. 兵工学报, 2017, 38(10): 1965-1973.
[6]	张民，陈亮，陈欣. 基于简便约束粒子群优化算法的空空导弹μ-PID控制器设计[J]. 兵工学报, 2017, 38(1): 89-96.
[7]	胡东方，姬源浩. 基于灰关联决策的模块化光电吊舱可靠性分析[J]. 兵工学报, 2016, 37(8): 1506-1516.
[8]	张松, 侯明善. 飞行器轨迹优化的造型降维方法[J]. 兵工学报, 2016, 37(6): 1125-1130.
[9]	李强，卢宝刚，王晓辉，王永海，庄凌. 一种导弹终端侵彻多约束最优制导方法[J]. 兵工学报, 2016, 37(6): 1131-1137.
[10]	张翼飞，董受全，毕开波. 基于Hough变换和聚类的舰艇编队队形识别算法[J]. 兵工学报, 2016, 37(4): 648-655.
[11]	王红辉，杨绍卿，吴成富，郝峰，车晓涛. 旋转矢量在高动态全姿态飞行器运动方程中的应用[J]. 兵工学报, 2016, 37(3): 439-446.
[12]	张尧，郭杰，唐胜景，商巍，张浩强. 机动目标拦截含攻击角约束的新型滑模制导律[J]. 兵工学报, 2015, 36(8): 1443-1457.
[13]	李成，李建勋，童中翔，贾林通，张志波. 红外成像制导末端局部图像识别跟踪研究[J]. 兵工学报, 2015, 36(7): 1213-1221.
[14]	赵江，周锐. 基于倾侧角反馈控制的预测校正再入制导方法[J]. 兵工学报, 2015, 36(5): 823-830.
[15]	范世鹏，林德福，姚怀瑾，路宇龙，祁载康. 基于最优二次型理论的滚转导弹三回路驾驶仪设计与研究[J]. 兵工学报, 2015, 36(5): 831-838.

一种改进型的GPS单频整周模糊度快速解算方法

An Improved Method for Rapid Ambiguity Calculation Using Single Frequency GPS Receiver

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价