航空学报 > 2012, Vol. 33 Issue (1): 102-109   doi: CNKI:11-1929/V.20110921.0830.002

基于改进型UDVT分解的单频整周模糊度快速解算

庞春雷, 赵修斌, 卢艳娥, 余永林, 严玉国   

  1. 空军工程大学 电讯工程学院, 陕西 西安 710077
  • 收稿日期:2011-05-03 修回日期:2011-06-28 出版日期:2012-01-25 发布日期:2012-01-16
  • 通讯作者: 卢艳娥 E-mail:lu_yan_e@sina.com
  • 作者简介:庞春雷 男,博士研究生.主要研究方向: 卫星导航的高精度定位定姿技术及组合导航技术. Tel: 029-84791511 E-mail: chunleipcl@yahoo.com.cn
    赵修斌 男,教授,博士生导师.主要研究方向: 无线电导航着陆、通信领域信道环境、系统仿真技术、卫星导航等. Tel: 029-84791511 E-mail: zhaoxiubin926@163.com
  • 基金资助:

    国家自然科学基金(61071014);电院科研创新基金(DYCX1001)

Algorithm of Rapid Integer Ambiguity Resolution for Single Frequency GPS Receivers Based on Improved UDVT Decomposition

PANG Chunlei, ZHAO Xiubin, LU Yan'e, YU Yonglin, YAN Yuguo   

  1. College of Telecommunication Engineering, Air Force Engineering University, Xi'an 710077, China
  • Received:2011-05-03 Revised:2011-06-28 Online:2012-01-25 Published:2012-01-16

摘要: 基于全球定位系统(GPS)快速定位中观测矩阵的病态性特点和Tikhonov正则化原理,研究了单频整周模糊度快速解算的改进方法.基于奇异值扰动理论,研究了改进型UDVT分解算法,即利用病态观测矩阵构造新的矩阵,然后化为上Hessenberg形式的三对角矩阵,利用移位QR算法得到精确的奇异值,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,设计了改善正则化矩阵的构造方法.实验结果表明,与传统最小二乘降相关平差(LAMBDA)算法和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: 全球定位系统, 整周模糊度, 浮点值, 病态矩阵, UDVT分解, 改善正则化矩阵

Abstract: Based on the ill-condition observation matrix and the principle of Tikhonov regularizer algorithm, an improved method of global positioning system (GPS) rapid ambiguity resolution using single frequency receivers is studied. Based on the wobble principle of singular values, an improved algorithm of UDVT decomposition is proposed. A new matrix is constructed by the observation matrix, and turned to upper Hessenberg 3-diagonal-matrix. Then accurate singular values are acquired using the shifting QR algorithm, and the non-stabilization of the regularizer matrix is avoided which is caused by small singular values. The improved regularizer matrix is deduced and the construction method is designed based on an analysis of the characteristics of the ill-condition matrix. Experiment results indicate that the improved method is more effective on improving ill-condition observation matrices as compared with the conventional least-squares ambiguity decorrelation adjustment (LAMBDA) algorithm and Tikhonov regularizer-LAMBDA algorithm, and more precise floating-point and fixing-point are acquired quickly and reliably by just 3-5 epochs.

Key words: global positioning system, integer ambiguity, floating-point, ill-condition matrix, UDVT decomposition, improved regularizer matrix

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