Conditional variance stationarity evaluation method for GNSS ambiguity decorrelation

doi:10.11947/j.AGCS.2020.20190417

Abstract

Abstract: GNSS ambiguity decorrelation is to optimize the permutation order of conditional variance by integer transformation, so as to improve the search efficiency. One of the key problems is how to evaluate the relationship between decorrelation and conditional variance. Aiming at this problem, this paper theoretically analyzes the numerical relationship between decorrelation and conditional variance after sorting. It is found that the decorrelation performance is related to the stationarity of the conditional variance sequence. The stronger the decorrelation performance, the more stable the conditional variance sequence. So based on this theoretical basis, the conditional variance stationarity is proposed as an index to evaluate the performance of decorrelation. The results are verified by both simulation and actual test experiments, and the conditional variance trend graph as well as search time are also used to qualitatively and quantitatively evaluate the performance of decorrelation, to determine the rationality of the conditional variance stationarity. The experimental results show that the conditional variance stationarity proposed in this paper can more accurately and intuitively measure the performance of ambiguity decorrelation. The index defined in this paper reveal the essence of GNSS ambiguity decorrelation.

Key words: GNSS, ambiguity, decorrelation, conditional variance, evaluation index

CLC Number:

P228

LU Liguo, LIU Wanke, LU Tieding, MA Liye, WU Tangting, YANG Yuanxi. Conditional variance stationarity evaluation method for GNSS ambiguity decorrelation[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(8): 955-964.

References

[1] ABIDIN H Z. On the construction of the ambiguity searching space for on-the-fly ambiguity resolution[J]. Navigation, 1993, 40(3):321-338.
[2] FREI E, BEUTLER G. Rapid static positioning based on the fast ambiguity resolution approach FARA:theory and first results[J]. Manuscripta Geodaetica, 1990, 15(6):325-356.
[3] EULER H J, LANDAU H. Fast GPS ambiguity resolution on-the-fly for real-time applications[C]//Proceedings of the 6th International Geodetic Symposium on Satellite Positioning. Ohio:[s.n.], 1992:650-659.
[4] CHEN Dingsheng. Development of a fast ambiguity search filtering (FASF) method for GPS carrier phase ambiguity resolution[D]. Calgary:University of Calgary, 1994.
[5] TEUNISSEN P J G. The least-squares ambiguity decorrelation adjustment:a method for fast GPS integer ambiguity estimation[J]. Journal of Geodesy, 1995, 70(1-2):65-82.
[6] TEUNISSEN P J G. An optimality property of the integer least-squares estimator[J]. Journal of Geodesy, 1999, 73(11):587-593.
[7] VERHAGEN S, LI Bofeng, TEUNISSEN P J G. Ps-LAMBDA:ambiguity success rate evaluation software for interferometric applications[J]. Computers & Geosciences, 2013, 54:361-376.
[8] LIU L T, HSU H T, ZHU Y Z, et al. A new approach to GPS ambiguity decorrelation[J]. Journal of Geodesy, 1999, 73(9):478-490.
[9] XU Peiliang. Random simulation and GPS decorrelation[J]. Journal of Geodesy, 2001, 75(7-8):408-423.
[10] XU Peiliang. Parallel Cholesky-based reduction for the weighted integer least squares problem[J]. Journal of Geodesy, 2012, 86(1):35-52.
[11] ZHOU Yangmei. A new practical approach to GNSS high-dimensional ambiguity decorrelation[J]. GPS Solutions, 2011, 15(4):325-331.
[12] TEUNISSEN P J G. A new method for fast carrier phase ambiguity estimation[C]//Proceedings of 1994 IEEE Position, Location and Navigation Symposium-PLANS'94. Las Vegas:IEEE, 1994:562-573.
[13] WANG Jun, FENG Yanming. Orthogonality defect and reduced search-space size for solving integer least-squares problems[J]. GPS Solutions, 2013, 17(2):261-274.
[14] WU Zemin, LI Houpu, BIAN Shaofeng. Cycled efficient V-BLAST GNSS ambiguity decorrelation and search complexity estimation[J]. GPS Solutions, 2017, 21(4):1829-1840.
[15] DENG Zhongliang, ZHU Di, YIN Lu. N-dimensional LLL reduction algorithm with pivoted reflection[J]. Sensors (Basel), 2018, 18(1):283.
[16] 楼立志. 对GPS模糊度解相关方法的一种改进[J]. 同济大学学报, 2004, 32(2):237-241. LOU Lizhi. One modified LLL algorithm in GPS decorrelation[J]. Journal of Tongji University, 2004, 32(2):237-241.
[17] 刘志平, 何秀凤. 改进的GPS模糊度降相关LLL算法[J]. 测绘学报, 2007, 36(3):286-289. DOI:10.3321/j.issn:1001-1595.2007.03.008. LIU Zhiping, HE Xiufeng. An improved LLL algorithm for GPS ambiguity solution[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(3):286-289. DOI:10.3321/j.issn:1001-1595.2007.03.008.
[18] 刘志平, 何秀凤, 郭广礼, 等. GNSS模糊度降相关算法及其评价指标研究[J]. 武汉大学学报(信息科学版), 2011, 36(3):257-261. LIU Zhiping, HE Xiufeng, GUO Guangli, et al. Decorrelation algorithms and its evaluation indexes for GNSS ambiguity solution[J]. Geomatics and Information Science of Wuhan University, 2011, 36(3):257-261.
[19] 杨荣华, 花向红, 李昭, 等. GPS模糊度降相关LLL算法的一种改进[J]. 武汉大学学报(信息科学版), 2010, 35(1):21-24. YANG Ronghua, HUA Xianghong, LI Zhao, et al. An improved LLL algorithm for GPS ambiguity solution[J]. Geomatics and Information Science of Wuhan University, 2010, 35(1):21-24.
[20] 刘宁, 熊永良, 冯威, 等. 单频GPS动态定位中整周模糊度的一种快速解算方法[J]. 测绘学报, 2013, 42(2):211-217. LIU Ning, XIONG Yongliang, FENG Wei, et al. An algorithm for rapid integer ambiguity resolution in single frequency GPS kinematical positioning[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(2):211-217.
[21] 范龙, 翟国君, 柴洪洲. 模糊度降相关的整数分块正交化算法[J]. 测绘学报, 2014, 43(8):818-826. FAN Long, ZHAI Guojun, CHAI Hongzhou. Ambiguity decorrelation with integer block orthogonalization algorithm[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(8):818-826.
[22] BORNO M A, CHANG Xiaowen, XIE X H. On "Decorrelation" in solving integer least-squares problems for ambiguity determination[J]. Survey Review, 2014, 46(334):37-49.
[23] JAZAERI S, AMIRI-SIMKOOEI A R, SHARIFI M A. On lattice reduction algorithms for solving weighted integer least squares problems:comparative study[J]. GPS Solutions, 2014, 18(1):105-114.
[24] 卢立果, 刘万科, 李江卫. 降相关对模糊度解算中搜索效率的影响分析[J]. 测绘学报, 2015, 44(5):481-487. DOI:10.11947/j.AGCS.2015.20140311. LU Liguo, LIU Wanke, LI Jiangwei. Impact of decorrelation on search efficiency of ambiguity resolution[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(5):481-487. DOI:10.11947/j.AGCS.2015.20140311.
[25] 谢恺, 柴洪洲, 范龙, 等. 一种改进的LLL模糊度降相关算法[J]. 武汉大学学报(信息科学版), 2014, 39(11):1363-1368. XIE Kai, CHAI Hongzhou, FAN Long, et al. An improved LLL ambiguity decorrelation algorithm[J]. Geomatics and Information Science of Wuhan University, 2014, 39(11):1363-1368.
[26] 吕浩, 吕志平, 翟树峰, 等. 一种改进的LLL模糊度规约算法[J]. 中国惯性技术学报, 2017, 25(5):611-617. LÜ Hao, LÜ Zhiping, ZHAI Shufeng, et al. Improved LLL ambiguity reduction algorithm[J]. Journal of Chinese Inertial Technology, 2017, 25(5):611-617.
[27] CHANG Xiaowen, YANG X, ZHOU T. MLAMBDA:a modified LAMBDA method for integer least-squares estimation[J]. Journal of Geodesy, 2005, 79(9):552-565.
[28] 刘经南, 于兴旺, 张小红. 基于格论的GNSS模糊度解算[J]. 测绘学报, 2012, 41(5):636-645. LIU Jingnan, YU Xingwang, ZHANG Xiaohong. GNSS ambiguity resolution using the lattice theory[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5):636-645.
[29] 刘万科, 卢立果, 单弘煜. 一种快速解算高维模糊度的LLL分块处理算法[J]. 测绘学报, 2016, 45(2):147-156. DOI:10.11947/j.AGCS.2016.20150370. LIU Wanke, LU Liguo, SHAN Hongyu. A new block processing algorithm of LLL for fast high-dimension ambiguity resolution[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(2):147-156. DOI:10.11947/j.AGCS.2016.20150370.
[30] 卢立果, 鲁铁定, 吴汤婷, 等. 下三角Cholesky分解的整数高斯变换算法[J]. 测绘科学, 2017, 42(12):57-62, 76. LU Liguo, LU Tieding, WU Tangting, et al. Integer Gauss transformation algorithm based on low triangular Cholesky decomposition[J]. Science of Surveying and Mapping, 2017, 42(12):57-62, 76.
[31] AGRELL E, ERIKSSON T, VARDY A, et al. Closest point search in lattices[J]. IEEE Transactions on Information Theory, 2002, 48(8):2201-2214.
[32] LI Bofeng, VERHAGEN S, TEUNISSEN P J G. GNSS integer ambiguity estimation and evaluation:LAMBDA and Ps-LAMBDA[C]//Proceeding of 2013 China Satellite Navigation Conference (CSNC). Berlin:Springer, 2013:291-301.
[33] 刘万科, 马立烨, 卢立果, 等. 一种改进的SEVB整数模糊度搜索算法[J]. 测绘学报, 2018, 47(1):17-24. DOI:10.11947/j.AGCS.2018.20170227. LIU Wanke, MA Liye, LU Liguo, et al. A modified SEVB integer ambiguity search algorithm[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(1):17-24. DOI:10.11947/j.AGCS.2018.20170227.
[34] 卢立果. GNSS整数最小二乘模糊度解算理论与方法研究[D]. 武汉:武汉大学, 2017. LU Liguo. Study on theory and method of GNSS integer least squares ambiguity resolution[D]. Wuhan:Wuhan University, 2017.