Impact of Decorrelation on Search Efficiency of Ambiguity Resolution

doi:10.11947/j.AGCS.2015.20140311

Abstract

Abstract:

The decorrelation performance of LAMBDA algorithm, LLL algorithm and Seysen algorithm are analyzed with evaluation indexes, i.e., condition number, orthogonal defect and S(A). Moreover, relationships between decorrelation performance of the above algorithms and ambiguity search efficiency are evaluated using theoretical and practical validation, respectively. The results validate that there is no inevitable relation between decorrelation performance of variance-covariance matrix of original ambiguity and search efficiency, whereas, traditional views consider that search efficiency can be enhanced just by improving decorrelation performance. Further analysis shows that the essence to improving search efficiency major depends on the permutation of basis vectors according to a certain direction.

Key words: integer ambiguity, decorrelation, lattice reduction, assessment criterion, search efficiency

CLC Number:

P228

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.

References

[1] TEUNISSENP J G, JONGEP J D, TIBERIUSC C J M. The Least-squares Ambiguity Decorrelation Adjustment: A Method for Fast GPS Integer Ambiguity Estimation[J]. Journal of Geodesy, 1995, 70(1): 65-82.
[2] TEUNISSENP J G. A New Method for Fast Carrier Phase Ambiguity Estimation[C]//Proceedings of the IEEE PLANS'94. Las Vegas: [s.n.], 1994.
[3] LIU L T, HSU H T, ZHU Y Z, et al. A New Approach to GPS Ambiguity Decorrelation[J]. Journal of Geodesy, 1999, 73(1): 478-490.
[4] XU P L. Random Simulation and GPS Decorrelation[J]. Journal of Geodesy, 2001, 75(1): 408-423.
[5] XU P L. Parallel Cholesky-based Reduction for the Weighted Integer Least Squares Problem[J]. Journal of Geodesy, 2012, 86(1): 35-52.
[6] 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.
[7] ZHOU Y M. A New Practical Approach to GNSS High-dimensional Ambiguity Decorrelation[J]. GPS Solutions, 2011, 15(1): 325-331.
[8] 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. (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.)
[9] ZHOU Yangmei, LIU Jingnan, LIU Jiyu. Return-calculating LAMBDA Approach and Its Search Space[J]. Acta Geodaetica et Cartographica Sinica, 2005, 34(4): 300-304. (周扬眉, 刘经南, 刘基余. 回代解算的LAMBDA方法及其搜索空间[J]. 测绘学报, 2005, 34(4): 300-304.)
[10] LENSTR A K, LENSTRA H W, LOVASZ L. Factoring Polynomials with Rational Coefficients[J]. Mathematische Annalen, 1982, 261(4): 515-534.
[11] YU Xingwang. Multi-frequency GNSS Precise Positioning Theory and Method Research[D]. Wuhan: Wuhan University, 2011. (于兴旺. 多频GNSS精密定位理论与方法研究[D]. 武汉: 武汉大学, 2011.)
[12] 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.
[13] BORNO M A, CHANG X W, XIE X. On “Decorrelation” in Solving Integer Least-squares Problems for Ambiguity Determination[J]. Survey Review, 2014, 46: 37-49.
[14] HASSIBI A, BOYD S. Integer Parameter Estimation in Linear Models with Applications to GPS[J]. IEEE Transactions on Signal Processing, 1998, 46(11): 2938-2952.
[15] GRAFAREND E W. Mixed Integer-real Valued Adjustment(IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm[J]. GPS Solutions, 2000, 4(2): 31-43.
[16] FAN Long, ZHAI Guojun, CHAI Hongzhou. Ambiguity Decorrelation Algorithm with Integer Block Orthogonalization[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(8): 818-826. (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.)
[17] LIU Zhiping, HE Xiufeng. An Improved LLL Algorithm for GPS Ambiguity Solution[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(3): 286-289. (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.)
[18] LIU Jingnan, YU Xingwang, ZHANG Xiaohong. GNSS Ambiguity Resolution Using Lattice Theory[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 636-645. (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.)
[19] LANNES A. On the Theoretical Link between LLL-reduction and LAMBDA Decorrelation[J]. Journal of Geodesy, 2013, 87(4): 323-335.
[20] SEYSEN M. Simultaneous Reduction of a Lattice Basis and Its Reciprocal Basis[J].Combinatorica, 1993, 13(3): 262-376.
[21] LU Liguo. The Research and Analysis Based on Sphere Search for Ambiguity on Reduction[D]. Wuhan: Wuhan University, 2013. (卢立果. 基于球形搜索的模糊度格基规约方法研究与分析[D]. 武汉: 武汉大学: 2013.)
[22] WANG J, FENG Y M. Orthogonality Defect and Reduced Search-space Size for Solving Integer Least-squares Problems[J]. GPS Solutions, 2013, 17(1): 261-274.
[23] GOLUB G H, VAN LOANC F. Matrix Computations[M]. YUAN Yaxiang, trans. Beijing: Science Press, 2001. (戈卢布 G H,范洛恩 C F. 矩阵计算[M]. 袁亚湘, 译. 北京: 科学出版社, 2001.)
[24] TEUNISSEN P J G. Success Probability of Integer GPS Ambiguity Rounding and Bootstrapping[J]. Journal of Geodesy, 1998, 72(10): 606-612.