GNSS Partial Ambiguity Resolution Based on Posterior Probability and Minimum Squares Error Solution

doi:10.11947/j.AGCS.2018.20180295

Abstract

Abstract: GNSS partial ambiguity resolution (PAR) is usually used in weak GNSS positioning model to gain an acceptable position solution. In order to further improve the positioning precise of PAR, this contribution modifies RAR from 3 aspects. ① Whether an element of the ambiguity vector is fixed is determined by the posterior probability instead of the Bootstrapping success rate. For the reason that posterior probability is based on data and model simultaneously, whereas Bootstrapping success rate is only determined by GNSS positioning model. ②In the ambiguity partially fixed cases, the minimum squares error (MSE) solution of unfixed elements is calculated by the correlation with other fixed ones. However, traditional PAR treats them as conditional float solutions. ③ In the ambiguity totally unfixed cases, the MSE solution of the whole ambiguity vector is used to take the place of its float solution. In the experiment, a set of BDS real observed data are used to testify the property of traditional and new PAR. The results show that the partial fixed and unfixed cases for our new PAR method are less than that for the traditional one, and the position precise is sufficiently improved.

Key words: GNSS, partial ambiguity resolution, positioning precise, posterior probability, MSE

CLC Number:

P228

WU Zemin, BIAN Shaofeng. GNSS Partial Ambiguity Resolution Based on Posterior Probability and Minimum Squares Error Solution[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(S0): 54-60.

References

[1] WU Zemin, BIAN Shaofeng, JI Bing, et al. Short Baseline GPS Multi-frequency Single-epoch Precise Positioning:Utilizing A New Carrier Phase Combination Method[J]. GPS Solutions, 2016, 20(3):373-384.
[2] 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.
[3] TEUNISSEN P J G, JOOSTEN P, TIBERIUS C C J M. Geometry-free Ambiguity Success Rates in Case of Partial Fixing[C]//Proceedings of 1999 National Technical Meeting of the Institute of Navigation. San Diego, CA:[s.n.], 1999:201-207.
[4] 潘宗鹏, 柴洪洲, 刘军, 等. 基于部分整周模糊度固定的非差GPS精密单点定位方法[J]. 测绘学报, 2015, 44(11):1210-1218. PAN Zongpeng, CHAI Hongzhou, LIU Jun, et al. GPS Partial Ambiguity Resolution Method for Zero-difference Precise Point Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(11):1210-1218.
[5] DAI L, ESLINGER D, SHARPE T. Innovative Algorithms to Improve Long Range RTK Reliability and Availability[C]//Proceedings of 2007 National Technical Meeting of the Institute of Navigation. San Diego, CA:Institute of Navigation, 2007:860-872.
[6] PARKINS A. Increasing GNSS RTK Availability with A New Single-Epoch Batch Partial Ambiguity Resolution Algorithm[J]. GPS Solutions, 2011, 15(4):391-402.
[7] KHANAFSEH S, PERVAN B. New Approach for Calculating Position Domain Integrity Risk for Cycle Resolution in Carrier Phase Navigation Systems[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(1):296-307.
[8] VERHAGEN S, TEUNISSEN P J G, VAN DER MAREL H, et al. GNSS Ambiguity Resolution:Which Subset to Fix?[C]//Proceedings of IGNSS Symposium 2011. Sydney, Australia:University of New South Wales, 2011.
[9] HOU Yanqing, VERHAGEN S. Model and Data Driven Partial Ambiguity Resolution for Multi-constellation GNSS[M]//SUN Jiadong, JIAO Wenhai, WU Haitao, et al. China Satellite Navigation Conference (CSNC) 2014 Proceedings:Volume Ⅱ. Berlin, Heidelberg:Springer, 2014:285-302.
[10] EULER H J, SCHAFFRIN B. On A Measure for the Discernibility between Different Ambiguity Solutions in the Static-kinematic GPS-mode[M]//SCHWARZ K P, Lachapelle G. Kinematic Systems in Geodesy, Surveying, and Remote Sensing. New York, NY:Springer, 1991:285-295.
[11] 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. 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.
[12] TEUNISSEN J P 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.
[13] TEUNISSEN P J G. An Optimality Property of the Integer Least-squares Estimator[J]. Journal of Geodesy, 1999, 73(11):587-593.
[14] BLEWITT G. Carrier Phase Ambiguity Resolution for the Global Positioning System Applied to Geodetic Baselines up to 2000 km[J]. Journal of Geophysical Research, 1989, 94(B8):10187-10203.
[15] 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. DOI:10.3321/j.issn:1001-1595.2005.04.004. 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. DOI:10.3321/j.issn:1001-1595.2005.04.004.
[16] 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. DOI:10.13485/j.cnki.11-2089.2014.0094. FAN Long, ZHAI Guojun, CHAI Hongzhou. Ambiguity Decorrelation with Integer Block Orthogonalization Algorithm[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(8):818-826. DOI:10.13485/j.cnki.11-2089.2014.0094.
[17] VERHAGEN S, TEUNISSEN P J G. The Ratio Test for Future GNSS Ambiguity Resolution[J]. GPS Solutions, 2013, 17(4):535-548.
[18] ZHU J, DING X, CHEN Y. Maximum-likelihood Ambiguity Resolution Based on Bayesian Principle[J]. Journal of Geodesy, 2001, 75(4):175-187.
[19] WU Zemin, BIAN Shaofeng. GNSS Integer Ambiguity Validation Based on Posterior Probability[J]. Journal of Geodesy, 2015, 89(10):961-977.
[20] DE JONGE P, TIBERIUS C C J M. LAMBDA Method for Integer Ambiguity Estimation:Implementation Aspects[R]. Delft:Delft University of Technology, 1996.