Evaluation and analysis of stochastic modeling of BeiDou GEO/IGSO/MEO satellite observation

doi:10.11947/j.AGCS.2020.20190492

Abstract

Abstract: Firstly, the importance of stochastic model in precise positioning is demonstrated from the perspectives of parameter estimation, accuracy evaluation and quality control. Then, based on the single-difference functional model, the rigorous variance component estimation (VCE) method is used to allow the estimation of satellite-specific variances, cross correlations between two arbitrary frequencies, as well as the time correlations for phase and c+ode observations per frequency. The influence of the stochastic model on baseline precisions and the overall statistics was subsequently analyzed. The results show that the observation precisions of the BeiDou user receiver are overall elevation-dependent for phase and code of all frequencies. It is recommended to use the elevation-dependent exponent weighting model; there are different degrees of correlation between the three frequency phase observations, and the cross correlation between other types of observations is not obvious. The time correlation between phase and code observations of different frequencies is obvious, and attention should be paid to high-precision positioning. Furthermore,the baseline precisions that used the correct stochastic model match the theoretical ones very well for the three baseline components. The paper provides support for users to correctly understand the three types of satellite observation of the BeiDou system and correctly apply the BeiDou system.

Key words: stochastic model, cross correlation, time correlation, BeiDou system, quality control

CLC Number:

P228

GAO Weiguang, MIAO Weikai, CHEN Gucang, JIA Song. Evaluation and analysis of stochastic modeling of BeiDou GEO/IGSO/MEO satellite observation[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(12): 1511-1522.

References

[1] 杨元喜. 抗差估计理论及其应用[M]. 北京:八一出版社, 1993. YANG Yuanxi. Robust estimation and its applications[M]. Beijing:Bayi Publishing House, 1993.
[2] TEUNISSEN P J G. Testing theory:an introduction[M].2nd ed. Delft:Delft University Press, 2006.
[3] AMIRI-SIMKOOEI A R, ZANGENEH-NEJAD F, ASGARI J. Least-squares variance component estimation applied to GPS geometry-based observation model[J]. Journal of Surveying Engineering, 2013, 139(4):176-187.
[4] TEUNISSEN P J G, AMIRI-SIMKOOEI A R. Least-squares variance component estimation[J]. Journal of Geodesy, 2008, 82(2):65-82.
[5] AMIRI-SIMKOOEI A R, TEUNISSEN P J G, TIBERIUS C C J M. Application of least-squares variance component estimation to GPS observables[J]. Journal of Surveying Engineering, 2009, 135(4):149-160.
[6] TIBERIUS C C J M, KENSELAAR F. Estimation of the stochastic model for GPS code and phase observables[J]. Survey Review, 2000, 35(277):441-454.
[7] EUELER H J, GOAD C C. On optimal filtering of GPS dual frequency observations without using orbit information[J]. Bulletin Géodésique, 1991, 65(2):130-143.
[8] WANG Jinling, STEWART M P, TSAKIRI M. Stochastic modeling for static GPS baseline data processing[J]. Journal of Surveying Engineering, 1998, 124(4):171-181.
[9] LI Bofeng, SHEN Yunzhong, XU Peiliang. Assessment of stochastic models for GPS measurements with different types of receivers[J]. Chinese Science Bulletin, 2008, 53(20):3219-3225.
[10] 李博峰, 沈云中, 楼立志. GPS中长基线观测值随机特性分析[J]. 武汉大学学报(信息科学版), 2010, 35(2):176-180. LI Bofeng, SHEN Yunzhong, LOU Lizhi. Analysis of the stochastic characteristics for medium and long base line GPS measurements[J]. Geomatics and Information Science of Wuhan University, 2010, 35(2):176-180.
[11] 何海波, 杨元喜. GPS观测量先验方差-协方差矩阵实时估计[J]. 测绘学报, 2001, 30(1):42-47. DOI:10.3321/j.issn:1001-1595.2001.01.009. HE Haibo, YANG Yuanxi. Real-time estimation of a prior variance-covariance for GPS observations[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(1):42-47. DOI:10.3321/j.issn:1001-1595.2001.01.009.
[12] LI Bofeng. Stochastic modeling of triple-frequency BeiDou signals:estimation, assessment and impact analysis[J]. Journal of Geodesy, 2016, 90(7):593-610.
[13] LI Bofeng, ZHANG Lei, VERHAGEN S. Impacts of BeiDou stochastic model on reliability:overall test, w-test and minimal detectable bias[J]. GPS Solutions, 2017, 21(3):1095-1112.
[14] YANG Yuanxi, GAO Weiguang, GUO Shuren, et al. Introduction to BeiDou-3 navigation satellite system[J]. Navigation, 2019, 66(1):7-18.
[15] ZHANG Zhiteng, LI Bofeng, NIE Liangwei, et al. Initial assessment of BeiDou-3 global navigation satellite system:signal quality, RTK and PPP[J]. GPS Solutions, 2019, 23(4):111.
[16] YANG Yuanxi, MAO Yue, SUN Bijiao. Basic performance and future developments of BeiDou global navigation satellite system[J]. Satellite Navigation, 2020, 1(1):1-8.
[17] HELMERT F. Die Ausgleichung nach der Methode der kleinsten quadrate[J]. Auflage, Verlagvon BG Teubner, Leipzig/Berlin, 1907.
[18] 王新洲, 刘经南, 陶本藻. 稳健最优不变二次无偏估计[J]. 武汉测绘科技大学学报, 1995, 20(3):240-245. WANG Xinzhou, LIU Jingnan, TAO Benzao. Robust best invariant quadratic unbiased estimation[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1995, 20(3):240-245.
[19] 於宗俦. Helmert型方差-协方差分量估计的通用公式[J]. 武汉测绘科技大学学报, 1991, 16(2):8-17. YU Zongchou. The general formulas of Helmert type for estimating variance and covarince components[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1991, 16(2):8-17.
[20] RAO C R. Estimation of variance and covariance components-MINQUE theory[J]. Journal of Multivariate Analysis, 1971, 1(3):257-275.
[21] KOCH K R. Parameter estimation and hypothesis testing in linear models[M].Berlin:Springer-Verlag, 1988.
[22] 朱建军. 方差分量的Bayes估计[J]. 测绘学报, 1991, 20(1):1-6. ZHU Jianjun. Bayes estimation of the components of variance[J]. Acta Geodaetica et Cartographica Sinica, 1991, 20(1):1-6.
[23] 李博峰, 沈云中, 楼立志. 基于等效残差的方差-协方差分量估计[J]. 测绘学报, 2010, 39(4):349-354, 363. LI Bofeng,SHEN Yunzhong, LOU Lizhi. Variance-covariance component estimation based on the equivalent residuals[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(4):349-354, 363.
[24] BONA P. Precision, cross correlation, and time correlation of GPS phase and code observations[J]. GPS Solutions, 2000, 4(2):3-13.
[25] XU Peiliang, LIU Jingnan. Variance components in errors-in-variables models:estimability, stability and bias analysis[J]. Journal of Geodesy, 2014, 88(8):719-734.
[26] LI Bofeng, ZHANG Zhetao. Several kinematic data processing methods for time-correlated observations[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(4):1-9.