Several Kinematic Data Processing Methods for Time-Correlated Observations

doi:10.11947/j.JGGS.2019.0401

Journal of Geodesy and Geoinformation Science ›› 2019, Vol. 2 ›› Issue (4): 1-9.doi: 10.11947/j.JGGS.2019.0401

Several Kinematic Data Processing Methods for Time-Correlated Observations

Bofeng LI¹,Zhetao ZHANG²

^1. College of Surveying and GeoInformatics, Tongji University, Shanghai 200092, China
^2. School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China

Received:2019-06-18 Accepted:2019-10-22 Online:2019-12-20 Published:2020-01-08
About author:Bofeng LI(1983—), PhD, professor, majors in multi?frequency, multi?GNSS data processing theory and new application technologies. E-mail: bofeng_li@tongji.edu.cn
Supported by:
The National Natural Science Foundation of China Nos(41574031);The National Natural Science Foundation of China Nos(41622401);The Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee Nos(17511109501);The Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee Nos(17DZ1100802);The Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee Nos(17DZ1100902);The Fundamental Research Funds for the Central Universities(2019B03714)

Abstract

Abstract:

Time correlations always exist in modern geodetic data, and ignoring these time correlations will affect the precision and reliability of solutions. In this paper, several methods for processing kinematic time-correlated observations are studied. Firstly, the method for processing the time-correlated observations is expanded and unified. Based on the theory of maximum a posteriori estimation, the third idea is proposed after the decorrelation transformation and differential transformation. Two types of situations with and without common parameters are both investigated by using the decorrelation transformation, differential transformation and maximum a posteriori estimation solutions. Besides, the characteristics and equivalence of above three methods are studied. Secondly, in order to balance the computational efficiency in real applications and meantime effectively capture the time correlations, the corresponding reduced forms based on the autocorrelation function are deduced. Finally, with GPS real data, the correctness and practicability of derived formulae are evaluated.

Key words: time correlation; kinematic solution; decorrelation transformation; differential transformation; maximum a posteriori estimation

Bofeng LI,Zhetao ZHANG. Several Kinematic Data Processing Methods for Time-Correlated Observations[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(4): 1-9.

Figures/Tables 4

References 31

[1]	HUANG Weibin. Modern Adjustment Theory and Its Application [M]. Beijing: PLA Publishing House, 1992.
[2]	YANG Yuanxi. Adaptive Navigation and Kinematic Positioning [M]. Beijing: Surveying and Mapping Press, 2006.
[3]	YANG Yuanxi, HE Haibo, XU Guochang . Adaptively Robust Filtering for Kinematic Geodetic Positioning[J]. Journal of geodesy, 2001,75(2):109-116. doi: 10.1007/s001900000157
[4]	LI Bofeng. Theory and Method of Parameter Estimation in Mixed Integer GNSS Model [M]. Beijing: Surveying and Mapping Press, 2014.
[5]	LI Bofeng, ZHANG Zhetao, SHEN Yunzhong , et al. A Procedure for the Significance Testing of Unmodeled Errors in GNSS Observations[J]. Journal of Geodesy, 2018: 1171-1186.
[6]	ZHANG Zhetao, LI Bofeng, SHEN Yunzhong . Comparison and Analysis of Unmodelled Errors in GPS and BeiDou Signals[J]. Geodesy and Geodynamics, 2017,8(1), 41-48. doi: 10.1016/j.geog.2016.09.005
[7]	GAZIT R . Digital Tracking Filters with High Order Correlated Measurement Noise[J]. IEEE Transactions on Aerospace and Electronic Systems, 1997,33(1):171-177. doi: 10.1109/7.570736
[8]	HUANG Xianyuan, SUI Lifen, FAN Pengpai . A New Approach for Colored Measurement Noises by Correcting Random Model[J]. Geomatics and Information Science of Wuhan University, 2008,33(6):644-647.
[9]	LIN Xu, LUO Zhicai, XU Chuang , et al. Autocovariance Least Squares Estimation for Colored Noise[J]. Acta Geodaetica et Cartographica Sinica, 2013,42(6):804-809.
[10]	YANG Yuanxi, XU Tianhe . An Adaptive Kalman Filter Combining Variance Component Estimation with Covariance Matrix Estimation Based on Moving Window[J]. Geomatics and Information Science of Wuhan University, 2003,28(6):714-718.
[11]	CUI Xianqiang, YANG Yuanxi, GAO Weiguang . Comparison of Adaptive Filter Arithmetics in Controlling Influence of Colored Noises[J]. Geomatics and Information Science of Wuhan University, 2006,31(8):731-735.
[12]	SONG Yingchun, ZHU Jianjun, CHEN Zhengyang . Kalman Filter for Kinematic Positioning with Timing Correlated Observation Noises[J]. Acta Geodaetica et Cartographica Sinica, 2006,35(4):328-331.
[13]	XUE Shuqiang, YANG Yuanxi . Adjustment Model and Colored Noise Compensation of Continuous Observation System[J]. Acta Geodaetica et Cartographica Sinica, 2014,43(4):360-365.
[14]	LI Bofeng . Stochastic Modeling of Triple-frequency BeiDou Signals: Estimation, Assessment and Impact Analysis[J]. Journal of Geodesy, 2016,90(7):593-610. doi: 10.1007/s00190-016-0896-7
[15]	HOWIND J, KUTTERER H, HECK B . Impact of temporal correlations on GPS-derived relative point positions[J]. Journal of Geodesy, 1999,73(5):246-258. doi: 10.1007/s001900050241
[16]	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. doi: 10.1007/s10291-016-0596-z
[17]	AMIRI-SIMKOEEI A, JAZAERI S, ZANGENEH-NEJAD F , et al. Role of Stochastic Model on GPS Integer Ambiguity Resolution Success Rate[J]. GPS solutions, 2016,20(1):51-61. doi: 10.1007/s10291-015-0445-5
[18]	CHANG Guobin . On Kalman Filter for Linear System with Colored Measurement Noise[J]. Journal of Geodesy, 2014,88(12):1163-1170. doi: 10.1007/s00190-014-0751-7
[19]	ZHAO Changsheng. Colored Noise Filtering Theory and Algorithms [M]. Beijing: Surveying and Mapping Press, 2011.
[20]	PETOVELLO M, O’KEEFE K, LACHAPELLE G, et al. Consideration of Time-correlated Errors in a Kalman Filter Applicable to GNSS[J]. Journal of Geodesy, 2009,83(1):51-56. doi: 10.1007/s00190-008-0231-z
[21]	HU Guorong, OU Jikun . The Improved Method of Adaptive Kalman Filtering for GPS High Kinematic Positioning[J]. Acta Geodaetica et Cartographica Sinica, 1999,28(4):290-294.
[22]	ZHAO Changsheng, TAO Benzao . Kalman Filtering of Linear System with Colored Noises[J]. Geomatics and Information Science of Wuhan University, 2008,33(2):180-182.
[23]	BRYSON J, HENRIKSON L . Estimation Using Sampled Data Containing Sequentially Correlated Noise[J]. Journal of Spacecraft and Rockets, 1968,5(6):662-665. doi: 10.2514/3.29327
[24]	KERMARREC G, SCHÖN S. Taking Correlations in GPS Least Squares Adjustments into Account with a Diagonal Covariance Matrix[J]. Journal of Geodesy, 2016,90(9):793-805. doi: 10.1007/s00190-016-0911-z
[25]	BONA P. Precision, Cross Correlation , Time Correlation of GPS Phase and Code Observations[J]. GPS solutions, 2000,4(2):3-13. doi: 10.1007/PL00012839
[26]	LI B, SHEN Y, XU P . Assessment of Stochastic Models for GPS Measurements with Different Types of Receivers[J]. Chinese Science Bulletin, 2008,53(20):3219-3225.
[27]	YANG Yuanxi, CUI Xianqiang . Influence Functions of Colored Noises on Kinematic Positioning—Taking the AR Model of First Class As an Example[J]. Acta Geodaetica et Cartographica Sinica, 2003,32(1):6-10.
[28]	ASHCRAFT C, GRIMES R, LEWIS J . Accurate Symmetric Indefinite Linear Equation Solvers[J]. SIAM Journal on Matrix Analysis and Applications, 1998,20(2):513-561. doi: 10.1137/S0895479896296921
[29]	GUO Jianfeng, OU Jikun, REN Chao . Partial Continuation Model and Its Application in Mitigating Systematic Errors of Double-Differenced GPS Measurements[J]. Progress in Natural Science, 2005,15(3):246-251. doi: 10.1080/10020070512331342060
[30]	ZHANG Zhetao, LI Bofeng, SHEN Yunzhong . Efficient Approximation for a Fully Populated Variance-Covariance Matrix in RTK Positioning[J]. Journal of Surveying Engineering, 2018,144(4):04018005. doi: 10.1061/(ASCE)SU.1943-5428.0000259
[31]	El-RABBANY A . The Effect of Physical Correlations on the Ambiguity Resolution and Accuracy Estimation in GPS Differential Positioning [D]. Fredericton: Department of Geodesy and Geomatics Engineering, University of New Brunswick, 1994.

No.	Mean			STD
No.	N	E	U		N	E	U
No.1	-4.01	0.72	-5.06	8.87		12.76	31.66
No.2	0.71	7.78	-41.65	17.75		15.29	41.18

Tactics	L1	L2	L1+L2
Ignoring the time correlation	47.2%	58.3%	85.7%
Considering the time correlation	55.0%	65.4%	92.2%

Several Kinematic Data Processing Methods for Time-Correlated Observations

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 4

References 31

Related Articles 0

Recommended Articles

Metrics

Comments