Single-baseline global navigation satellite system (GNSS) data are able to be processed into a batch of parameters such as positions, timing information as well as atmospheric delays. The applications of relevance, therefore, consist of relative positioning, time and frequency transfer and so forth. To achieve real-time capability, these parameters are usually estimated by means of Kalman-filter. Moreover, the reliability of these parameters can be further strengthened by forming and then successfully fixing a set of independent double-differenced (DD) integer ambiguities. For this purpose, the filter function model is commonly set up based on the DD observation equations (DD filter model). In order to preserve the continuity of the filter, DD filter model needs to explicitly refer to another pivot satellite once the previous one becomes invisible. This thereby implies that, before being predicted to the next epoch, the former filtered DD ambiguity vector has to be “mapped” with respect to the newly-defined pivot satellite. In addition to that, the estimated receiver phase clocks using DD filter model may soak up distinct between-receiver single-differenced (SD) ambiguities belonging to different pivot satellites and would thereby be subject to apparent “integer jumps”. In this contribution, SD observation equations involving estimable DD ambiguity parameters are alternatively selected as the filter function model (SD filter model). Our analyses suggest that, both DD and SD filter models are equivalent in theory, but differ from each other as far as their implementations are concerned. Typically, for SD filter model, no effort should be made to map DD ambiguities, thus implying less intensive computational burden and better flexibility than DD filter model. At the same time, receiver phase clocks determined by SD filter model are free from “integer jumps” and thus are particularly beneficial for frequency transfer.
[1] WANG Qianxin, XU Tianhe, XU Guochang. Adaptively Changing Reference Station Algorithm and Its Application in GPS Long Range Airborne Kinematic Relative Positioning [J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4): 429-434. (王潜心, 徐天河, 许国昌. 自适应换站算法及其在长距离机载 GPS 动态相对定位中的应用[J]. 测绘学报, 2011, 40(4): 429-434.)
[2] WEI Ziqing, GE Maorong. Mathematical Models for GPS Relative Positioning [M]. Beijing: Surveying and Mapping Press, 1998. (魏子卿, 葛茂荣. GPS 相对定位的数学模型[M]. 北京: 测绘出版社, 1998.)
[3] HU Congwei. The Basic Models for Short GPS Baseline and Data Process Methods for GPS Kinematic Positioning [J]. Acta Geodaetica et Cartographica Sinica, 2000, 29(3): 282-285. (胡丛玮. GPS短基线模型与动态定位[J]. 测绘学报, 2000, 29(3): 282-285.)
[4] GAO Xingwei, LIU Jingnan, GE Maorong. An Ambiguity Searching Method for Network RTK Baselines between Base Stations at Single Epoch [J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(4): 305-309. (高星伟, 刘经南, 葛茂荣. 网络 RTK 基准站间基线单历元模糊度搜索方法[J]. 测绘学报, 2002, 31(4): 305-309.)
[5] RIZOS C. Network RTK Research and Implementation—A Geodetic Perspective [J]. Journal of Global Positioning Systems, 2002, 1(2): 144-150.
[6] ZHANG Xiaohong, CAI Shixiang, LI Xingxing, et al. Accuracy Analysis of Time and Frequency Transfer Based on Precise Point Positioning [J]. Geomatics and Information Science of Wuhan University, 2010, 35(3): 274-278. (张小红, 蔡诗响, 李星星, 等. 利用GPS精密单点定位进行时间传递精度分析[J]. 武汉大学学报: 信息科学版, 2010, 35(3): 274-278.)
[7] HUANG Guanwen, YANG Yuanxi, ZHANG Qin, et al. A New Continuous Time and Frequency Transfer Algorithm Based on GPS Single Different Carrier Phase Observations [J]. Geomatics and Information Science of Wuhan University, 2013, 38(9): 1018-1022. (黄观文, 杨元喜, 张勤, 等. 一种单差观测值的连续实时载波相位时频传递方法[J]. 武汉大学学报: 信息科学版, 2013, 38(9): 1018-1022.)
[8] GUO Hairong, YANG Sheng, YANG Yuanxi, et al. Numerical Prediction Methods for Clock Difference Based on Two-way Satellite Time and Frequency Transfer Data[J]. Geomatics and Information Science of Wuhan University, 2007, 32(1): 43-46. (郭海荣, 杨生, 杨元喜, 等. 基于卫星双向时间频率传递进行钟差预报的方法研究[J]. 武汉大学学报: 信息科学版, 2007, 32(1): 43-46.)
[9] DEFRAIGNE P, BAIRE Q. Combining GPS and GLONASS for Time and Frequency Transfer [J]. Advances in Space Research, 2011, 47(2): 265-275.
[10] BRUYNINX C, DEFRAIGNE P, SLEEWAEGEN J M. Time and Frequency Transfer Using GPS Codes and Carrier Phases: Onsite Experiments [J]. GPS Solutions, 1999, 3(2): 1-10.
[11] LI Wei, CHENG Pengfei, BEI Jinzhong, et al. Calibration of Regional Ionospheric Delay with Uncombined Precise Point Positioning and Accuracy Assessment [J]. Journal of Earth System Science, 2012, 121(4): 989-999.
[12] ZHANG Baocheng, OU Jikun, YUAN Yunbin, et al. Calibration of Slant Total Electron Content and Satellite-receiver's Differential Code Biases with Uncombined Precise Point Positioning Technique [J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(4): 447-453. (张宝成, 欧吉坤, 袁运斌, 等. 利用非组合精密单点定位技术确定斜向电离层总电子含量和站星差分码偏差[J]. 测绘学报, 2011, 40(4): 447-453.)
[13] JIANG Weiping, ZOU Xuan, TANG Weiming. A New Kind of Real-time PPP Method for GPS Single-frequency Receiver Using CORS Network [J]. Chinese Journal of Geophysical Research, 2012, 55(5): 1549-1556. (姜卫平, 邹璇, 唐卫明. 基于CORS网络的单频GPS实时精密单点定位新方法[J]. 地球物理学报, 2012, 55(5): 1549-1556.)
[14] YANG Yuanxi, JING Yifan, ZENG Anmin. Adaptive Parameter Estimation and Inner and External Precision [J]. Acta Geodaetica et Cartographica Sinica, 2013, 43(5): 441-445. (杨元喜, 景一帆, 曾安敏. 自适应参数估计与内外部精度的关系[J]. 测绘学报, 2014, 43(5): 441-445.)
[15] YANG Yuanxi, LI Jinlong, XU Junyi, et al. Contribution of the Compass Satellite Navigation System to Global PNT Users [J]. Chinese Science Bulletin, 2011, 56(26): 2813-2819. (杨元喜, 李金龙, 徐君毅, 等. 中国北斗卫星导航系统对全球PNT用户的贡献[J]. 科学通报, 2011, 56(21): 1734-1740.)
[16] ZOU Xuan, GE Maorong, TANG Weiming, et al. URTK: Undifferenced Network RTK Positioning [J]. GPS Solutions, 2013, 17(3): 283-293.
[17] XU Guochang. GPS—Theory, Algorithms and Applications [M]. Heidelberg: Springer, 2003.
[18] DE JONGE P J. A Processing Strategy for the Application of the GPS in Networks [D]. Delft: Delft University of Technology, 1998.
[19] LI Zhenghang, HUANG Jinsong. GPS Surveying and Data Processing [M]. Wuhan: Wuhan University Press, 2005. (李征航, 黄劲松. GPS 测量与数据处理[M]. 武汉: 武汉大学出版社, 2005.)
[20] LIU Jingnan YE Shirong. GPS Precise Point Positioning Using Undifferenced Phase Observation [J]. Geomatics and Information Science of Wuhan University, 2002, 27(3): 234-240. (刘经南, 叶世榕. GPS 非差相位精密单点定位技术探讨 [J]. 武汉大学学报: 信息科学版, 2002, 27(3): 234-240.)
[21] TEUNISSEN P.Zero Order Design:Generalized Inverses,Adjustment, the Datum roblem and S-transformations [C]//GRAFAREND E W, SANSÒ F. Optimization and Design of Geodetic Networks.Berlin: Springer, 1985: 11-55.
[22] ZHANG Xiaohong, LI Pan, LI Xingxing, et al. An Analysis of Time-varying Property of Widelane Carrier Phase Ambiguity Fractional Bias [J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(6): 798-803. (张小红, 李盼, 李星星, 等. 宽巷载波相位模糊度小数偏差估计及其时变特性分析. 测绘学报, 2013, 42(6): 798-803.)
