Page 177 - 卫星导航2021年第1-2合期

Zhang et al. Satell Navig (2021) 2:11 Satellite Navigation
https://doi.org/10.1186/s43020-021-00040-4
https://satellite-navigation.springeropen.com/

ORIGINAL ARTICLE Open Access

Functional model modifcation of precise

point positioning considering the time-varying

code biases of a receiver

1,2
1*
1
3
Baocheng Zhang , Chuanbao Zhao , Robert Odolinski and Teng Liu

Abstract
Precise Point Positioning (PPP), initially developed for the analysis of the Global Positing System (GPS) data from a
large geodetic network, gradually becomes an efective tool for positioning, timing, remote sensing of atmospheric
water vapor, and monitoring of Earth’s ionospheric Total Electron Content (TEC). The previous studies implicitly
assumed that the receiver code biases stay constant over time in formulating the functional model of PPP. In this
contribution, it is shown this assumption is not always valid and can lead to the degradation of PPP performance,
especially for Slant TEC (STEC) retrieval and timing. For this reason, the PPP functional model is modifed by taking into
account the time-varying receiver code biases of the two frequencies. It is diferent from the Modifed Carrier-to-Code
Leveling (MCCL) method which can only obtain the variations of Receiver Diferential Code Biases (RDCBs), i.e., the dif-
ference between the two frequencies’ code biases. In the Modifed PPP (MPPP) model, the temporal variations of the
receiver code biases become estimable and their adverse impacts on PPP parameters, such as ambiguity parameters,
receiver clock ofsets, and ionospheric delays, are mitigated. This is confrmed by undertaking numerical tests based
on the real dual-frequency GPS data from a set of global continuously operating reference stations. The results imply
that the variations of receiver code biases exhibit a correlation with the ambient temperature. With the modifed
functional model, an improvement by 42% to 96% is achieved in the Diferences of STEC (DSTEC) compared to the
original PPP model with regard to the reference values of those derived from the Geometry-Free (GF) carrier phase
4
4
observations. The medium and long term (1 × 10 to 1.5 × 10 s) frequency stability of receiver clocks are also signif-
cantly improved.
Keywords: Global positioning system, International GNSS service, Precise point positioning, Receiver code bias, Slant
total electron content, Timing

Introduction clock products provided by the International GNSS
In exploring the potential of Global Positioning System (Global Navigation Satellite System) Service (IGS)
(GPS) for a variety of applications, Precise Point Posi- (Kouba and Héroux 2001). Te PPP can deliver various
tioning (PPP) has been developed as a tool for process- types of parameters, including station positions, receiver
ing code and phase observations from a stand-alone clock ofsets, Zenith Troposphere Delays (ZTDs), and
GPS receiver at the undiferenced level (Zumberge et al. slant ionosphere delays, which are of great importance
1997a) along with the use of precise satellite orbit and for practical uses. Te positioning accuracy is at the level
of a few centimeters in static mode and below one deci-
meter in kinematic mode (Bisnath and Gao 2009). Tis
*Correspondence: b.zhang@whigg.ac.cn
1 State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation suggests PPP can be used for crustal deformation mon-
Academy for Precision Measurement Science and Technology, Chinese itoring (Wright et al. 2012; Xu et al. 2013), marine sur-
Academy of Sciences, Wuhan, China veying (Alkan and Öcalan 2013; Geng et al. 2010), and
Full list of author information is available at the end of the article

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and
the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material
in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material
is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the
permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco
mmons. org/ licen ses/ by/4. 0/.