Citation: Zhao, B.; Xiong, Y.
Evaluating the Performance of Two
Inter-Frequency Code Bias (IFCB)
Models in Combined Precise Point
Positioning (PPP). Remote Sens. 2022,
14, 1476. https://doi.org/10.3390/
rs14061476
Academic Editors: Damian
Wierzbicki and Kamil Krasuski
Received: 26 February 2022
Accepted: 17 March 2022
Published: 18 March 2022
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Article
Evaluating the Performance of Two Inter-Frequency Code Bias
(IFCB) Models in Combined Precise Point Positioning (PPP)
Ban Zhao and Yongliang Xiong *
Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China;
banzhao@my.swjtu.edu.cn
* Correspondence: yl-xiong@swjtu.edu.cn
Abstract:
The main purpose of this article is to evaluate the comprehensive performance of two inter-
frequency code bias (IFCB) models using undifferenced and uncombined observations. These two
IFCB models estimate IFCB parameters for each GLONASS satellite (EG model) and IFCB parameters
using a quadratic function of frequency channels K (K =
−
7
. . .
6) (QF model). The data sampled
in 30 s from 140 stations of the IGS network on 1–7 September 2021, are used for this study. We
analyze all the combinations, including the GLONASS data, from the perspective of positioning
accuracy, convergence time, and data utilization. The results show that the positioning accuracy of
these two IFCB models for the same combination is comparable in three directions in both static and
kinematic modes under long-term observation; the positioning accuracies of each IFCB model for all
the combinations are almost the same in three directions in static mode, and the positioning accuracy
of the combinations including the GPS data in three directions is better than that of the combinations
not including the GPS data for kinematic mode. For some combinations, such as GLONSS-only and
GPS/GLONASS, the convergence time of the EG model is better than that of the QF model, but the
improvement rate does not exceed 22%. However, for other combinations, such as GLONASS/BDS
and GLONASS/BDS/GALILEO, the convergence time of the QF model is better than that of the
EG model, and the improvement rate in some directions is more than 50%. For the combinations
including GPS data, the data utilization of the EG and QF models are almost the same for both static
and kinematic modes; however, for combinations without GPS data, the data utilization of the QF
model is better than that of the EG model. For these two IFCB models (EG and QF models), all
combinations can achieve the set accuracy thresholds in three directions, but the EG model has more
parameters to estimate than the QF model. From the perspectives of positioning accuracy, solution
convergence time, data utilization, and the number of estimated parameters for each IFCB model, we
suggest that the IFCB should be estimated using the QF model when performing combined PPP for
different combinations.
Keywords:
precise point positioning (PPP); undifferenced and uncombined observations; inter-
frequency code bias (IFCB)
1. Introduction
Precise point positioning (PPP) is a prevalent technology first proposed in 1997 [
1
].
Its good stability and high accuracy have been widely used for various applications [
2
,
3
].
Although the performance of PPP has been greatly improved in recent years, the long
convergence time of PPP still limits its application in time-critical fields. Multisystem
integration increases the number of available satellites and is an effective way to improve
PPP performance. The global positioning system (GPS), which is the first component
of the global navigation satellite system (GNSS), has achieved great success in geodesy,
geophysics, atmospheric sciences, navigation, positioning, and timing [
3
]. In addition,
error correction models for GPS are increasingly precise and accurate. Next, the global
navigation satellite system of Russia (GLONASS) was revitalized in October 2011 and
Remote Sens. 2022, 14, 1476. https://doi.org/10.3390/rs14061476 https://www.mdpi.com/journal/remotesensing
