Citation: Shi, C.; Tian, Y.; Zheng, F.;
Hu, Y. Accounting for Signal
Distortion Biases for Wide-Lane and
Narrow-Lane Phase Bias Estimation
with Inhomogeneous Networks.
Remote Sens. 2022, 14, 191. https://
doi.org/10.3390/rs14010191
Academic Editor: Kamil Krasuski
Received: 29 November 2021
Accepted: 29 December 2021
Published: 1 January 2022
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Article
Accounting for Signal Distortion Biases for Wide-Lane and
Narrow-Lane Phase Bias Estimation with
Inhomogeneous Networks
Chuang Shi
1,2,3
, Yuan Tian
1,3
, Fu Zheng
2,3,
* and Yong Hu
1,3
1
School of Electronic and Information Engineering, Beihang University, 37 Xueyuan Road,
Beijing 100083, China; shichuang@buaa.edu.cn (C.S.); by2002139@buaa.edu.cn (Y.T.);
Yong@buaa.edu.cn (Y.H.)
2
Research Institute for Frontier Science, Beihang University, 37 Xueyuan Road, Beijing 100083, China
3
Key Laboratory of Satellite Navigation and Mobile Communication Fusion Technology, Ministry of Industry
and Information Technology, Beijing 100083, China
* Correspondence: fzheng@buaa.edu.cn
Abstract:
Due to different designs of receiver correlators and front ends, receiver-related pseudorange
biases, called signal distortion biases (SDBs), exist. Ignoring SDBs that can reach up to 0.66 cycles
and 10 ns in Melbourne-Wübbena (MW) and ionosphere-free (IF) combinations can negatively affect
phase bias estimation. In this contribution, we investigate the SDBs and evaluate the impacts on
wide-lane (WL) and narrow-lane (NL) phase bias estimations, and further propose an approach to
eliminating these SDBs to improve phase bias estimation. Based on a large data set of 302 multi-
global navigation satellite system (GNSS) experiment (MGEX) stations, including 5 receiver brands,
we analyze the characteristics of these SDBs The SDB characteristics of different receiver types for
different GNSS systems differ from each other. Compared to the global positioning system (GPS)
and BeiDou navigation satellite system (BDS), SDBs of Galileo are not significant; those of BDS-3
are significantly superior to BDS-2; Septentrio (SEPT) receivers show the most excellent consistency
among all receiver types. Then, we apply the corresponding corrections to phase bias estimation
for GPS, Galileo and BDS. The experimental results reveal that the calibration can greatly improve
the performance of phase bias estimation. For WL phase biases estimation, the consistencies of WL
phase biases among different networks for GPS, Galileo, BDS-2 and BDS-3 improve by 89%, 77%,
76% and 78%, respectively. There are scarcely any improvements of the fixing rates for Galileo due
to its significantly small SDBs, while for GPS, BDS-2 and BDS-3, the WL ambiguity fixing rates can
improve greatly by 13%, 27% and 14% after SDB calibrations with improvements of WL ambiguity
fixing rates, the corresponding NL ambiguity fixing rates can further increase greatly, which can
reach approximately 16%, 27% and 22%, respectively. Additionally, after the calibration, both WL
and NL phase bias series become more stable. The standard deviations (STDs) of WL phase bias
series for GPS and BDS can improve by more than 46%, while those of NL phase bias series can yield
improvements of more than 13%. Ultimately, the calibration can make more WL and NL ambiguity
residuals concentrated in ranges within
±
0.02 cycles. All these results demonstrate that SDBs for
phase bias estimation cannot be ignored and must be considered when inhomogeneous receivers
are used.
Keywords: BDS-3; multi-GNSS; phase biases; signal distortion biases; ambiguity resolution
1. Introduction
Precise point positioning (PPP) is a high-precision positioning technique that can
achieve centimeter-level positioning with a single receiver [
1
]. However, undifferenced am-
biguities cannot be estimated as integers directly, thus limiting the application of
PPP [2,3]
.
Remote Sens. 2022, 14, 191. https://doi.org/10.3390/rs14010191 https://www.mdpi.com/journal/remotesensing
