Article
Initial Results of Modeling and Improvement of BDS-2/GPS
Broadcast Ephemeris Satellite Orbit Based on BP and PSO-BP
Neural Networks
Hanlin Chen
1
, Fei Niu
2
, Xing Su
1,3,
* , Tao Geng
4
, Zhimin Liu
1
and Qiang Li
1
Citation: Chen, H.; Niu, F.; Su, X.;
Geng, T.; Liu, Z.; Li, Q. Initial Results
of Modeling and Improvement of
BDS-2/GPS Broadcast Ephemeris
Satellite Orbit Based on BP and
PSO-BP Neural Networks. Remote
Sens. 2021, 13, 4801. https://doi.org/
10.3390/rs13234801
Academic Editors:
Damian Wierzbicki and
Kamil Krasuski
Received: 6 September 2021
Accepted: 24 November 2021
Published: 26 November 2021
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1
College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;
201982020022@sdust.edu.cn (H.C.); liuzhimin@sdust.edu.cn (Z.L.); 202083020033@sdust.edu.cn (Q.L.)
2
Beijing Satellite Navigation Center, Beijing 100094, China; niufei009@163.com
3
Key Laboratory of Geomatics and Digital Technology of Shandong Province, Shandong University of Science
and Technology, Qingdao 266590, China
4
GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China; gt_gengtao@whu.edu.cn
* Correspondence: suxing@sdust.edu.cn; Tel.: +86-532-8605-8006
Abstract:
With the rapid development and gradual perfection of GNSS in recent years, improving
the real-time service performance of GNSS has become a research hotspot. In GNSS single-point
positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit
parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate
the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research
background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm
Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast
ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that
the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the
results of the two models were roughly the same. The one-day and three-day improvement rates of
RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of
errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural
network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP
neural network model results were better than those of the BP neural network. In the GEO satellite
outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were
reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO
satellite results showed that the PSO–BP neural network model output accuracy of the along- and
radial-track directions experienced a 70–80% improvement in one and three days. The one- and
three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater
ability to resist gross errors than that of the BP neural network for modeling the changing trend
of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to
model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy
of broadcast ephemeris.
Keywords: satellite orbit error; neural network; PSO; AODE; BDS
1. Introduction
With the construction of GNSS in recent years, single-point positioning as one of the
main functions of GNSS has become a research hotspot [
1
–
3
]. In single-point positioning
and navigation, the accuracy of broadcast ephemeris is very important [
4
,
5
]. Currently, the
accuracy of GPS and BDS is evaluated from multiple aspects based on MGEX broadcast
ephemeris and precision ephemeris. The overall orbit accuracy of GPS is better than 0.3 m,
the clock error of the RMS is better than 0.4 m, and the SISRE (Signal-In-Space Range Error)
of the RMS is better than 0.5 m; for BDS, the overall orbit accuracy of BDS-2 is better than
Remote Sens. 2021, 13, 4801. https://doi.org/10.3390/rs13234801 https://www.mdpi.com/journal/remotesensing
