Citation: Kim, E.; Kim, S.-k. Global
Navigation Satellite System
Real-Time Kinematic Positioning
Framework for Precise Operation of a
Swarm of Moving Vehicles. Sensors
2022, 22, 7939. https://doi.org/
10.3390/s22207939
Academic Editors: Kamil Krasuski
and Damian Wierzbicki
Received: 10 September 2022
Accepted: 15 October 2022
Published: 18 October 2022
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Article
Global Navigation Satellite System Real-Time Kinematic
Positioning Framework for Precise Operation of a Swarm of
Moving Vehicles
Euiho Kim
1,
* and Sae-kyeol Kim
2
1
Department of Mechanical & System Design Engineering, Hongik University, Seoul 04066, Korea
2
Department of Mechanical Engineering, Hongik University, Seoul 04066, Korea
* Correspondence: euihokim@hongik.ac.kr
Abstract:
The global navigation satellite system (GNSS) real-time kinematic (RTK) technique is used
to achieve relative positioning centimeter levels among multiple agents on the move. A typical GNSS
RTK estimates the relative positions of multiple rover receivers with respect to a single-base receiver.
In a fleet of rover GNSS receivers, this approach is inefficient because each rover receiver only uses
GNSS measurements of its own and those sent from a single-base receiver. In this study, we propose
a novel GNSS RTK framework that facilitates the precise positioning of a swarm of moving vehicles
through the GNSS measurements of multiple receivers and broadcasts fixed-integer ambiguities of
GNSS carrier phases. The proposed framework not only provides efficient RTK positioning but also
reliable performance with a limited number of GNSS satellites in view. Our experimental flight tests
with six GNSS receivers showed that the systematic procedure of the proposed framework could
maintain lower than 6 cm of 3D RMS positioning errors, whereas the conventional RTK failed to
resolve the correct integer ambiguities of double difference carrier phase measurements more than
13% in five out of nine total baselines.
Keywords: global navigation satellite systems; RTK; relative position; multi agent operation
1. Introduction
Real-time kinematic (RTK) positioning of global navigation satellite systems (GNSS)
have been widely used for the realization of precise relative positions [
1
–
3
]. The RTK
system can achieve centimeter-level positioning by processing carrier phase measurements
as ranging sources. The RTK process includes integer ambiguity resolution through various
algorithms, such as the least-squares ambiguity decorrelation adjustment (LAMBDA) [
4
,
5
].
The success probability of correctly resolved integer ambiguities of LAMBDA improves
as the number of GNSS constellations and measurement frequencies increases [
6
–
9
]. An-
other approach to further improve the probability of a correct integer fix is to use known
baseline information between the reference and rover GNSS receivers, which is commonly
incorporated in GNSS-based attitude determination problems [10,11].
For the interoperability of RTK among different GNSS receiver manufacturers, the re-
quired GNSS measurements and satellite information for a rover to compute RTK solutions
were established by the Radio Technical Commission Maritime Services (RTCM) Special
Committee-104 (SC-104). The RTCM1040 v2.3 standards were used for a conventional RTK
process between a pair of rovers and reference receivers. The RTCM 1040 v2.3 standards
had 64 types of messages, of which, 1 through 17 messages were defined for a differential
GNSS process, whereas messages 18 to 21 were added for future RTK solutions. The added
messages included uncorrected carrier phase measurements, uncorrected pseudorange
measurements, RTK carrier phase corrections, and RTK pseudorange corrections [
12
]. Later,
RTCM 1040 v3 was released to support the operation of an RTK network with higher effi-
ciency in terms of the broadcast bandwidth and higher integrity [
13
–
15
]. Currently, various
Sensors 2022, 22, 7939. https://doi.org/10.3390/s22207939 https://www.mdpi.com/journal/sensors
