Article
GPS Week Number Rollover Timestamp Complement
Majdi K. Qabalin
1,2,
*, Muawya Naser
1
, Wafa M. Hawajreh
2
and Saja Abu-Zaideh
1
Citation: Qabalin, M.K.; Naser, M.;
Hawajreh, W.M.; Abu-Zaideh, S. GPS
Week Number Rollover Timestamp
Complement. Sensors 2021, 21, 7826.
https://doi.org/10.3390/s21237826
Academic Editors: Kamil Krasuski
and Damian Wierzbicki
Received: 21 October 2021
Accepted: 22 November 2021
Published: 24 November 2021
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1
Department of Computer Science, Princess Sumaya University for Technology, 1438 Al-Jubaiha,
Amman 11941, Jordan; M.Aldalaien@psut.edu.jo (M.N.); saj20208080@std.psut.edu.jo (S.A.-Z.)
2
Engineering Department, Traklink Co., Amman 11941, Jordan; Wafa@trak-link.com
* Correspondence: maj20208012@std.psut.edu.jo; Tel.: +962-780177770
Abstract:
Global Positioning System (GPS) is a global navigation satellite system and the most
common satellite system used in navigation and tracking devices. The phenomenon of week number
rollover happened recently—a year ago—due to a design limitation in the week number variable that
counting weeks which causes vast losses. As many fleet management systems depend on GPS raw
data, such systems stopped working due to inaccurate data provided by GPS receivers. In this paper,
we propose a technical and mathematical analysis for the GPS week number rollover phenomenon
and suggest a solution to avoid the resulting damage to other subsystems that depend on the GPS
device’s raw data. In addition, this paper seeks to provide precautionary measures to deal with
the problem proactively. The Open Systems Interconnection model (OSI) and transport layer level
solution that has been suggested depends on a TCP packet reforming tool that re-formats the value
of the week number according to a mathematical model based on a timestamp complement. At the
level of the database, a solution is also suggested which uses triggers. A hardware-level solution is
suggested by applying a timestamp complement over the GPS internal controller. Complete testing
is applied for all suggested solutions using actual data provided by Traklink—a leading company in
navigation and fleet management solutions. After testing, it is evident that the transport layer level
solution was the most effective in terms of speed, efficiency, accuracy, cost, and complexity. Applying
a transport layer level complement mathematical model can fix the consequences of GPS week
number rollover and provide stability to all subsystems that used GPS data from infected devices.
Keywords:
GPS rollover; global navigation satellite system; timestamp complement; week number;
Global Positioning System; trigger
1. Introduction
Time data that is transmitted by operational satellites and used by the Global Nav-
igation System (GPS) is mathematically referenced as the GPS until 1990 and GPS Time
(GPST), based on the U.S. Naval Observatory (USNO) Atomic time scale. USNO is based
on both International Atomic Time (TAI) and UTC, using periodic corrections. After 1990,
time information was calculated using all operational stations and satellite clocks. Few
microseconds can be accepted as a difference between the GPS and global time standard or
the so-called Universal Time Coordinated (UTC), which is calculated by the International
Bureau of Weights and Measures (BIMP) by applying a mathematical model that includes
data from about 240 atomic clocks around the globe that maintain a local version of UTC [
1
].
BIPM achieves ultimate precision, by a few nanoseconds, using comparison processes.
For this reason, leap seconds are added in calculations for UTC every specific period in
order to maintain ultimate synchronization with the Earth’s rotational period concerning
the sun. Such a process is necessary to obtain the proper correction for the time [
2
]. Due
to the physics of the Earth’s rotation and some uncontrolled variables, we can see such
differences; for example, the yearly average length of the day is currently about two
milliseconds longer than it was 20 years ago [
3
]. GPS Time has no leap-seconds within
the integer level. Leap-seconds added to UTC have affected GPS relational difference, as
Sensors 2021, 21, 7826. https://doi.org/10.3390/s21237826 https://www.mdpi.com/journal/sensors
