Users must account for the previous 1024 weeks, and this means that a GPS receiver should precisely determine reaching the maximum limit of week number by itself as the navigation message does not include year or week rollover information. Within the first version of the GPS interface control document ICD-GPS-200, a note stated: “At the expiration of GPS week number 1023, the GPS week number will rollover to zero (0)”. GPS time is based on modular arithmetic and is restricted to integers with a finite value that is defined for example, in the 24-h time system, if it is currently 1800, then 8 h later, we say it is 0200, not 2600. As such, the GPS week number is modulo 1024, and at the end of the week 1023, the week counter will reset and rollover to zero herein lies the problem. Using 10 bits, the maximum number that can be represented is 210, which equals 1024, and thus we have a range of 0–1023 for week representation. The current GPS week segment is included in the sub-frame as one of the navigation messages that is considered part of the satellite clock, and other user information is accommodated to represent only 10 bits for the week value. While the Standard Positioning Service (SPS), a positioning and timing service, provides almost 340 nanoseconds of accuracy. The corresponding precise GPS time accuracy is within 200 nanoseconds. Leap-seconds added to UTC have affected GPS relational difference, as GPS time is always ahead of UTC by a few nanoseconds, and this value varies from day to day. GPS Time has no leap-seconds within the integer level. 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. Such a process is necessary to obtain the proper correction for the time. 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.
īIPM achieves ultimate precision, by a few nanoseconds, using comparison processes. 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. After 1990, time information was calculated using all operational stations and satellite clocks. USNO is based on both International Atomic Time (TAI) and UTC, using periodic corrections. Naval Observatory (USNO) Atomic time scale.
Time data that is transmitted by operational satellites and used by the Global Navigation System (GPS) is mathematically referenced as the GPS until 1990 and GPS Time (GPST), based on the U.S.
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. After testing, it is evident that the transport layer level solution was the most effective in terms of speed, efficiency, accuracy, cost, and complexity. Complete testing is applied for all suggested solutions using actual data provided by Traklink-a leading company in navigation and fleet management solutions.
A hardware-level solution is suggested by applying a timestamp complement over the GPS internal controller. At the level of the database, a solution is also suggested which uses triggers. 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. In addition, this paper seeks to provide precautionary measures to deal with the problem proactively. 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. As many fleet management systems depend on GPS raw data, such systems stopped working due to inaccurate data provided by GPS receivers. 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. Global Positioning System (GPS) is a global navigation satellite system and the most common satellite system used in navigation and tracking devices.
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