How GPS Locates Your Position at Any Time?

How does the GPS system work?

The Global Positioning System (GPS) relies on a constellation of 24 active satellites (plus a few spare satellites) evenly distributed around the Earth, each orbiting at about 20,200 km altitude. These satellites continuously emit a signal containing their position and the very precise time at which the signal is sent, synchronized via an onboard cesium or rubidium atomic clock.

A GPS receiver (like the one in your phone) picks up these signals. By measuring the time it takes for the signal to arrive, it calculates its distance to each satellite. With the signal from four or more satellites, it can determine its position in space (latitude, longitude, altitude) by spatial triangulation (actually, trilateration).

Spatial Trilateration: How GPS Calculates Position

Contrary to popular belief, GPS does not rely on triangulation (angle measurement), but on spatial trilateration: the receiver's position is determined from the measured distances between it and several satellites. Each satellite continuously transmits a signal containing its position at a given time and a precise timestamp. The receiver compares the transmission time (inscribed in the message) to the reception time (internal clock) to deduce the propagation time, and thus the distance traveled by the signal.

The Fundamental Physical Principle

The signal emitted by each satellite propagates at the speed of light \(\,c\,\). If the signal takes a time \(\,\Delta t_i\,\) to reach the receiver from satellite \(i\), then the distance \(d_i\) is given by:

\[ d_i = c \cdot \Delta t_i \]

Each distance defines a sphere centered on the satellite \(i\), with radius \(d_i\). The intersection of these spheres in space determines the receiver's position.

Why Four Satellites Are Necessary

Three satellites are theoretically sufficient to locate a point in space (intersection of three spheres). However, GPS receivers do not have an atomic clock: they are therefore unable to perfectly synchronize their time with that of the satellites. This synchronization error between the receiver's clock and GPS time generates a common offset in all measurements.

We must therefore solve a system of four equations with four unknowns:

• The three unknown coordinates of the receiver: \((x, y, z)\)
• The receiver's clock bias: \(\delta t\)

The general form of the equations is:

\[ (x - x_i)^2 + (y - y_i)^2 + (z - z_i)^2 = \left[c \cdot (\Delta t_i - \delta t)\right]^2 \]

where \((x_i, y_i, z_i)\) are the known coordinates of satellite \(i\), and \(\Delta t_i\) is the measured signal travel time. At least four satellites are needed to solve this system and correct the receiver's clock error.

3D Position + Synchronization

With signals from four or more satellites, GPS can determine:

• Latitude (angle with the equator)
• Longitude (angle with the reference meridian)
• Altitude above the Earth's geoid
• The time correction to apply to the local clock

The positioning algorithm typically uses a Kalman filter to refine the solution, integrating signal uncertainties, orbitographic errors, and atmospheric models. In clear environments, with good satellite geometry (Dilution of Precision), real-time accuracy of a few meters is achieved.

Accuracy, Relativity, and Error Correction

For GPS to be accurate to within a few meters, or even a few centimeters in some cases (RTK, DGPS), relativistic effects must be taken into account. Indeed, the atomic clocks on board the satellites tick faster due to general relativity (less gravity in orbit) and slower due to special relativity (due to their speed). The combined shift is on the order of 38 microseconds per day, or more than 10 km of daily error if it were not corrected!

Complex algorithms also correct errors due to signal propagation (ionospheric atmosphere, troposphere), multipaths (parasitic reflections), or small orbital drifts.

GPS is therefore a system at the crossroads of fundamental physics (relativity, orbital mechanics, radio frequency), precision engineering, and embedded computing.

Sub-Meter Precision: The Physical Secrets of GPS

The GPS system is often perceived as a practical geolocation tool, but it is actually based on high-precision physical engineering, mobilizing concepts from general relativity, orbital mechanics, atomic synchronization, and signal processing. While consumer-grade accuracy is on the order of a few meters, advanced techniques allow for sub-meter precision, even centimetric.

Time and Speed of Light

The position of a GPS receiver is calculated from the propagation time of signals sent by multiple satellites, all equipped with ultra-stable atomic clocks. These signals travel at the speed of light (\(c = 299,792,458\) m/s): an error of 1 nanosecond already corresponds to a position error of 30 centimeters. Hence the critical importance of absolute time measurement.

Special and General Relativity

GPS satellites orbit at an altitude of about 20,200 km at a speed of 14,000 km/h. According to special relativity, the rapid movement of the satellite causes a slowing down of its clock relative to an observer on the ground (about -7 µs/day). Simultaneously, according to general relativity, the weaker gravity in orbit speeds up the clock (about +45 µs/day). The net imbalance is about +38 microseconds per day, which would induce an error of 10 km/day if not corrected! These effects are therefore integrated from the design of the satellites.

Errors and Corrections

Various sources of error affect the signal: orbital errors, clock drifts, ionospheric and tropospheric delays, multipath reflections. To compensate for these errors, ground control stations continuously monitor the satellites and update the navigation parameters. Additionally, atmospheric models correct the delays induced by passing through the ionosphere (dispersion effect) and the troposphere (wet and dry refraction effect).

Sub-Meter Precision Techniques

• Differential GPS (DGPS): compares GPS signals received simultaneously by a fixed station (whose position is known) and by a mobile to correct errors in real time.
• RTK (Real-Time Kinematic): uses the phases of the carrier waves rather than just the code-based pseudo-distances. This technique allows for centimetric precision, provided millimetric synchronization between antennas.
• PPP (Precise Point Positioning): relies on extremely precise orbit and clock models provided by global networks, without a local reference station, to achieve centimeter-level accuracy.

Thus, the sub-meter precision of GPS is the result of advanced physical models, complex algorithms, and extreme synchronization technologies. Each position displayed on our screens results from sophisticated processing of light signals from satellites more than 20,000 km away, where celestial mechanics and relativity interact with embedded electronics.

Difference with the European Galileo System

The Galileo system is the European equivalent of GPS, designed to ensure Europe's strategic autonomy in the field of satellite positioning. Although its operating principle is also based on trilateration from satellite signals synchronized by atomic clocks, several technical and political differences distinguish it from GPS:

• Origin: GPS is a US military system launched in the 1970s, open to civilian uses. Galileo is a civilian project, under the control of the European Union and the European Space Agency (ESA).
• Precision: Galileo promises a precision of less than one meter (down to 20 cm with the paid service), superior to that of standard civilian GPS.
• Onboard Clocks: Galileo uses hydrogen maser clocks that are more stable than the rubidium clocks of GPS, allowing for an even more rigorous time signal.
• Global Availability: Galileo has been fully operational since 2020 with a planned constellation of 30 satellites. It is compatible with GPS, Glonass (Russian), and BeiDou (Chinese) in modern multi-constellation receivers.
• Specialized Services: Galileo offers a search and rescue service (SAR), a regulated public service (PRS) reserved for authorities, and a high-precision service (HAS).

In summary, Galileo represents an advance in precision and strategic independence, while enhancing interoperability with other GNSS (Global Navigation Satellite Systems). Together, these constellations enable reliable and resilient global geolocation.

Difference with the Chinese BeiDou System

The BeiDou system (BDS – BeiDou Navigation Satellite System) is the Chinese satellite navigation system, developed and operated by the People's Republic of China. Unlike GPS (American) or Galileo (European), BeiDou has been deployed in several phases, starting with regional coverage in Asia (BeiDou-1, then BeiDou-2) before achieving global coverage with BeiDou-3 in 2020.

• Strategic Independence: BeiDou is an instrument of technological sovereignty for China, enabling navigation without relying on foreign systems, especially in the event of geopolitical crises.
• Hybrid Architecture: Unlike GPS or Galileo, BeiDou uses a mixed architecture including satellites in geostationary orbit (GEO), orbiting at 35,786 km, in addition to medium Earth orbits (MEO) and inclined geosynchronous orbits (IGSO), which improves regional coverage in Asia.
• Differentiated Services: BeiDou offers a free civilian service, similar to that of GPS or Galileo, but also an encrypted military service for exclusive use by Chinese authorities. It also offers a short messaging function allowing users to send text messages via satellite, unique among GNSS.
• Compatibility: Many recent smartphones and professional GNSS receivers are compatible with BeiDou, in addition to GPS, Galileo, and Glonass, which improves the availability of signals and precision in challenging environments (urban canyons, dense forests).
• Precision and Correction: The BeiDou system achieves accuracies on the order of 2.5 meters globally and less than one meter with real-time correction services offered in Chinese territory.

In summary, BeiDou is a fully operational global satellite navigation system, designed for both mass civilian use and military and strategic purposes. Its deployment strengthens the resilience of global positioning and materializes a form of geopolitical multipolarity in the sky, with each major power now having its own GNSS constellation.

Difference with the Russian GLONASS System

The GLONASS system (GLObal NAvigation Satellite System) is the Russian equivalent of the American GPS. Established by the USSR in the 1980s and then upgraded by Russia during the 2000s, GLONASS is today a fully operational global GNSS system.

• Orbital Architecture: GLONASS uses 24 satellites in medium circular orbit (MEO) at an altitude of about 19,100 km, distributed across three orbital planes inclined at 64.8°, giving it better coverage of high latitudes, particularly the northern Russian territories.
• Geodetic Reference: Unlike GPS, which is based on the WGS 84 (World Geodetic System), GLONASS uses its own geodetic system, called PGSK-2011, which is closer to Russia's reference system.
• Frequency Differences: GLONASS employs frequency division multiple access (FDMA), whereas GPS primarily uses code division multiple access (CDMA). This difference has implications for the design of multi-constellation receivers.
• Combined Use: Modern receivers (smartphones, professional GPS) often combine GPS and GLONASS signals, which improves precision and reliability, especially in urban or mountainous areas.
• Military and Civilian Applications: Like GPS, GLONASS offers a free civilian service as well as an encrypted military service. Both systems are strategic for their respective countries in the event of conflicts or technological isolation.

GLONASS is thus a robust navigation system, supported by the Russian state, and constitutes a credible and redundant alternative to GPS. It reflects the desire of major powers to have their own space infrastructure to ensure strategic autonomy in global positioning.

Difference with the Indian IRNSS / NavIC System

The IRNSS system (Indian Regional Navigation Satellite System), officially called NavIC (Navigation with Indian Constellation), is a regional satellite navigation system developed by ISRO (Indian Space Research Organisation) to meet the specific needs of India and its surrounding region.

• Regional Coverage: Unlike global systems like GPS or GLONASS, NavIC mainly covers India and an area of about 1,500 km around it, although an extension to global range is envisaged with NavIC-2.
• Specific Architecture: NavIC uses a constellation of 7 satellites placed in geosynchronous and geostationary orbits, which allows constant visibility over the Indian subcontinent, enhancing reliability in this region.
• Services Provided: The system offers two types of services: an open standard service (OS) for civilian users, and a restricted service (RS) encrypted, reserved for military and governmental uses.
• Precision: NavIC claims a precision better than 10 meters on Indian territory, with high availability and integrity, adapted to the geographical and climatic needs of the region.
• Increasing Usage: India is pushing for the integration of NavIC into smartphones and vehicles, with compatible chips already present in some models since 2019, making it a rapidly expanding regional GNSS system.

NavIC reflects India's desire to ensure its technological independence in navigation and to have a robust system, optimized for its own geographical needs. It is an example of a regional GNSS designed as a complement or alternative to global systems.

Comparison of GNSS Systems

Global satellite positioning systems (GNSS) have become critical infrastructures for communications, transportation, meteorology, civilian geolocation, precision agriculture, and military operations. Each system has particularities related to its geopolitical origin, architecture, coverage, and performance. The table below compares the main technical and strategic characteristics of the five major operational GNSS.

The combined use of multiple GNSS (multi-constellation receivers) increases precision, signal availability, and robustness against interference or local outages. It is an essential component of modern navigation, both in civilian applications and critical infrastructures.