The Global Positioning System, commonly known as GPS, is a satellite-based navigation system that allows a receiver on Earth to determine its precise location. Operated by the United States government, it consists of at least 24 satellites orbiting the planet at an altitude of about 20,200 kilometres. These satellites continuously broadcast radio signals containing their exact position and the precise time the signal was sent. A GPS receiver listens to these signals from multiple satellites and uses the time delay to calculate its distance from each one. By combining distance measurements from at least four satellites, the receiver can pinpoint its three-dimensional location—latitude, longitude, and altitude—with remarkable accuracy.

This process, called trilateration, forms the foundation of modern navigation, enabling everything from driving directions to aircraft landing systems. Central to GPS accuracy is the use of atomic clocks aboard each satellite. These clocks keep time with incredible precision, losing or gaining only one second every 100,000 years. The satellites transmit their location and a time stamp every millisecond. When the signal reaches the receiver, it compares the time stamp with its own internal clock. The difference reveals how long the signal travelled. Since radio waves move at the speed of light (about 300,000 kilometres per second), the distance to the satellite is simply the travel time multiplied by the speed of light.

However, the receiver's clock is much less accurate than the atomic clocks, so it introduces a small time error. To compensate, the receiver must lock onto at least four satellites instead of three, allowing it to solve for both position and time simultaneously. Trilateration with three satellites would theoretically provide a location if the receiver's clock were perfect, but real-world receivers need a fourth signal. With four satellites, the receiver has four equations and four unknowns: x, y, z, and time error. The mathematics behind this is complex, but the principle is straightforward.

Since radio waves move at the speed of light (about 300,000 kilometres per second), the distance to the satellite is simply the travel time multiplied by the speed of light.

Imagine each satellite at the centre of a sphere whose radius equals the distance to the receiver. The receiver's location is where all these spheres intersect. If the distances are slightly off due to clock errors, the spheres do not meet at a single point. By adjusting the time error, the receiver can shift the spheres until they converge. This is why a GPS receiver often displays '3D fix' after capturing four satellites. In open areas, many more satellites are visible, improving accuracy further. The distance calculation relies on knowing the signal's exact travel time.

Because the signals travel at the speed of light, even a tiny timing error—one microsecond—causes a distance error of 300 metres. Hence the need for atomic clocks on satellites and sophisticated error correction. The receiver measures the time difference between when the signal was sent and when it was received. However, the signal slows slightly as it passes through the ionosphere and troposphere, introducing a delay. GPS receivers use models to estimate this delay, and dual-frequency receivers can measure the delay directly by comparing signals on two different frequencies.

Additionally, the satellite's orbit may have small errors, and the Earth's rotation affects signal path. All these factors are accounted for in the receiver's calculations to achieve typical accuracies of a few metres for civilian use. Differential GPS (DGPS) significantly improves accuracy by correcting for common errors. A base station at a known location receives GPS signals and computes the difference between its measured position and true position. This correction is then broadcast to nearby receivers, which apply it to their own measurements. DGPS can reduce errors to less than one metre.

Similarly, satellite-based augmentation systems like WAAS (in the US) or EGNOS (in Europe) provide corrections over wide areas via geostationary satellites. For high-precision work, such as surveying or agriculture, real-time kinematic (RTK) GPS achieves centimetre-level accuracy by using carrier-phase measurements. These techniques exploit the fact that the carrier wave of the signal has a much shorter wavelength than the code, allowing phase differences to be measured precisely. Such refinements have expanded GPS applications far beyond basic navigation. The uses of GPS pervade modern life. In transport, it enables real-time traffic updates, route optimisation, and fleet management.

Aviation relies on GPS for precision approaches and en-route navigation, increasing safety and efficiency. Surveyors use GPS to map land boundaries and structures with high accuracy. Farmers employ GPS-guided tractors for precise planting and fertilising, boosting yields and reducing waste. Search and rescue teams locate lost hikers using personal locator beacons that transmit GPS coordinates. Even financial networks synchronise their operations using GPS time signals, ensuring consistency across global markets. The technology has become so embedded that many people depend on it daily without realising the complex physics and engineering that make it possible.

Its integration with smartphones has democratised navigation, making it accessible to billions. Despite its capabilities, GPS has limitations. Signals are weak and can be blocked by buildings, tunnels, or dense foliage, leading to degraded performance indoors or in urban canyons. Interference, whether accidental from electronics or intentional jamming, can disrupt service. To mitigate these issues, other global navigation satellite systems (GNSS) are being developed, such as Russia's GLONASS, Europe's Galileo, and China's BeiDou. These systems increase satellite availability and redundancy, improving reliability. Future enhancements include more robust signals, better atomic clocks, and advanced error models.

Additionally, combining GPS with other sensors (like inertial measurement units or WiFi positioning) provides continuous location even when satellite signals are lost. As the world becomes increasingly reliant on precise positioning, GPS and its counterparts will continue to evolve, supporting autonomous vehicles, augmented reality, and countless innovations yet to come.