GPS, components and working principle

A GPS (Global Positioning System) is a satellite-based radio navigation system, owned by the USA, which gives three-dimensional position (latitude, longitude, height) and time anywhere on or near the Earth in all weather, day and night.

Components (segments)

     Space segment (24+ satellites, ~20,200 km)
            |  signals
     Control segment  <-->  User segment
     (master & monitor        (receivers)
      stations, uplink)

1. Space segment: at least 24 satellites in six orbital planes inclined at 55°, at an altitude of about 20 200 km, with an orbital period of about 12 h. Each satellite sends signals on carrier frequencies L1 (1575.42 MHz) and L2 (1227.60 MHz), carrying the ranging codes and the navigation message (satellite position and clock).
2. Control segment: a master control station, monitor stations and ground antennas; they track the satellites, compute orbits (ephemeris) and clock corrections, and upload them to the satellites.
3. User segment: the GPS receivers (handheld, geodetic or surveying types) and their users; the receivers pick up the signals and compute the position.

Working principle

GPS works by trilateration using the travel time of the signal. The satellite sends a signal stamped with the time of transmission and its own position. The receiver notes the time of arrival, and the distance (pseudo-range) is

$$\rho = c\,(t_r - t_s)$$

where $c$ is the speed of light, $t_s$ the transmission time and $t_r$ the reception time. Each range puts the receiver on a sphere centred on the satellite. Three satellites would fix the position (three unknowns $X, Y, Z$), but the receiver clock is not as accurate as the atomic clocks in the satellites, so a fourth unknown (the clock error $\delta t$) is added. At least four satellites are required to solve for $X, Y, Z$ and $\delta t$:

$$\rho_i = \sqrt{(X_i - X)^2 + (Y_i - Y)^2 + (Z_i - Z)^2} + c\,\delta t,\quad i=1,\dots,4$$

The accuracy of a point depends on the satellite geometry (DOP), atmospheric delay, multipath and receiver quality. Using two receivers removes most of the common errors: code-based differential GPS (DGPS) gives sub-metre to metre accuracy, and carrier-phase relative positioning (static or RTK) gives centimetre to millimetre accuracy.