Editing Satellite navigation (section)

== Principles ==
{{further|GPS#Principles|GPS#Navigation equations}}

Part of an orbiting satellite's broadcast includes its precise orbital data. Originally, the [[US Naval Observatory|US Naval Observatory (USNO)]] continuously observed the precise orbits of these satellites. As a satellite's orbit deviated, the USNO sent the updated information to the satellite. Subsequent broadcasts from an updated satellite would contain its most recent [[ephemeris]].

Modern systems are more direct. The satellite broadcasts a signal that contains orbital data (from which the position of the satellite can be calculated) and the precise time the signal was transmitted. Orbital data include a rough [[almanac]] for all satellites to aid in finding them, and a precise ephemeris for this satellite. The orbital [[ephemeris]] is transmitted in a data message that is superimposed on a code that serves as a timing reference. The satellite uses an [[atomic clock]] to maintain synchronization of all the satellites in the constellation. The receiver compares the time of broadcast encoded in the transmission of three (at sea level) or four (which allows an altitude calculation also) different satellites, measuring the time-of-flight to each satellite. Several such measurements can be made at the same time to different satellites, allowing a continual fix to be generated in real time using an adapted version of [[trilateration]]: see [[GNSS positioning calculation]] for details.

Each distance measurement, regardless of the system being used, places the receiver on a spherical shell centred on the broadcaster, at the measured distance from the broadcaster. By taking several such measurements and then looking for a point where the shells meet, a fix is generated. However, in the case of fast-moving receivers, the position of the receiver moves as signals are received from several satellites. In addition, the radio signals slow slightly as they pass through the ionosphere, and this slowing varies with the receiver's angle to the satellite, because that angle corresponds to the distance which the signal travels through the ionosphere. The basic computation thus attempts to find the shortest directed line tangent to four oblate spherical shells centred on four satellites. Satellite navigation receivers reduce errors by using combinations of signals from multiple satellites and multiple correlators, and then using techniques such as [[Kalman filter]]ing to combine the noisy, partial, and constantly changing data into a single estimate for position, time, and velocity.

[[Einstein]]'s theory of [[general relativity]] is applied to GPS time correction, the net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day.<ref name=einstein>{{cite web |url=https://www.e-education.psu.edu/geog862/node/1714|publisher=The Pennsylvania State University|title=Relativistic Effects on the Satellite Clock}}</ref>