Editing Global Positioning System (section)

== Principles ==
{{more citations needed section|date=March 2015}}

The GPS satellites carry very stable [[atomic clocks]] that are synchronized with one another and with the reference atomic clocks at the ground control stations; any drift of the clocks aboard the satellites from the reference time maintained on the ground stations is corrected regularly.<ref>{{Cite web |last=Nelson |first=Jon |date=June 19, 2019 |title=What Is an Atomic Clock? |url=http://www.nasa.gov/feature/jpl/what-is-an-atomic-clock |access-date=2023-04-04 |website=NASA |url-status=live |archive-url=https://web.archive.org/web/20230405131119/https://www.nasa.gov/feature/jpl/what-is-an-atomic-clock |archive-date= April 5, 2023 }}</ref> Since the speed of [[radio wave]]s ([[speed of light]])<ref>{{Cite web |title=Radio wave {{!}} Examples, Uses, Facts, & Range |url=https://www.britannica.com/science/radio-wave |access-date=2023-04-04 |website=Britannica |language=en}}</ref> is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the ground station receives it is proportional to the distance from the satellite to the ground station. With the distance information collected from multiple ground stations, the location coordinates of any satellite at any time can be calculated with great precision.

Each GPS satellite carries an accurate record of its own position and time,<ref>{{Cite web |title=How does my sat-nav really know where I am? |url=https://www.bbc.com/future/article/20130927-how-does-sat-nav-really-work |access-date=2025-01-05 |website=www.bbc.com |language=en-GB}}</ref> and broadcasts that data continuously. Based on data received from multiple GPS [[satellite]]s, an end user's GPS receiver can calculate its own [[Four-dimensional space|four-dimensional position]] in [[spacetime]]; However, at a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and the deviation of its own clock from satellite time).<ref>{{Cite web |title=JAXA {{!}} Positioning to know your location and time |url=https://global.jaxa.jp/countdown/f18/overview/gps_e.html |access-date=2023-04-04 |website=global.jaxa.jp}}</ref>

=== More detailed description ===
Each GPS satellite continually broadcasts a signal ([[carrier wave]] with [[modulation]]) that includes:
* A [[Pseudorandom binary sequence|pseudorandom]] code (sequence of ones and zeros) that is known to the receiver. By time-aligning a receiver-generated version and the receiver-measured version of the code, the time of arrival (TOA) of a defined point in the code sequence, called an epoch, can be found in the receiver clock time scale
* A message that includes the time of transmission (TOT) of the code epoch (in GPS time scale) and the satellite position at that time

Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. From the TOAs and the TOTs, the receiver forms four [[time of flight]] (TOF) values, which are (given the speed of light) approximately equivalent to receiver-satellite ranges plus time difference between the receiver and GPS satellites multiplied by speed of light, which are called pseudo-ranges. The receiver then computes its three-dimensional position and clock deviation from the four TOFs.

In practice the receiver position (in three dimensional [[Cartesian coordinate system|Cartesian coordinates]] with origin at the Earth's center) and the offset of the receiver clock relative to the GPS time are computed simultaneously, using the [[#Navigation equations|navigation equations]] to process the TOFs.

The receiver's Earth-centered solution location is usually converted to [[latitude]], [[longitude]] and height relative to an ellipsoidal Earth model. The height may then be further converted to height relative to the [[geoid]], which is essentially mean sea level. These coordinates may be displayed, such as on a [[moving map display]], or recorded or used by some other system, such as a vehicle guidance system.

=== User-satellite geometry ===
{{further|#Geometric interpretation}}

Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry. Each TDOA corresponds to a [[hyperboloid]] of revolution (see [[Multilateration]]). The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect.<ref name="Abel1">{{cite journal |last1=Abel |first1=J. S. |last2=Chaffee |first2=J. W. |year=1991 |title=Existence and uniqueness of GPS solutions |journal=IEEE Transactions on Aerospace and Electronic Systems |publisher=Institute of Electrical and Electronics Engineers (IEEE) |volume=27 |issue=6 |pages=952–956 |bibcode=1991ITAES..27..952A |doi=10.1109/7.104271 |issn=0018-9251}}</ref><ref name="Fang">{{cite journal |last=Fang |first=B. T. |year=1992 |title=Comments on "Existence and uniqueness of GPS solutions" by J.S. Abel and J.W. Chaffee |journal=IEEE Transactions on Aerospace and Electronic Systems |publisher=Institute of Electrical and Electronics Engineers (IEEE) |volume=28 |issue=4 |page=1163 |bibcode= |doi=10.1109/7.165379 |issn=0018-9251}}</ref>

It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is the case only if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are marked performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If it were an essential part of the GPS concept that all users needed to carry a synchronized clock, a smaller number of satellites could be deployed, but the cost and complexity of the user equipment would increase.

=== Receiver in continuous operation ===
The description above is representative of a receiver start-up situation. Most receivers have a [[track algorithm]], sometimes called a ''tracker'', that combines sets of satellite measurements collected at different times—in effect, taking advantage of the fact that successive receiver positions are usually close to each other. After a set of measurements are processed, the tracker predicts the receiver location corresponding to the next set of satellite measurements. When the new measurements are collected, the receiver uses a weighting scheme to combine the new measurements with the tracker prediction. In general, a tracker can (a) improve receiver position and time accuracy, (b) reject bad measurements, and (c) estimate receiver speed and direction.

The disadvantage of a tracker is that changes in speed or direction can be computed only with a delay, and that derived direction becomes inaccurate when the distance traveled between two position measurements drops below or near the [[random error]] of position measurement. GPS units can use measurements of the [[Doppler shift]] of the signals received to compute velocity accurately.<ref>{{cite book |title=Global Positioning Systems, Inertial Navigation, and Integration |edition=2nd |first1=Mohinder S. |last1=Grewal |first2=Lawrence R. |last2=Weill |first3=Angus P. |last3=Andrews |publisher=John Wiley & Sons |year=2007 |isbn=978-0-470-09971-1 |pages=[{{google books|plainurl=y|id=6P7UNphJ1z8C|page=92 |title=Extract of pages 92–93}} 92–93] |url={{google books|plainurl=y|id=6P7UNphJ1z8C}}}}</ref> More advanced navigation systems use additional sensors like a [[compass]] or an [[inertial navigation system]] to complement GPS.

=== Non-navigation applications ===
{{for|a list of applications|#Applications}}
GPS requires four or more satellites to be visible for accurate navigation.<ref>{{Cite web |last= |first= |last2= |first2= |last3= |first3= |title=The Global Positioning System: Global Positioning Tutorial |url=https://oceanservice.noaa.gov/education/tutorial_geodesy/geo09_gps.html#:~:text=It%20takes%20four%20GPS%20satellites,error%20in%20the%20receiver's%20clock. |access-date=2025-01-05 |website=oceanservice.noaa.gov |language=EN-US}}</ref> The solution of the [[#Navigation equations|navigation equations]] gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a more precise and possibly impractical receiver based clock. Applications for GPS such as [[time transfer]], traffic signal timing, and [[IS-95#Physical layer|synchronization of cell phone base stations]], [[#Timekeeping|make use of]] this cheap and highly accurate timing. Some GPS applications use this time for display, or, other than for the basic position calculations, do not use it at all.

<!--This paragraph seems to be in the wrong section, or possibly the section heading needs changing to reflect its current content.-->Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship on the open ocean usually has a known elevation [[tidal range|close to 0m]], and the elevation of an aircraft may be known.{{efn|In fact, the ship is unlikely to be at precisely 0m, because of tides and other factors which create a discrepancy between mean sea level and actual sea level. In the open ocean, high and low tide typically only differ by about 0.6m, but there are locations closer to land where they can differ by over 15m. See [[tidal range]] for more details and references.}} Some GPS receivers may use additional clues or assumptions such as reusing the last known altitude, [[dead reckoning]], [[inertial navigation system|inertial navigation]], or including information from the vehicle computer, to give a (possibly degraded) position when fewer than four satellites are visible.<ref>{{cite web |last1=zur Bonsen |first1=Georg |last2=Ammann |first2=Daniel |last3=Ammann |first3=Michael |last4=Favey |first4=Etienne |last5=Flammant |first5=Pascal |date=April 1, 2005 |title=Continuous Navigation Combining GPS with Sensor-Based Dead Reckoning |url=http://www.gpsworld.com/gpsworld/article/articleDetail.jsp?id=154870&pageID=6 |archive-url=https://web.archive.org/web/20061111202317/http://www.gpsworld.com/gpsworld/article/articleDetail.jsp?id=154870&pageID=6 |archive-date=November 11, 2006 |publisher=GPS World}}</ref><ref name="NAVGPS">{{cite web|title=NAVSTAR GPS User Equipment Introduction|url=http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf|publisher=United States Government|access-date=August 22, 2008|archive-url=https://web.archive.org/web/20080910184805/http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf|archive-date=September 10, 2008|url-status=live}} Chapter 7</ref><ref>{{cite web|title=GPS Support Notes|url=http://www.navmanwireless.com/uploads/EK/C8/EKC8zb1ITsNwDqWcqLQxiQ/Support_Notes_GPS_OperatingParameters.pdf|date=January 19, 2007|access-date=November 10, 2008|archive-url=https://web.archive.org/web/20090327051208/http://www.navmanwireless.com/uploads/EK/C8/EKC8zb1ITsNwDqWcqLQxiQ/Support_Notes_GPS_OperatingParameters.pdf|archive-date=March 27, 2009}}</ref>