All About GPS <META name ="description" content = " All About GPS -- Global Positioning system -- how it works -- atomic clocks -- receivers -- accuracy -- SPS and PPS systems " <META name = "keywords" content = " GPS, Global, Positioning, System, satellites, naviagation, fix, latitude, longitude, altitude, time GPS signals, FedSat, SPS, PPS ">
All About GPS
GPS = Global Positioning System is a an advanced naviagation system based on a satellite system that enables anyone possessing a GPS receiver to determine their position (latitude, longitude, height) and time with extraordinary accuracy.
This web page gives an overview of the basic ideas which make GPS work. Velocity of light and radio waves
Light, as well as radio-waves, travels through space at a constant speed, called c = 300,000 km/sec. This means that if one knows the exact location (x,y,z) and the time t when a radio signal left that position, then the coordinates where one is (X,Y,Z) and the local time T are constraned to satisfy the equation:
(x - X)² + (y - Y)² + (z - Z)² = c²(t - T)²
We can't solve this single equation for the four unknowns. but suppose at time T(which one doesn't know very exactly) one receives signals from four satellites, whose exact positions are known: How is this applied in GPS?
The four satellite FIX idea
GPS satellites send out signals from which an intelligent receiver can deduce
  • The precise position of the satellite when the signal set out
  • The precise time when the signal set out
The four satellite FIX idea is that if a receiver receives all four signals at the same time, the position of the receiver in space, as well as the time can be computed.
The proof of this idea is somewhat mathematical (about Y11 level), and can be skipped. It goes like so:
Suppose four sigals are received at some unknown position (X,Y,Z) at some unknown time T from four satellites, whose positions are precisely known, as well as the accurate times when signals set out:
  • Signal left satellite 1 at (x1,y1,z1) at time t1
  • Signal left satellite 2 at (x2,y2,z2) at time t2
  • Signal left satellite 3 at (x3,y3,z3) at time t3
  • Signal left satellite 4 at (x4,y4,z4) at time t4
then if these signals reach us at (X,Y,Z) at the (same) time T there are four equations available:
  1. (x1 - X)² + (y1 - Y)² + (z1 - Z)² = c²(t1 - T)²
  2. (x2 - X)² + (y2 - Y)² + (z2 - Z)² = c²(t2 - T)²
  3. (x3 - X)² + (y3 - Y)² + (z3 - Z)² = c²(t3 - T)²
  4. (x3 - X)² + (y3 - Y)² + (z4 - Z)² = c²(t4 - T)²
There are computational techniques for solving four equations for four unknowns.
Refining the FOUR FIX idea.
Radio signals are sent from GPS satellites in short duration bursts, containing various items of digital data. The time of arrival of the data packets is when the first bit of the signal arrives. Contary to the assumption we made above, the arrival time of packets from various satellites won't be the same. However, even a handheld receiver can accurately measure the small difference in time between the arrival of the most recent data packets from the detected satellites. Suppose the differences in arrivals of the four signals are d1, d2, d3, d4, then the equation of arrival is just:
  1. (x1 - X)² + (y1 - Y)² + (z1 - Z)² = c²(t1 - T-d1)²
  2. (x2 - X)² + (y2 - Y)² + (z2 - Z)² = c²(t2 - T-d2)²
  3. (x3 - X)² + (y3 - Y)² + (z3 - Z)² = c²(t3 - T-d3)²
  4. (x3 - X)² + (y3 - Y)² + (z4 - Z)² = c²(t4 - T-d4)²
In these four equations, everything is known, and known accurately, except the four quantities (X,Y,Z) and T. So that the signals from four satellites, although not received precisely simultltaneously, can accurately determine a precise location and time.
In fact, GPS satellite system is organised so that at the earth's surface away from hills and mountains, eight satellites can be seen at any one time. The receivers are programmed so that the very best position estimate is determined using as much satellite data as is procurable.

GPS Satellite Data Packets
As indicated elsewhere, GPS satellites send out radio signals in packets of digital data, each paket indicating where and when it set out on its journey to the receiver. How does a GPS satellite "know"this information? The main reason that this information is available to the computer on-board the GPS satellite is that there is on-board a very accurate atomic clock, which keeps time to an impressive accuracy, which is regularly compared (and corrected against) even more accurate atomic clocks at groundstations. Thus all the clocks on the GPS satellites are both highly accurate and almost precisely synchronised, essential for accurate position fixes by receivers.
As to the satellites position. Each satellite is accurately tracked by groundstations, so a computer model of the orbit is constantly updated. Regular updates of details of the next orbit are given to each satellite by the groundstations, so that it can compute its actual position to within centimetres at each instant.

Ionospheric Effects on GPS
Light, and radio wave travels at a constant speed in empty space, the velocity of light. Signals from GPS satellites are most effected by their passage through the ionosphere, the region above the atmosphere starting about 50 km up, where most of the very scant gas molecules present are ionised. Thus for instant, rather than oxygen molecules floating around, what's in the ionosphere are oxygen atoms that have lost one electron, called oxygen ions, together with electrons. Overall the ionosphere is neutral, but this mix of ions and elctrons is called a plasma and has several effects on light and radio waves, of which one is simply to delay passage. In order to compensate for the ionosphere, GPS signals are sent at two frequencies, so that for precise navigation, the ionospheric error can be roughly corrected. Nevertheless, even for the best precision GPS location, there's an error of about 30 m due to ionospheric uncertainies. If this figure appears large in comparison to various claims as to GPS accuracy, please note that our discussion is about ordinary GPS, using only a single receiver. Much higher accuracy in relative distances is obtained by Differential GPS.

Operational Details re GPS
The GPS Operational Constellation consists of 24 satellites: 21 navigational SVs and 3 active spares orbit the earth in 12 hour orbits. These orbits repeat the same ground track (as the earth turns beneath them) once each day. The orbit altitude is such that the satellites repeat the same track and configuration over any point approximately each 24 hours (4 minutes earlier each day). There are six orbital planes (with nominally four SVs in each), equally spaced (60 degrees apart), and inclined at about fifty-five degrees with respect to the equatorial plane. This constellation provides the user with between five and eight SVs visible from any point on the earth. The Master Control facility is located at Falcon Air Force Base in Colorado. These monitor stations measure signals from the SVs which are incorporated into orbital models for each satellites. The models compute precise orbital data (ephemeris) and SV clock corrections for each satellite. The Master Control station uploads ephemeris and clock data to the SVs. The SVs then send subsets of the orbital ephemeris data to GPS receivers over radio signals.

Precision of GPS
Standard Positioning System
Precise Positioning Service
SPS Predictable Accuracy
  • 100 meter horizontal accuracy
  • 156 meter vertical accuracy
  • 340 nanoseconds time accuracy
PPS Predictable Accuracy
  • 22 meter Horizontal accuracy
  • 27.7 meter vertical accuracy
  • 100 nanosecond time accuracy

Civil users worldwide use the SPS without charge or restrictions. Most receivers are capable of receiving and using the SPS signal. The SPS accuracy is intentionally degraded by the DOD by the use of Selective Availability.
Authorized users with cryptographic equipment and keys and specially equipped receivers use the Precise Positioning System. U. S. and Allied military, certain U. S. Government agencies, and selected civil users specifically approved by the U. S. Government, can use the PPS.
t is anticipated that the GPS receiver to be used on the Australian scientific satellite FedSat 1, will have PPS capabilities. Thus the GPS system will supply position data required for the magnetometer experiment (NEWMAG) on board. However, more notably, the GPS signals themselves will be used for ionospheric studies, especially of the Southern Ocean region, where no effective models exist for the ionosphere,
The figures for the precision of SPS and PPS given above are credible for periods of low solar activity, but are overly generous for the Southern Pacific region. Errors due to poor modelling of the ionosphere can exceed 30 m.


Prepared by Dr Harvey Cohen,

Black Hole

Australia in Space
a History
Bouncing radar off the sea
Experiment designed to monitor sea heights gives data yielding sea heights yields ionospheric data.

Australian Satellite Science and Engineering