GPS - Positioning System
Do you want the best tool for locating and marking your spots? Then GPS is for you!
The Global Positioning System, usually called GPS (the US military refers to it as NAVSTAR GPS - Navigation Signal Timing and Ranging Global Positioning System), is a satellite navigation system used for determining one's precise location and providing a highly accurate time reference almost anywhere on Earth or in Earth orbit. It uses an intermediate circular orbit (ICO) satellite constellation of at least 24 satellites.
<< NAVSTAR GPS satellite undergoing pre-launch testing.
The GPS system was designed by and is controlled by the United States Department of Defense and can be used by anyone, free of charge. The GPS system is divided into three segments: space, control, and user. The space segment comprises the GPS satellite constellation. The control segment comprises ground stations around the world that are responsible for monitoring the flight paths of the GPS satellites, synchronizing the satellites' onboard atomic clocks, and uploading data for transmission by the satellites. The user segment consists of GPS receivers used for both military and civilian applications. A GPS receiver decodes time signal transmissions from multiple satellites and calculates its position by trilateration.
The cost of maintaining the system is approximately US$400 million per year, including the replacement of aging satellites. The first of 24 satellites that form the current GPS constellation (Block II) was placed into orbit on February 14, 1989. The 52nd GPS satellite since the beginning in 1978 was launched November 6, 2004 aboard a Delta II rocket.
The system consists of a "constellation" of at least 24 satellites in 6 orbital planes. The GPS satellites were initially manufactured by Rockwell; the first was launched in February 1978, and the most recent was launched November 6, 2004. Each satellite circles the Earth twice every day at an altitude of 20,200 kilometres (12,600 miles). The satellites carry atomic clocks and constantly broadcast the precise time according to their own clock, along with administrative information including the orbital elements of their own motion, as determined by a set of ground-based observatories.
The receiver does not need a precise clock, but does need a clock with good short-term stability and the ability to receive signals from four satellites in order to determine its own latitude, longitude, elevation, and the precise time. The receiver computes the distance to each of the four satellites from the difference between local time and the time the satellite signals were sent (this distance is called a pseudorange). It then decodes the satellites' locations from their radio signals and an internal database. The receiver should now be located at the intersection of four spheres, one around each satellite, with a radius equal to the time delay between the satellite and the receiver multiplied by the speed of the radio signals. Because the receiver does not have a very precise clock it cannot compute the time delays. However, it can measure with high precision the differences between the times when the various messages were received. This yields 3 hyperboloids of revolution of two sheets, whose intersection point gives the precise location of the receiver. This is why at least four satellites are needed: fewer than 4 satellites yield 2 hyperboloids, whose intersection is a curve; it is impossible to know where the receiver is located along the curve without supplemental information, such as elevation. If elevation information is already known, only signals from three satellites are needed (the point is then defined as the intersection of two hyperboloids and an ellipsoid representing the Earth at this altitude).
When there are n > 4 satellites, the n-1 hyperboloids should, assuming a perfect model and measurements, intersect on a single point. In reality, the surfaces rarely intersect, because of various errors. The question of finding the point P can be reformulated into finding its three coordinates as well as n numbers ri such that for all i, PSi-ri is close to zero, and the various ri-rj are close to C.Δij where C is the speed of light and Δij are the time differences between signals i and j. For instance, a least squares method may be used to find an optimal solution. In practice, GPS calculations are more complex (repeat measurements, etc.).
There are several causes: The initial local time is a guess due to the relatively imprecise clock of the receiver, the radio signals move more slowly as they pass through the ionosphere, and the receiver may be moving. To counteract these variables, the receiver then applies an offset to the local time (and therefore to the spheres' radii) so that the spheres finally do intersect in one point. Once the receiver is roughly localized, most receivers mathematically correct for the ionospheric delay, which is least when the satellite is directly overhead and becomes greater toward the horizon, as more of the ionosphere is traversed by the satellite signal. Since it is common for the receiver to be moving, some receivers attempt to fit the spheres to a directed line segment.
The receiver contains a mathematical model to account for these influences, and the satellites also broadcast some related information which helps the receiver in estimating the correct speed of propagation. High-end receiver/antenna systems make use of both L1 and L2 frequencies to aid in the determination of atmospheric delays. Because certain delay sources, such as the ionosphere, affect the speed of radio waves based on their frequencies, dual frequency receivers can actually measure the effects on the signals.
In order to measure the time delay between satellite and receiver, the satellite sends a repeating 1,023 bit long pseudo random sequence; the receiver knows the seed of the sequence, constructs an identical sequence and shifts it until the two sequences match.
Different satellites use different sequences, which lets them all broadcast on the same frequencies while still allowing receivers to distinguish between satellites. This is an application of Code Division Multiple Access, or CDMA.