текст по английскому (GPS)

The Global Position System

1. Introduction.

The Navigation Satellite Timing and Ranging (NAVSTAR) Global Positioning System (GPS) is a network of orbiting satellites that can be used to provide information on the location of a signal receiver on the earth's surface. The system has the potential to revolutionize the practice of surveying and navigation, and investigations and applications to date give some truth to this prediction.

It it's simplest form a signal receiver on the surface of the Earth (say mounted on a surveyor's tripod, on a boat, or in an aircraft) receives signals from the satellites that enable the distance (or range) from the satellite to the receiver to be determined. If 4 of these distances can be measured, then the three dimensional location of the receiver can be determined with respect to the satellites, and if the positions of the satellites can be determined then absolute location can be derived. This can be performed in a matter of minutes in a hand-held receiver for less than $1000AUD, or to around centimeter precision using more sophisticated (and hence more expensive) instruments.

The availability of the system now means that anybody can determine a unique location on the surface of the planet or navigate across it, not just those lucky few learned in the black arts of astronomy and geodetic positioning (that is, Geomatics professionals). Yacht owners, bush walkers, 4 wheel drivers, BMW Series 7 owners, ambulances, CFA fire tenders, fliers, explorers, inhuman Serbian snipers, Polaris missiles, the French Marines, Greenpeace and techno-junkies all now have access to positioning information previously unavailable.

The topic of GPS will be dealt with in these notes at a very introductory level. These reference notes are designed to accompany a course inplane surveying, whereas GPS positioning takes place on a complex surface which can be only approximately modelled by a spheroid. In order to understand fully the solution to GPS positioning a high level of geodetic and mathematical knowledge is required. This will be provided in the later years of the Geomatics courses.

2. The System

The GPS network (or constellation) of satellites is owned and operated by the US Navy, and made available for civilian use in a less precise mode than that available for the military. When fully configured, the constellation will consist of 24 (or so) satellites, some 18 of which should be operational at any one time (but this is still under debate in the US). They are in a geocentric orbit around the planet at an altitude of 26,000km± (the path is elliptical), with 4 satellites in each of six orbital planes and a period of orbit of 12 hours. The height of the orbit means that they are not affected to a great extent by the Earth's gravitational field, and the effect of the sun and the moon on the GPS orbits are modelled as systematic errors. They transmit the main positioning codes at two frequencies, 1575.42MHz and 1227.6MHz (multiples of the fundamental frequency of 10.23MHz), modulated with the navigation message and the carrier wave These frequencies were chosen partly so the effect of the ionosphere and troposphere on the transmitted signal are minimized (but not eliminated).

A Schematic Diagram of the GPS Constellation

The secret to the operation of the GPS network is the use of atomic clocks to measure time. The two time systems of the vehicles generally use caesium clocks accurate to around 1 part in 10-12sec per day, and are based on the international standard for time (being the duration of 9,192,631,770 periods of radiation corresponding to the transition between two energy levels of Caesium 133). The times of these clocks are monitored by ground stations and corrected as necessary, and kept within 1msec of Universal Coordinated Time (UTC). The time base of the GPS is so well monitored and accurate that it has become the standard for the transfer of time , the time is even corrected for relativity effects caused by the differing gravity in the orbit and the eccentricity of the orbit. The receivers also contain accurate clocks (but luckily not atomic clocks) however we need to compensate for the errors that accumulate in these. It is possible to determine relative positions on the surface of the earth to within centimeters from the use of GPS. The determination of absolute position is governed by many factors like the actual shape of the planet, the coordinate datum used to express location and including the US Navy's intentional corruption of the satellite ephemeris (known as selective availability). It can be around 20-30m on a good day, but up to 150± whenever the US Navy decides.

The reference books on GPS surveying mention three concepts of the ground segment, the space segment and the user segment. It is within the ground segment that the time corrections are generated and broadcast to the satellites. The main ground control station is located at Colorado Springs in the USA, and there are three transmission stations that track the satellites and relay data to the ground control. The position of the satellites (the ephemeris, same term as used for position of the sun and stars), the health of the satellites, the clock errors and the ionospheric corrections are determined at the control station and broadcast to the satellites. This continual interface between the ground segment and the space segment (the satellites, obviously) contributes greatly to the success of the system for accurate navigation and positioning. We the users are the user segment, which is where the processing occurs, where the dynamic positioning takes place, and where the ingenuity of civilian minds defeats the US Navy's attempts to degrade our precision.

3. The Position Solution

If we know the distance from one satellite to our receiver, we know we are somewhere on the surface of a sphere of this radius distant from the satellite. If we can determine another distance from¹ another satellite, we narrow down our possible location to somewhere on the surface where these two spheres meet. If we can determine a third distance then this gives us only two possible locations for our receiver. One of these locations is usually nonsensical (for example inside the planet) so the other location is our position.

If we needed to be certain, we would determine the position from another satellite, so 4 distance determinations gives our location as well as eliminate clock errors in the receivers (a systematic error). As you are aware by now, surveyors would like to have a few redundant measurements so the precision and accuracy can be determined, so we often take readings to as many satellites as are above the cut off angle. The use of GPS for high precision positioning involves quite convoluted processing of measurements made to as many satellites as are available.

4. Hardware

GPS receivers come in a variety of shapes and prices, the more expensive the unit the more satellites can be observed and the higher the precision possible through post-processing of data. Units like the Trimble Ensign cost around $1000 and can give positions to around 20-50m without selective availability (and around 100-200m with selective availability and we do not know whether this phenomenon is present). These units are sometimes known as single channel units as in early models one receiver channel used to swap between satellites to receive the signals. Some of the newer units however use multiple channels. The accuracy is more than adequate for people who wish to know where they are and where they are going from the point of view of navigation. Other units with similar accuracies are available as an antenna/OEM board for a computer configuration, an antenna and PCMCIA card for lap-tops or installed as one of the options on luxury cars like the BMW Series 7 and Toyota Landcruiser Stationwagons.

This accuracy is not often adequate from the point of view of mapping or survey coordination, and certainly not for high precision cadastral surveying or engineering measurement. In order to achieve the sort of positional accuracy geomatics professionals are accustomed to we need to (unfortunately) purchase other hardware.

More expensive units like the Ashtech XII and the Leica System 300 are designed to store all the data that is received by the unit from all the available satellites, allowing the signals to be computer processed at a later stage to achieve much higher precisions and accuracies. The Leica unit also allows communication between the various components to real-time differential positioning can be undertaken. More on this later. Multi channel geodetic quality receivers cost from $25000 to $50000, several will be demonstrated during the practical classes accompanying these lectures.

5. Ionospheric and Atmospheric Delays

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As we know the speed of light is a constant only in a vacuum, when light (or radio waves) travel through a denser medium the velocity decreases. The ionosphere is a band of electrically charged particles that slow down the incoming signals from GPS satellites. As our distance determination is based on assuming a constant speed of travel, this delay will affect the accuracy and precision of our positioning.

This 'error' can be reduced in the observations by using the time taken by signals using two different frequencies, or dual frequency receivers. The error in each will be different, and the on board processing functions of sophisticated receivers can eliminate this effect.

There are other sources of systematic and random error that degrades the accuracies available from

GPS positioning, however with advanced error modelling most of these can be eliminated.

6. The signals

The signals sent by the satellites to earth are fairly low powered and are barely discernible from the background radiation or noise of the heavens. If, say, we were receiving satellite television we would need a large parabolic dish to receive the signal, just look at the roof of any hotel that receives Sky Channel. An antenna of this design would severely limit the portability of GPS receivers. Instead the satellites generate pseudo-random code which can be deciphered only by receivers that generate a similar signal. Our GPS units shift their version of the pseudo-random code around the incoming signal until a pattern is seen that makes the signal stand out from the noise. As a result of this, only small antennae are required. Another benefit is that the US military can change this code to exclude access to the system.

7. Dynamic Positioning

GPS can be used from almost any platform, from cars, boats and aircraft to incoming inter­continental ballistic missiles. (GPS is not yet an FAA Approved Primary Navigation Device for aircraft in the US, there must be another navigation system installed as well as GPS). Most GPS receivers are capable of supplying derived SOG (speed over ground), VMG (velocity made good) and BRG (heading) information, as well as distances from or to navigation landmarks (way points). The receivers do this by taking positions at regular intervals and determining the change of position over that time, and then converting this into the navigation units. One of the more noticeable limitations of single channel positioning units is that when stationary the units may show a velocity as the positions wander around anywhere from 2m to 100m.

Dynamic GPS is becoming the default method of navigation for small craft as the complex computations previously necessary are all performed on-board the receiver. They work independently of the weather, 24 hours per day (but not under trees or water), perform spheroidal calculations and automatically convert between coordinate datums.

7.1 High accuracy Dynamic (or Kinematic) Positioning

The techniques used for high accuracy positioning of dynamic receivers will be discussed in the section dealing with differential positioning. The method of differential positioning can be used on both static and dynamic receivers so there is little point in repeating the material here.

8. Static Positioning

The Global Positioning System has revolutionized the geomatics industry, it is now not only possible to perform traditional surveying tasks in radically less time but there is a vastly increased scope of tasks to be performed. Recent examples in the Department of Geomatics include the use of GPS to develop a mapping system that can coordinate rail tracks at 60kmh-l, developing computational procedures to include GPS positioning in aero-triangulation, using GPS to coordinate facility mapping systems, incorporating high precision GPS measurements into dam movement surveys, and the much more routine use of GPS to coordinate sea floor mapping. Where once we would use laser or radio distance measuring machines for determining coordinates of control points we now use two GPS units.

The highest level of accuracy obtainable with GPS is to use two units, one on a base station and the other visiting the points of interest. It is then possible to compute the vector between these two units to a much higher degree of accuracy than we can compute absolute latitude and longitude. Practically all the systematic errors that can occur in GPS positioning can be eliminated if we measure to a set of satellites simultaneously from two receivers, a process known as differential positioning.

8.1 Differential Positioning