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 revolutionise
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 centimetre 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
in plane 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.
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 minimised (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 centimetres 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.
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
from 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.
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.
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.
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.
GPS can be used from almost any platform, from cars, boats and
aircraft to incoming inter-continental 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.
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.
The Global Positioning System has revolutionised 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-1, 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.
The typical configuration for differential positioning is shown
below, two units receiving signals from the same constellation
of satellites at the same time. The relative position of the two
units can be determined to a very high accuracy, in many cases
better than a centimetre. If one of these units was located over
a point for which we had ground control coordinates it is then
theoretically possible to obtain highly accurate coordinates for
the other point. This is indeed the case, providing all the computations
are performed in the one coordinate system.
This technique can be also applied if one of the receivers is
on a moving platform, or is moved between points of interest while
the base station remains fixed and continues to observe to the
same satellites. This produces new procedures known as rapid-static positioning,
kinematic positioning and pseudo-kinematic positioning. By the time these notes are
copied and distributed
there will no doubt be other new pieces of scientific jargon to
describe new procedures. In general the units store the observations
to the satellites and are down-loaded to PC type computers at
the end of the project. The differential solution is then computed
using the complete set of data from all the receivers. The latest
hardware systems can transmit the corrections between the base
station and the rover allowing the solution to be determined on-the-fly
so that positioning accuracies of around 0.01m are available in
real-time.
The type of coordinate system used in GPS surveying is an earth-centred cartesian system, of which a detailed discussion is beyond the scope of these reference notes in plane surveying. Generally coordinates produced by GPS units are geocentric coordinates which appear nothing like geographic coordinates. Geocentric coordinates are based on the centre of the earth and have an X, Y and Z component. The Z axis is from the centre of the earth through the north pole, the XZ plane passes through the Greenwich meridian and the XY plane passes through the equator. Geographic coordinates are in the form latitude and longitude and are located on a spheroid of 'best fit' over the surface of the planet. Transformations between the cartesian coordinates and the spheroidal coordinates can easily be performed in the receivers, as well as transformations between grid mapping systems like AMG. There is also a selection of spherical models that can be used as a coordinate datum, some of these can be seen during the set-up options on the navigational GPS units. If one wishes to output AMG coordinates in Australia one selects the Australian National Spheroid as the datum, UTM coordinates as the type and the appropriate zone if necessary.
There will be considerable more information provided on coordinate
datums in the later years of the geomatics program. We have only
looked at the matter superficially, the problem of coordinate
frames of reference is part of on-going investigations and developments.
The Global Positioning system offers navigational precision positioning
in all weather 24 hours per day. This facility offers people from
a wide variety of non-technical backgrounds access to navigation
facilities impossible even 10 years ago, ensuring increased safety
and surety in travelling from one location to another. Anybody
can stand in an open space, push a button and determine their
location to 50m or so within minutes.
The full impact of this technology in the geomatics industries
is still to be felt. Units like the Leica System 300 enable tasks
like field-to-office topographic surveys to be performed using
GPS instead of electronic theodolites and EDM, practically eliminating
the need for control surveys and traverses. It is possible to
achieve 0.1m positional accuracy at speeds of 100kmh-1, enabling
the mapping of facilities and resources in a fraction of the time
taken even only 4 years ago. If synchronised video cameras are
coupled with kinematic GPS it is possible to map the position
of road furniture simply by driving along the road. Ground control
for mapping can be coordinated in a matter of days instead of
months, and maps can be produced almost as fast as conditions
change in the real world.
Further applications and implications of GPS positioning will
be presented in the later years of the geomatics course. The technology
and methodology is changing so rapidly that even the most current
reference material is almost out of date by the time it is published.
Elfick, M., J. Fryer, R. Brinkler and P. Wolf. 1995. Elementary Surveying, S.I.
Edition. Harper Collins. pp 321-344.
Bannister, A., S. Raymond and R. Baker. Surveying, 6th Edition. Longman
Scientific and Professional. pp 232-235.
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