The concept of satellite position fixing commenced with the launch of the first Sputnik satellite by the USSR in October 1957. This was rapidly followed by the development of the Navy Navigation Satellite System (NNSS) by the US Navy. This system, commonly referred to as the Transit system, was created to provide a worldwide navigation capability for the US Polaris submarine fleet. The Transit system was made available for civilian use in 1967 but ceased operation in 1996. However, as the determination of position required very long observation periods and relative positions determined over short distances were of low accuracy, its application was limited to geodetic and low dynamic navigation uses.
In 1973, the US Department of Defense (DoD) commenced the development of NAVSTAR (Navigation System with Time and Ranging) Global Positioning System (GPS), and the first satellites were launched
in 1978.
The system is funded and controlled by the DoD but is partially available for civilian and foreign users. The accuracies that may be obtained from the system depend on the degree of access available to the user, the sophistication of his/her receiver hardware and data processing software, and degree of mobility during signal reception.
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| Global Positioning System logo |
In very broad terms, the geodetic user in a static location may obtain ‘absolute’ accuracy (with respect to the mass centre of the Earth within the satellite datum) to better than ±1 metre and position relative to another known point, to a few centimetres over a range of tens of kilometres, with data post-processing. At the other end of the scale, a technically unsophisticated, low dynamic (ship or land vehicle) user, with limited access to the system, might achieve real time ‘absolute’ accuracy of 10–20 metres.
The GPS navigation system relies on satellites that continuously broadcast their own position in space and in this the satellites may be thought of as no more than control stations in space. Theoretically, a user who has a clock, perfectly synchronized to the GPS time system, is able to observe the time delay of a GPS signal from its own time of transmission at the satellite, to its time of detection at the user’s equipment. The time delay, multiplied by the mean speed of light, along the path of the transmission from the satellite to the user equipment, will give the range from the satellite at its known position, to the user. If three such ranges are observed simultaneously, there is sufficient information to compute the user’s position in three-dimensional space, rather in the manner of a three-dimensional trilateration. The false assumption in all this is that the user’s receiver clock is perfectly synchronized with the satellite clocks.
1. GPS Observing Methods
The use of GPS for positioning to varying degrees of accuracy, in situations ranging from dynamic (navigation) to static (control networks), has resulted in a wide variety of different field procedures using one or other of the basic observables. Generally pseudo-range measurements are used for navigation, whilst the higher precision necessary in engineering surveys requires carrier frequency phase measurements.
The basic point positioning method used in navigation gives the X, Y, Z position to an accuracy of better than 20 m by observation to four satellites. However, the introduction of Selective Availability (SA), see below, degraded this accuracy to 100 m or more and so led to the development of the more accurate differential technique. In this technique the vector between two receivers (baseline) is obtained, i.e. the difference in coordinates (ΔX, ΔY, ΔZ). If one of the receivers is set up over a fixed station whose coordinates are known, then comparison with the observed coordinates enables the differences to be transmitted as corrections to the second receiver (rover). In this way, all the various GPS errors are lumped together in a single correction. At its simplest the corrections transmitted could be in a simple coordinate format, i.e. δX, δY, δZ, which are easy to apply. Alternatively, the difference in coordinate position of the fixed station may be used to derive corrections to the ranges to the various satellites used. The rover then applies those corrections to its own observations before computing its position.
The fundamental assumption in Differential GPS (DGPS) is that the errors within the area of survey would be identical. This assumption is acceptable for most engineering surveying where the areas involved are small compared with the distance to the satellites.
Where the area of survey becomes extensive this argument may not hold and a slightly different approach is used called Wide Area Differential GPS.
It can now be seen that, using DGPS, the position of a roving receiver can be found relative to a fixed master or base station without significant errors from satellite and receiver clocks, ionospheric and tropospheric refraction and even ephemeris error. This idea has been expanded to the concept of having permanent base stations established throughout a wide area or even a whole country.
As GPS is essentially a military product, the US Department of Defense has retained the facility to reduce the accuracy of the system by interfering with the satellite clocks and the ephemeris of the satellite. This is known as Selective Availability (SA) of the Standard Positioning Service (SPS). This form of degradation has been switched off since May 2000 and it is unlikely, though possible, that it will be reintroduced as there are other ways that access to the system can be denied to a hostile power. The P can also be altered to a Y code, to prevent imitation of the PPS by hostile forces, and made unavailable to civilian users. This is known as Anti-Spoofing (AS). However, the carrier wave is not affected and differential methods should correct for most SA effects.
Using the carrier phase observable in the differential mode produces accuracies of 1 ppm of the baseline length. Post-processing is needed to resolve for the integer ambiguity if the highest quality results are to be achieved. Whilst this, depending on the software, can result in even greater accuracies than 1 ppm (up to 0.01 ppm), it precludes real-time positioning. However, the development of Kinematic GPS and ‘on-the-fly’ ambiguity resolution makes real-time positioning possible and greatly reduces the observing times.
The following methods are based on the use of carrier phase measurement for relative positioning using two receivers.
1.1 Static positioning
This method is used to give high precision over long baselines such as are used in geodetic control surveys. At its simplest, one receiver is set up over a station of known X, Y, Z coordinates, preferably in the WGS84 reference system, whilst a second receiver occupies the station whose coordinates are required.
Observation times may vary from 45 min to several hours. This long observational time is necessary to allow a change in the relative receiver/satellite geometry in order to calculate the initial integer ambiguity terms.
More usually baselines are observed when the precise coordinates of neither station are known. The approximate coordinates of one station can be found by averaging the pseudo-range solution at that station.
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| Artist's impression of GPS Block IIR satellite in Earth orbit |
Provided that those station coordinates are known to within 10 m it will not significantly affect the computed difference in coordinates between the two stations. The coordinates of a collection of baselines, provided they are interconnected, can then be estimated by a least squares free network adjustment. Provided that at least one, and preferably more, stations are known in WGS84 or the local datum then the coordinates of all the stations can be found in WGS84 or the local datum.
Accuracies in the order of 5 mm ±1 ppm of the baseline are achievable as the majority of errors in GPS, such as clock, orbital and atmospheric errors, are eliminated or substantially reduced by the differential process. The use of permanent active GPS networks established by a government agency or private company results in a further increase in accuracy for static positioning.
Apart from establishing high precision control networks, it is used in control densification, measuring plate movement in crustal dynamics and oil rig monitoring.
1.2 Rapid static
Rapid static surveying is ideal for many engineering surveys and is halfway between static and kinematic procedures. The ‘master’receiver is set up on a reference point and continuously tracks all visible satellites throughout the duration of the survey. The ‘roving’ receiver visits each of the remaining points to be surveyed, but stays for just a few minutes, typically 2–10 min.
This method is accurate and economic where there are many points to be surveyed. It is ideally suited for short baselines where systematic errors such as atmospheric, orbital, etc., may be regarded as equal at all points and so differenced out. It can be used on large lines (>10 km) but may require longer observing periods due to the erratic behaviour of the ionosphere. If the observations are carried out at night when the ionosphere is more stable observing times may be reduced.
1.3 Reoccupation
This technique is regarded as a third form of static surveying or as a pseudo-kinematic procedure. It is based on repeating the survey after a time gap of one or two hours in order to make use of the change in receiver/satellite geometry to resolve the integer ambiguities.
The master receiver is once again positioned over a known point, whilst the roving receiver visits the unknown points for a few minutes only. After one or two hours, the roving receiver returns to the first unknown point and repeats the survey. There is no need to track the satellites whilst moving from point to point. This technique therefore makes use of the first few epochs of data and the last few epochs that reflect the relative change in receiver/satellite geometry and so permit the ambiguities and coordinate differences to be resolved.
Using dual frequency data gives values comparable with the rapid static technique. Due to the method of
changing the receiver/satellite geometry, it can be used with cheaper single-frequency receivers (although extended measuring times are recommended) and a poorer satellite constellation.
1.4 Kinematic positioning
The major problem with static GPS is the time required for an appreciable change in the satellite/receiver geometry so that the initial integer ambiguities can be resolved. However, if the integer ambiguities could be resolved (and constrained in a least squares solution) prior to the survey, then a single epoch of data would be sufficient to obtain relative positioning to sub-centimetre accuracy. This concept is the basis of kinematic surveying. It can be seen from this that, if the integer ambiguities are resolved initially and quickly, it will be necessary to keep lock on these satellites whilst moving the antenna.
1.4.1 Resolving the integer ambiguities
The process of resolving the integer ambiguities is called initialization and may be done by setting up both receivers at each end of a baseline whose coordinates are accurately known. In subsequent data processing, the coordinates are held fixed and the integers determined using only a single epoch of data.
These values are now held fixed throughout the duration of the survey and coordinates estimated every epoch, provided there are no cycle slips.
The initial baseline may comprise points of known coordinates fixed from previous surveys, by static GPS just prior to the survey, or by transformation of points in a local coordinate system to WGS84. An alternative approach is called the ‘antenna swap’ method. An antenna is placed at each end of a short base (5–10 m) and observations taken over a short period of time. The antennae are interchanged, lock maintained, and observations continued. This results in a big change in the relative receiver/satellite geometry and, consequently, rapid determination of the integers. The antennae are returned to their original position prior to the surveys.
It should be realized that the whole survey will be invalidated if a cycle slip occurs. Thus, reconnaissance of the area is still of vital importance, otherwise reinitialization will be necessary. A further help in this matter is to observe to many more satellites than the minimum four required.
1.4.2 Traditional kinematic surveying
Assuming the ambiguities have been resolved, a master receiver is positioned over a reference point of known coordinates and the roving receiver commences its movement along the route required. As the movement is continuous, the observations take place at pre-set time intervals, often less than 1 s. Lock must be maintained to at least four satellites, or re-established when lost. In this technique it is the trajectory of the rover that is surveyed and points are surveyed by time rather than position, hence linear detail such as roads, rivers, railways, etc., can be rapidly surveyed. Antennae can be fitted to fast moving vehicles, or even bicycles, which can be driven along a road or path to obtain a three-dimensional profile.
1.4.3 Stop and go surveying
As the name implies, this kinematic technique is practically identical to the previous one, only in this case the rover stops at the point of detail or position required (Figure 9.17). The accent is therefore on individual points rather than a trajectory route, so data is collected only at those points. Lock must be maintained, though the data observed when moving is not necessarily recorded. This method is ideal for engineering and topographic surveys.
1.4.4 Real-time kinematic (RTK)
The previous methods that have been described all require post-processing of the results. However, RTK provides the relative position to be determined instantaneously as the roving receiver occupies a position.
The essential difference is in the use of mobile data communication to transmit information from the reference point to the rover. Indeed, it is this procedure that imposes limitation due to the range over which the communication system can operate.
The system requires two receivers with only one positioned over a known point. A static period of initialization will be required before work can commence. If lock to the minimum number of satellites is lost then a further period of initialization will be required. Therefore the surveyor should try to avoid working close to major obstructions to line of sight to the satellites. The base station transmits code and carrier phase data to the rover. On-board data processing resolves the ambiguities and solves for a change in coordinate differences between roving and reference receivers. This technique can use single or dual frequency receivers. Loss of lock can be regained by remaining static for a short time over a point of known position.
The great advantage of this method for the engineering surveyor is that GPS can be used for setting-out on site. The setting-out coordinates can be entered into the roving receiver, and a graphical output indicates the direction and distance through which the pole-antenna must be moved. The positions of the point to be set-out and the antenna are shown. When the two coincide, the centre of the antenna is over the setting-out position.
1.4.5 Real-time kinematic on the fly
Throughout all the procedures described above, it can be seen that initialization or reinitialization can only be done with the receiver static. This may be impossible in high accuracy hydrographic surveys or road profiling in a moving vehicle. Ambiguity Resolution On the Fly (AROF) enables ambiguity resolution whilst the receiver is moving. The techniques require L1 and L2 observations from at least five satellites with a good geometry between the observer and the satellites. There are also restrictions on the minimum periods of data collection and the presence of cycle slips. Both these limitations restrict this method of surveying to GPS friendly environments. Depending on the level of ionospheric disturbances, the maximum range from the reference receiver to the rover for resolving ambiguities whilst the rover is in motion is about 10 km, with an achievable accuracy of 10–20 mm.
For both RTK and AROF the quality of data link between the reference and roving receiver is important. Usually this is by radio but it may also be by mobile phone. When using a radio the following issues should be considered:
- In many countries the maximum power of the radio is legally restricted and/or a radio licence may be required. This in turn restricts the practical range between the receivers.
- The radio will work best where there is a direct line of sight between the receivers. This may not always be possible to achieve so for best performance the reference receiver should always be sited with the radio antenna as high as possible.
- Cable lengths should be kept as short as possible to reduce signal losses.