Sect_5.2.3

5.2.3 GPS Survey Planning

OBSERVATION SCHEDULING

There are three considerations:

Those that relate to the satellites themselves: how many to observe, for how long, etc.

Those that relate to satellite-receiver geometry.

Those that relate to logistical design: number of observation sessions per day, number of multiple site occupancies, etc.

Satellite Considerations

To prepare an observation schedule for a GPS survey it is necessary to first define the satellite constellation to be tracked, including such information as:

Rise and set times of satellites above the observing horizon of a site. (Due to atmospheric refraction modelling difficulties GPS satellites are not normally tracked at elevations less than 15° to 20° above the horizon.)
Health of the satellites. Each satellite broadcasts a health status indicator within its Navigation Message. This should be monitored during tracking, but a history of health problems may indicate a satellite which should be avoided if at all possible. (Note that although a satellite may be "unhealthy" for GPS navigation this does not mean that it cannot be used for surveying.)
Satellite-site geometry: azimuth and elevation of satellites as a function of time.
Information on the status of satellites (section 3.4.2), for example, planned orbit manoeuvres, shutdowns, testing, new satellite launches, etc.

This information is largely provided (in various graphical and tabular forms) by the "planning" software provided by GPS instrument manufacturers. Obviously the optimum "window" of satellite availability is required, but it may not always be possible to have such a window coincide with the daylight hours of the "working day". Hence, observation scheduling may be considered an exercise in avoiding the worst observing windows! An important criteria is the azimuth and elevation of the satellites over the day of interest, presented in the form of a "sky plot". (Azimuth and elevation can be computed using the formulae given in section 1.2.2)

Two tasks within the observation window scheduling process can be identified:

Determine the minimum length of observation period per station. This is dependent on, amongst other factors, the following:
- the satellite constellation to be observed,
- the length of the baseline,
- whether a "conventional" static GPS survey is being carried out, or "kinematic" and "rapid static" survey techniques will be used (section 5.5.1),
- - the observation period, as some periods may have better "geometric strength" than periods of the same length at other times. (This is not an important issue for "conventional" GPS surveys, but it is important for modern "kinematic" techniques.)
Determine the satellites to be observed by all simultaneously operating GPS receivers. If instrumentation can only track less than the number visible satellites, then satellite selection becomes an issue. Modern instrumentation however tends to have "all-in-view" tracking capability.

The most critical is the observation session length. Unfortunately estimating the appropriate length of an observing session is very difficult, as it is a function of baseline length and environmental factors, as well as being dependent on the satellite constellation. Once the sites, instrumentation to be used, accuracy sought and time of day is fixed, then the constellation that can be tracked is known, and what remains to be determined is the session length. The following factors should be borne in mind:

For GPS surveying, the minimum number of satellites that must be observed simultaneously by GPS receivers is two (to form one double-difference observable).
The more satellites observed simultaneously, the shorter the observation period can be.
The shorter the observation session, the more care is needed to guard against multipath and other biases.
The "total" satellite geometry (all satellites tracked over a session) has an important bearing on the quality of the results. That is, sessions in which the constellation changes (satellites set and new ones rise) should be avoided, hence continuous tracking is preferred.
The preferred solution is an "ambiguity-fixed" solution, hence any tracking beyond that required to successfully resolve the integer cycle ambiguities is useless. In other words, the optimum period of tracking is the one that permits ambiguity resolution to occur in the minimum period of time.
An "ambiguity-free" solution, on the other hand, tends to improve with longer observation sessions.
An "ambiguity-fixed" solution is unlikely to be possible for baselines longer than 20-30km using commercial GPS software packages.
Experience indicates that to adequately resolve ambiguities, it is necessary to observe at least four satellites simultaneously for a minimum of 30 minutes. However, it has also been shown that in the presence of multipath, it can take two hours or more to properly resolve the ambiguities, if at all.
In the case of baseline lengths greater than 20-30km, longer session lengths are recommended (see Figure 1 below).
It is not yet possible to predict in advance, with absolute certainty, how long an observing period should be to maximise the chances of an "ambiguity-fixed" solution being obtained.

There is unfortunately no GPS planning aid that takes all these factors into account: type of solution sought, baseline configuration, data sampling rate, available satellite constellation; and indicates the appropriate observation session length. Some attempts have been made to develop simple indicators of "good" and "bad" satellite geometry for GPS surveying, but even with these there is still great uncertainty in the expected baseline results due to unmodelled external factors influencing GPS adjustments, such as orbit errors, multipath and atmospheric refraction.

For conventional static GPS surveys it is generally recommended that the observation session lengths should be 0.5 - 2 hours in length, though this is dependent on the number of satellites to be tracked, baseline length, and to some extent the instrumentation and software being used (see, for example, Figure 1 below).

Figure 1. Suggested observation session lengths for "conventional" static GPS surveys.

Observation session lengths for "rapid static" GPS techniques are recommended as being of the order of 5-15 minutes. These are guidelines only, adequate for short baselines (<20km) and conditions of low PDOP (section1.4.9). Observation sessions lengths are a non-issue for "kinematic" and "stop & go" techniques as station occupancies are only of the order of seconds.

Measures of Satellite Geometry

The accuracy of GPS-derived coordinates is generally a function of:

(1) the measurement precision,

(2) the systematic errors present,

(3) the processing strategy used, and

(4) the receiver-satellite geometry during the observing session.

Of these, items (2) and (4) are the most variable. The receiver-satellite geometry is highly predictable and is manifest in the Normal Equations for the Least Squares solution for the site coordinates. In fact the elements of the design matrix (the unit vectors for the receiver-satellite in question) can be computed beforehand and "optimised", similar to the planning procedures used for conventional terrestrial surveys. Hence, given a satellite constellation, the approximate coordinates of the receivers, the time of day and length of session, the Normal Equation System can be determined, inverted and the formal errors of the estimable parameters obtained. This process is described in, for example, MERMINOD et al (1990).

Unfortunately GPS receivers do not output this information. Instead, the "indicators of precision" (or more correctly the influence of satellite geometry on the solution) are borrowed from GPS navigation. In conventional surveying, the often used indicators of precision are the components of the error ellipse (in the case of 2-D Least Squares solutions) or error ellipsoid (for 3-D Least Squares solutions). The error ellipse associated with a computed point is described by three parameters: the lengths of the axes, and the azimuth of the major axis. Similarly, the error ellipsoid is described by six parameters: the lengths of the three axes of the ellipsoid, and the three orientation angles. However, the use of six parameters to describe the instantaneous precision of a GPS navigation "fix" is rather awkward, and hence GPS navigation has tended to use simplified precision indicators.

The error ellipsoid is approximated by an error sphere whose radius is equal to the root of the sum of the squares (RSS) of the ellipsoid axes. The Position Dilution Of Precision (PDOP) is defined as the radius of the RSS sphere, assuming the standard deviation of the pseudo-range measurements is unity (section 1.4.9). Hence the six precision indicators associated with an error ellipsoid are compressed into one PDOP quantity which depends only on the relative geometry of the four or more satellites, and the approximate location of the point whose coordinates are to be determined (Figure 2).

Figure 2. Example of PDOP plot for a 24 hour period at Sydney, Australia.

Other DOP factors can also be defined, in particular HDOP and VDOP, the horizontal and vertical DOP respectively, and GDOP. It is these DOPs (in particular PDOP and GDOP) that are output by GPS receivers, and have tended to be used (perhaps incorrectly) for accuracy studies. The inappropriateness of using PDOP for conventional GPS survey planning can be readily seen if a GPS survey adjustment is compared with a GPS navigation solution:

The navigation solution is based on the instantaneous satellite-receiver geometry, whereas the GPS carrier phase adjustment is governed by the continually changing geometry of an observing session which may last up to several hours.
PDOP gives the geometric strength of a point position, whereas the GPS carrier phase adjustment provides the relative position of two or more receivers.
The pseudo-ranges are considered to be biased only by the errors of the receiver clock (which changes from epoch to epoch). In a GPS carrier phase adjustment, the double-differenced observation is predominantly biased by the integer cycle ambiguities (the satellite and receiver clock biases are eliminated). The geometric strength of double-differenced ambiguous range measurements (integrated carrier phase) is quite different to that of pseudo-range.

A simple example of the inappropriateness of GDOP for GPS carrier phase adjustment is the fact that GDOP is undefined for three satellites (it would involve the estimation of four parameters from three observations) and yet three satellites can be used in a baseline solution using integrated carrier beat phase. Alternative DOPs have been introduced, such as BDOP, RDOP and DGDOP (see IBID, 1990). Their usefulness, however, has been restricted by the unpredictable nature of the systematic errors, and in some cases by the lack of distinction being made between an "ambiguity-free" solution and an "ambiguity-fixed" one. As a consequence, mere "rules-of-thumb" can be given, such as: the best time to carry out a GPS survey is when the PDOP (or GDOP) is changing rapidly (rather than when it is low). But with the deployment of the full satellite constellation it unlikely that there will be periods when the conditions for a "good" geometry for GPS surveying are significantly better than at other times.

Modern GPS surveying techniques are in fact closer to GPS navigation solutions, hence PDOP does have a role to play in GPS planning.

So what constitutes a good tracking session?

As a rule-of-thumb, a good session is one which has four or more visible satellites above the 15° - 20° elevation angle at the start of the tracking period, and ends before the fourth satellite sets below this cutoff elevation angle.

The length of session then is a function of the baseline length, and whether it is a conventional static survey (say 30-120 mins in duration), or a "rapid static" survey (5-15 mins) or "stop & go" (<1 min).

Observation Scheduling: Some Logistical Factors

Observation scheduling within a network relates to:

The number of observation sessions in a day (dependent on length of the work day, and minimum session length).

Total non-productive times: travel time between stations, station setup/takedown time, data downloading, etc.

Number of occupations of each station (new and unknown).

The main consideration, however, relates to multiple occupancy of sites. These are required for a number of purposes:

To provide a "link" in the datum between each session. The datum station's WGS84 coordinates can then be propagated through an entire network (Figure 3 below). How many common stations between sessions? The issue is simply that:
- one is a bare minimum,
- two provides one redundant link, and
- three or more is even better.
A quality control measure, as multiple occupancies provide different "pathways" through a network for checking on blunders, wrongly identified stations, errors in antenna height measurement, etc. However, the larger the number of links between sessions, the slower the progress and hence the more expensive the GPS survey.

Figure 3a & b. Moving from session to session: multiple station occupancy.

The minimum number n of sessions in a network with s stations, using r receivers is (HOFMANN-WELLENHOF et al, 1998):

(5.2-2)

where o denotes the number of "link" or "pivot" stations between sessions, o1, r2, r>o and n is an integer. An alternative relation that is simply based on the notion that all stations should have multiple occupancies (as is recommended by certain GPS "standards & specifications" -- section 10.2.5) is (HOFMANN-WELLENHOF et al, 1998):

(5.2-3)

where m is the number of times a station must be occupied, and n must be rounded up to the next higher integer. With this basic information a session-by-session plan is made that has as one of its major aims the survey of a network with relatively homogeneous accuracy and reliability. The outcome of this observation scheduling exercise is the preparation of an observation plan that is to be followed by the field parties. The Table in the next chapter is an example of such a plan, for the session-by-session survey appropriate for the project plan in Figure 3b.

Often the common link stations will be occupied by the same receiver and field party during two successive sessions. However, this does not constitute an independent set-up! Nevertheless, a link between sessions is established even if the field party is setting-up over the wrong groundmark! If stations linking successive sessions are occupied independently, and if the antenna is not set-up over the same mark, or the antenna height is incorrectly measured, the link between sessions is lost. Having a suitable degree of network redundancy (multiple setups, preferably independent) may permit such errors to be identified and remedied. Alternatively such common errors as setting-up over the wrong mark, or not measuring antenna height correctly, can be minimised if field surveyors are properly trained in GPS field procedures.

Guidelines on multiple occupancy of GPS stations, and the percentage of independent occupations of common stations, can usually be found in the prescribed GPS survey "standards & specifications" (section 5.2.5).

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