10.4.3 Quality Control Procedures for GPS Networks
With regards to multi-session testing, the following comments can be made:
- The primary source of information to gauge the ultimate quality of
the minimally constrained (multi-session) network is obtained from the
network adjustment program. In particular, certain statistical tests can
be applied to the network results, as much of the data that the analyst
needs is often provided. (Many network adjustment programs will carry out
a battery of statistical tests as a matter of course.)
- Multi-session testing is capable of (a) confirming the existence of
data quality problems affecting the session results, AND (b) identifying
any anomalous result arising from inconsistent or incorrect station occupation,
antenna height measurements, etc.
- The level of quality control information in relation to both (a) and
(b) is, however, directly proportional to the number of redundant
connections (between sessions) in the GPS network.
- The number and type of redundant connections is often defined by recommended
standards and specification (section10.3.1), contract
obligations, etc.
- Greater benefit will be obtained if some (or all) sites are occupied
more than once in order to satisfy the requirement for redundancy, rather
than having more than one baseline in a session terminating at a site.
- The greater the number of redundancies, the better the chance of pinpointing
the problem through a process of elimination (or "trouble-shooting").
- The quality testing may also be influenced by the nature of the individual
session solutions. The "detectability" of type (a) and (b) problems
is to some extent dependent on whether processing is by the single baseline
or multi-baseline mode.
- Remedial action can be: (i) leave out
a suspect station, or (ii) possible correction of type (b) problem, or
(iii) reobserve all or some of the session stations.
Some statistical information derived from secondary adjustments that should
be evaluated (though not an exhaustive list!) include:
- Network variance factor and the degrees of freedom. The VF can
be influenced through the modification of the baseline VCV matrices as
described in section 9.4.2.
- The RMS, minimum and maximum residual values, and the standard deviation
of the absolute observation residuals.
- The standardised residuals (absolute residuals
divided by their propagated standard error) can be compared against the
Chi-square test (tests appropriateness of apriori errors) and the Tau criterion
(for data outlier detection) -- section
9.1.5.
- Aposteriori errors at the 95% (2 sigma) confidence level for the adjusted
station coordinates and for the relative positions for all station combinations.
Error ellipses/ellipsoids provide a useful evaluation of the station
solution confidence: nearly circular and uniformly small error figures
are an indication of a well-conditioned network, while irregularly shaped
or unusually large error figures indicate problems with solutions or weakness
in network design.
- Relative confidence between station combinations can be evaluated according
to the claimed geometric accuracy standard. The propagated relative
error (at the 95% confidence level) should be less than the maximum allowable
for the accuracy standard sought.
- Prior to carrying out a constrained adjustment the existing control
coordinates should be examined and transformation parameters determined.
The rms and standard deviation of the computed transformation parameters,
and the coordinates, should be investigated.
- Any significant changes between the statistics of the minimally constrained
adjustment and the constrained adjustment should be flagged and investigated.
The Nature and Detectability of Observational Errors
To master multi-session testing, an understanding of the nature of the observational
errors and how they propagate through session and, ultimately, network solutions
is necessary.
There are two classes of errors:
Those that cannot be detected because they
do not propagate into baselines containing redundant stations.
Those that are detectable because they
propagate into the coordinates of redundant stations.
These statements need amplification, and should be compared with the notions
of "quality control" as practised in conventional geodetic networks:
- Data quality problems will propagate into other station coordinates
during a session (and ultimately through the entire network) if the station
at which the problem has occurred is connected directly to other stations
(as in a traverse). The effect of the error on other stations "downstream"
is unpredictable, as is the case of an error in the early part of a traverse.
If the station were part of a "spur" (or radiation in conventional
survey practice), then the problem will be undetectable.
- Each instrument setup in a traverse (from which backsights and foresight
observations are made) is analogous to a GPS session. It is the sites
common to two sessions that provide the link in the "GPS traverse".
- In a similar way, any problem with a station setup is detectable "downstream"
only if the station is occupied in at least two independent sessions, and
if one was "correct" and the other was "incorrect".
If the same mistake (for example, misidentification of station) is made
both times, the error is undetected (until perhaps some years
later when this station is connected into another survey network). This
is equivalent to the foresight station in the previous setup not being
the same as the instrument station in the current setup. Hence an inconsistency is introduced, and although the measurement
process is satisfactory, all subsequent station coordinates are corrupted.
- If the station is occupied only once (and hence the mistake occurs
once) then, as in the case of the same mistake being made twice, the error
lies dormant. This is equivalent to a single radiation from the main traverse
line. The radiated point cannot be checked.
Redundancy
"Redundancy", in relation to a multi-session network solution,
is provided by the multiple occupation of a station
(for two or more sessions) over and above that required to transfer
datum from one session to another. Thus if more than one of the stations
in a session has been previously occupied, then there is a redundancy (equal
to the number of stations occupied more than once, minus one).
The following comments may be made regarding to GPS network redundancy:
- They provide independent "pathways" joining all the network
stations (Figure 1). Investigation of the closes around different pathways
can assist in pinpointing the source of inconsistent
session results.
Figure 1. Loops formed from multi-session connections.
- The multiple occupation of a pair of stations in the same sessions
leads to repeat baseline results (Figure 2), which can provide a measure
of GPS repeatability.
Figure 2. Repeated baselines.
- The amount of redundancy that is required (multiple stations or baselines)
is often explicitly indicated in the standards and specifications for GPS
surveys (section 10.3.1). They may in fact be integral to the classification of the GPS survey.
- The provision of adequate redundancy is therefore an integral part
of the network design process (section 5.2.2).
Loop Closure Tests
Quasi-independent "loops" can be constructed by linking stations
from different sessions (Figure 1 above). They are useful whether the multi-session
solution is performed with the aid of network software, or the vectors extracted
manually from several adjustments. They may serve two purposes:
- A sampling of loops can provide verification
of the overall consistency of the GPS network results. This may be required
in the U.S. to satisfy the authorities as to the "class" of GPS
survey performed. In this case, such parameters as the maximum and average
allowable misclose may need to be explicitly stated. Note, however, that
if the multi-session solution is being accumulated within a geodetic network
program, the final summary residuals and station coordinate standard deviations
provide the same information. Hence Australian geodetic authorities
do not require an explicit loop closure test to be performed.
- Judicious selection of loops can assist with problem
diagnosis. If a problem has been detected by first carrying out
a GPS (multi-session) network solution and studying the residuals, etc.,
the aim may be to see if it is possible to salvage part of a session solution
by eliminating the problem station from the final adjustment. Generally,
however, such tests are carried out to find out "where" the problem
is, and "why". The most likely outcome is to reobserve if
there is insufficient redundancy.
Standards & Specifications: Quality Control Guidelines
The basic criteria for survey classification is the relative accuracy
of neighbouring stations. These are given in Table
1 in section 10.2.2 (for the Australian recommended standards and practices)
and Table 2 in section 10.2.2 (for the U.S.
standards and specifications), and are the values which must not be exceeded
by the semi-major axes of the relative error ellipses (or ellipsoids). The
relative error is composed of two parts: a constant part ( a
) and a length-dependent part ( b ):
| e = a + b.L |
(for Australia) |
 |
(for the USA) |
where L is the interstation distance in kilometres,
e and a are in millimetres, and b is in
parts per million.
The CLASS of the GPS survey is dependent on whether the semi-major axes
are all below the error level defined by the appropriate standards &
specifications (section 10.2.2). An example of the
application of this is given below, in which the magnitudes of the semi-major
and semi-minor axes of the relative 2-D error ellipses, and their orientation,
have been calculated for some baselines from the Molong (N.S.W.) GPS survey
(section 9.3.4). The error ellipses
have been plotted in the Figure 2 in section
9.1.3. Note that the last column shows, for the selected baseline, the
"class" label that can be applied, according to the survey specifications
given in Table 1 in section 10.2.2.
However, even these values cannot be considered "objective"
as they are influenced by the network redundancy. The same network, but
compiled using only the independent baseline solutions, can have error ellipses
50% larger (see Figure section 9.4.5,
compared with the Figure 3 section 9.1.3).
Hence the classification of the GPS survey can be manipulated!
RELATIVE HORIZONTAL ERROR ELLIPSES & VERTICAL UNCERTAINTY
=========================================================
AT STATION DISTANCE AXES LENGTH AZIM STD.DEV. CLASS
TO STATION AZIMUTH (m) (deg) (m)
-----------------------------------------------------------------------------
PM43494 1798.188 .0064 115.1 .0065 2A
PM69992 50.1 .0064 205.1
PM43494 3690.144 .0058 51.7 .0060 2A
BRYMEDURA 242.6 .0058 141.7
PM43494 7273.225 .0065 118.4 .0067 3A
MOLONG 109.1 .0065 208.4
PM43494 11773.821 .0111 113.7 .0113 3A
GOANNA 288.6 .0109 203.7
PM69992 1499.537 .0070 123.3 .0071 A
VALE HEAD 46.4 .0069 213.3
PM69992 6310.905 .0079 132.5 .0080 2A
MOLONG 123.5 .0079 222.5
PM69992 11494.322 .0121 117.4 .0123 2A
GOANNA 296.4 .0119 207.4
BRYMEDURA 8982.113 .0060 62.3 .0062 3A
MOLONG 81.6 .0060 152.3
BRYMEDURA 14278.616 .0113 116.1 .0115 3A
GOANNA 278.3 .0111 206.1
VALE HEAD 5909.096 .0059 120.2 .0061 3A
MOLONG 132.4 .0059 210.2
VALE HEAD 11380.181 .0100 115.8 .0102 3A
GOANNA 303.4 .0098 205.8
-
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© Chris Rizos, SNAP-UNSW, 1999