Global Positioning System Reference
In-Depth Information
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detection can be carried out before the adjustment or as part of the adjustment. Be-
fore the adjustment, the discrepancies (angle and/or distance of simple figures such as
triangles and traverses) are analyzed. A priori blunder detection is helpful in detect-
ing extralarge blunders caused by, e.g., erroneous station numbering. Blunder detec-
tion in conjunction with the adjustment is based on the analysis of the residuals. The
problem with using least-squares adjustments when blunders are present is that the
adjustments tend to hide (reduce) their impact and distribute their effects more or less
throughout the entire network (see (4.364) and (4.365), noting that the redundancy
number varies between zero and 1). The prerequisite for any blunder-detection pro-
cedure is the availability of a set of redundant observations. Only observations with
redundancy numbers greater than zero can be controlled.
It is important to understand that if a residual does not pass a statistical test, this
does not mean that there is a blunder in that observation. The observation is merely
flagged so that it can be examined and a decision about its retention or rejection can
be made. Blind rejection is never recommended. A blunder in one observation usually
affects the residuals in other observations. Therefore, the tests will often flag other
observations in addition to the ones containing blunders. If one or more observations
are flagged, the search begins to determine if there is a blunder.
The first step is to check the field notes to confirm that no error occurred during the
transfer of the observations to the computer file, and that all observations are reason-
able “at face value.” If a blunder is not located, the network should be broken down
into smaller networks, and each one should be adjusted separately. At the extreme,
the entire network may be broken down into triangles or other simple geometric en-
tities, such as traverses, and adjusted separately. Alternatively, the observations can
be added sequentially, one at a time, until the blunder is found. This procedure starts
with weights assigned to all parameters. The observations are then added sequentially.
The sum of the normalized residuals squared is then inspected for unusually large
variations. When searching for blunders, the coordinate system should be defined by
minimal constraints.
Blunder detection in conjunction with the adjustment takes advantage of the total
redundancy and the strength provided by the overall geometry of the network, and
thus is more sensitive to smaller blunders. Only if the existence of a blunder is
indicated does action need to be taken to locate the blunder. The flagged observations
are the best hint where to look for errors and thus avoid unnecessary and disorganized
searching of the whole observation data set.
[16
Lin
—
0.8
——
Sho
PgE
[16
4.
11.1 The
τ
Test
The
test was introduced by Pope (1976). The test belongs to the group of Studen-
tized tests, which make use of the a posteriori variance of unit weight as estimated
from the observations. The test statistic is
τ
v
i
σ
v
i
=
σ
0
v
i
τ
i
=
σ
0
σ
i
√
r
i
∼ τ
n
−
r
(4.376)
