The GNSS integer ambiguities: estimation and validation
The GNSS integer ambiguities: estimation and validation
The GNSS integer ambiguities: estimation and validation
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• <strong>The</strong> discrimination tests – ratio tests, difference test, projector test – as used in<br />
practice belong to the class of <strong>integer</strong> aperture estimators, <strong>and</strong> the performance<br />
of the ratio test <strong>and</strong> difference test is shown to be close to optimal. So, based on<br />
the theory of Integer Aperture inference the theoretical foundation as well as the<br />
practical relevance of the ratio test <strong>and</strong> difference test have been shown.<br />
• Using the fixed fail rate approach implies that the critical value depends on the<br />
model (<strong>and</strong> thus the precision) at h<strong>and</strong>. This means that the time to first fix will<br />
be shorter, <strong>and</strong> at the same time it is guaranteed that the probability of incorrect<br />
fixing is below a user-defined threshold.<br />
A problem with IA <strong>estimation</strong> is the determination of the aperture parameter for a given<br />
fail rate. For that purpose simulations must be used. More research is needed on the<br />
consequences on the computation times <strong>and</strong> on the performance.<br />
In theory, the Optimal IA estimator is of course to be preferred since it maximizes the<br />
success rate. However, computationally it is the most complex estimator because the<br />
probability density of the ambiguity residual must be computed.<br />
<strong>The</strong> ratio test <strong>and</strong> difference test IA estimator are easier to apply <strong>and</strong> computationally<br />
simple. <strong>The</strong>se estimators have been shown to perform close to optimal, if <strong>and</strong> only if<br />
the appropriate aperture parameter is determined by the fixed fail rate. <strong>The</strong> ratio test<br />
is already often used in practice <strong>and</strong> seems therefore a logical choice.<br />
<strong>The</strong> IALS estimator might be a good alternative: close to optimal performance, <strong>and</strong><br />
easy to apply, although computationally much more dem<strong>and</strong>ing than the ratio test <strong>and</strong><br />
difference test IA estimators.<br />
More research is needed on the implementation aspects <strong>and</strong> on how the IA method will<br />
work in practice for different applications. With respect to the implementation aspects<br />
it will be important to find an efficient way of determining the aperture parameter such<br />
that close to optimal solutions will be obtained. <strong>The</strong> approach followed in this thesis<br />
was to use simulations with a fairly small number of samples. It must be investigated<br />
how this will work in practice. Alternative methods would be to somehow determine<br />
empirical values of the aperture parameter that can be used under certain conditions,<br />
e.g. depending on the ILS success rate or the number of <strong>ambiguities</strong>. Or it may be<br />
possible to obtain a good approximation of the appropriate aperture parameter based on<br />
information from previous epochs.<br />
6.2 Quality of the baseline estimators<br />
Integer ambiguity <strong>validation</strong> focuses on the question whether or not the <strong>ambiguities</strong><br />
should be fixed. This decision is based on the residuals of the float <strong>and</strong> fixed solution. A<br />
user, however, will be mainly interested in the impact of either decision on the baseline<br />
solution. <strong>The</strong>refore, in this thesis several baseline probabilities were evaluated using<br />
simulations.<br />
<strong>The</strong> first probability is the probability that a baseline estimate will be within a certain<br />
Quality of the baseline estimators 141