The GNSS integer ambiguities: estimation and validation

convex region symmetric with respect to the true baseline. It followed that the probability
that the fixed solution is close to the true solution is always larger than for any of the other
baseline estimators. At the same time, the fixed solution also has the highest probability
of being far from the true solution. The opposite is true for the float estimator: smallest
probability of being close to the true solution, but also small probability that it will be far
off. The probabilities of both the BIE and the IA estimators generally are inbetween those
of the fixed and float estimators. So, as could be expected the BIE and IA estimators
take the best of the float and fixed estimators.
Another probability considered here is the probability that a baseline estimator is better
than the corresponding float estimator. Especially if IA estimation with a small fixed
fail rate is used, this probability will be close to one and larger than for any of the other
estimators.
A problem is that the probabilities cannot be evaluated exactly, and no strict lower and
upper bounds are available, so that simulations are needed. It would be interesting to
have an easy-to-evaluate measure of the quality of the baseline solution. This is a point
of further research.
6.3 Reliability of the results
In this thesis simulations were used in order to assess the theoretical performance of
different estimators and to make comparison possible, since one can be sure that the
simulated data correspond to the mathematical model that is used. In practice, one cannot
be sure that this will be the case, whereas the reliability of the ambiguity resolution
results depends on the validity of the input. Only if one can assume that the input is
correct, one can trust the outcome of integer estimation and validation.
The input of the ambiguity resolution process consists of the float ambiguity estimates
and their vc-matrix, and thus depends on the functional as well as the stochastic model
that is used. Furthermore, it is important that the quality of the float solution is evaluated,
such that errors due to for example multipath and cycle slips are eliminated.
In practice the stochastic model is often assumed to be correct, although recent studies
have shown that in many cases a refinement is possible. Possible refinements are the
application of satellite elevation dependent weighting of the observations, and considering
cross-correlation of the different observations. This means an appropriate stochastic
model must be determined for the receiver at hand.
Another assumption that was made is that the variance factor of unit weight, σ 2 , is
known. If, on the other hand, it is assumed that this variance factor is not known, it
must be estimated a posteriori by means of variance component estimation. It must be
investigated how this affects the results presented in this thesis.
Furthermore, it is assumed that the observations are normally distributed. The results
in this thesis are all based on this assumption, although it would also be possible to
apply the theory to parameters with different distributions. This is also an issue open
for further research.
142 Conclusions and recommendations