The GNSS integer ambiguities: estimation and validation

is maximum. The degrees of freedom qi may be different, and the level of significance
αqi depends on λ(αqi , γ, qi), which is chosen as:
λ(αqi , γ, qi) = λ(αm−n, γ, m − n) (2.81)
This means that the non-centrality parameters and detection powers are chosen equal
for both the detection and the identification test, implying that a certain model error
can be found with the same probability by both tests. This approach is the B-method
of testing, (Baarda 1968).
In practice the identification step is started with the so-called data snooping, (Baarda
1968), which means that each individual observation is screened for the presence of an
outlier. In that case q = 1 and the matrix C reduces to a vector, denoted as c. The test
statistic of equation (2.70) becomes:
T 1 = (w) 2
w =
c T Q −1
y ê
c T Q −1
y QêQ −1
y c
(2.82)
The test statistic w has a standard normal distribution N(0, 1) under H0. An observation
j is suspected to be biased if:
|wj| ≥ |wi| ∀i and |wj| > N 1
2 α(0, 1) (2.83)
The final step in the DIA-procedure is adaptation, in which the model is corrected for one
or more of the most likely model errors identified in the previous step. This may involve
replacement of the erroneous data, e.g. by re-measurement, or a new null hypothesis is
set up which takes into account the identified model errors. After this step, one has to
make sure that the new situation will lead to acceptance of the null hypothesis, meaning
that the DIA-procedure needs to be applied iteratively.
2.5.3 GNSS quality control
In this section a general testing procedure was described that can be applied in the case
of linear estimation with normally distributed data, so that the parameter distribution
is completely captured by the vc-matrix of the estimators. Unfortunately, this approach
cannot be applied when integer parameters are involved in the estimation process, since
these parameters do not have a Gaussian distribution, and therefore the parameter distribution
itself is needed to obtain appropriate test statistics in order to validate the
integer solution. This problem is the subject of section 3.5 and chapter 5.
Least-squares estimation and quality control 25