SEPTENTRIO PolaRx5TR, Reference Manual

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2 Operation Details
The probability computations are based on the assumption that the residuals are distributed
as a Normal distribution (central if there is no outlier, and non-central if there is one), as
illustrated in Figure 2-5.
Figure 2-5:
Statistical test outcomes.
Samples corresponding to the four test outcomes are represented in Figure 2-5: samples A
and B are from the unbiased measurement distribution, while samples C and D are from a bi-
ased measurement distribution corresponding to an outlier. Since sample A is larger than the
test threshold, it will be incorrectly flagged as an outlier (false alarm). Sample C is not detected
as an outlier although it is part of the biased distribution (missed detection). The acceptable
probability of false alarm and the probability of missed detection for the application must
be determined and provided to the receiver. This is the purpose of the
setRAIMLevels
command.
2.7.1 Integrity Algorithm
Two kinds of statistical tests are performed: the detection step uses an
overall model
test to
evaluate the integrity of the position solution as a whole, and the identification step uses the
w
-test (also known as "datasnooping") to evaluate the integrity of individual measurements.
Depending on the positioning mode, the overall model test is computed for range, range-rate
and/or phase measurements simultaneously, while the
w
-test is computed for each range,
range rate and/or phase measurement individually. Both the overall model and the
w
-tests
are of the
Generalized Likelihood Ratio Test
type.
The overall model test uses the weighted sum of the squared residuals as test statistic. This
test statistic is distributed as a
χ
2
distribution with
r
degrees of freedom, where
r
is the re-
dundancy number equal to the number of satellites used in the position computation minus
4. The test reads:
σ
2
= e
T
Q
−
1
y
e > χ
2
α
( r , 0)
where:
•
σ
2
is the overall model test statistic;
•
e
is the vector of residuals;
•
Q
y
is the variance-covariance matrix of the measurements;
•
χ
2
α
( r , 0)
is the test threshold yielding a probability
α
of false alarm.
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