2 Operation Details
The probability of false alarm of the overall model test is selectable by the user with the
ModelReliability
argument of the
command.
If the overall model test statistic is lower than the test threshold, the test is passed and the
integrity is guarantueed under the statistical assumptions specified by the
command.
If the overall model test statistic is higher than the threshold, the test is rejected. In this case,
the identification step will attempt to identify the measurement responsible for the rejec-
tion using the
w
-test discussed below. After removal of the responsible outlier(s), the overall
model test statistic is recomputed to verify the integrity of the solution without the outlier
present. This iterative process continues until either the overall model test along with the
associated
w
-tests are accepted, or until the
w
-tests for each individual measurement are
accepted with a rejected overall model test. In the latter case an integrity loss is declared; in
the former case integrity is available. Note that under extreme circumstances the interactive
D-I-A process can also halt due to insufficient available measurements for testing, after re-
moval of outliers. In this case the "too many outliers" error is reported in the PVT related SBF
blocks.
For the evaluation of the
w
-test statistic, the following inequality is verified:
−
k
1
/
2
α
<
w
i
=
e
i
σ
e
i
<
+
k
1
/
2
α
where:
•
w
i
is the
w
-test statistic for the
i
th satellite;
•
e
i
is the residual for the
i
th satellite;
•
σ
e
i
is the standard deviation of the residual for the
i
th satellite;
•
k
1
/
2
α
is the test threshold yielding a probability
α
of false alarm.
The probability of false alarm of the
w
-test is selectable by the user with the
Pfa
argument of
the
command.
The test threshold is computed by the receiver with the assumption that the
w
-test statistic
is distributed as a Normal distribution. For instance, if
Pfa
is set to 10%, residuals larger than
1.64 sigma are flagged as outliers. If
Pfa
is 0.01% the threshold will be 3.89.
2.7.2
Internal and External Reliability Levels
To assess the impact of undetected measurement errors on the computed position, the min-
imal detectable bias (MDB) in the range domain is computed and propagated to the position
domain.
The MDB describes the internal reliability of the corresponding
w
-test. It is a measure of the
range error that can be detected with a given probability of missed detection. It is computed
as follows for each satellite (neglecting the probability that the biased measurement falls on
the left-hand side of the non-biased distribution shown in Figure 2-5):
71
Summary of Contents for PolaRx5TR
Page 1: ...PolaRx5TR Reference Guide Applicable to version 5 5 0 of the Firmware ...
Page 73: ...3 Command Line Reference Chapter 3 Command Line Reference 73 ...
Page 130: ...3 Command Line Reference COM1 gim CR R gim IonosphereModel off COM1 130 ...
Page 237: ...3 Command Line Reference COM1 237 ...
Page 279: ...3 Command Line Reference COM1 279 ...
Page 294: ...4 SBF Reference Chapter 4 SBF Reference 294 ...