IEEE - Aerospace and Electronic Systems - May 2023 - 38

Opportunistic Autonomous Integrity Monitoring for Enhanced UAV Safety
Table 1.
Inputs to the GPS-SOP OARAIM Algorithm
Input
fzGPS;ig
fzSOP;ig
NGPS
i¼1
NSOP
i¼1
fsURA;GPS;ig
fsURA;SOP;ig
fsURE;GPS;ig
fsURE;SOP;ig
fbnom;GPS;ig
fbnom;SOP;ig
fPGPS;ig
fPSOP;ig
PConst;GPS
PConst;SOP
NGPS
i¼1
NSOP
i¼1
NGPS
i¼1
NSOP
i¼1
NGPS
i¼1
NSOP
i¼1
NGPS
i¼1
NSOP
i¼1
Description
Obtained from
GPS pseudorange measurements
SOP pseudorange measurements
Standard deviation of GPS user range accuracy
Standard deviation of SOP user range accuracy
Standard deviation of the GPS user range error
Standard deviation of the SOP user range error
Maximum bias for a GPS measurement
Maximum bias for a SOP measurement
Probability of a single GPS fault
Probability of a single SOP fault
Probability of GPS constellation fault
Probability of SOP constellation fault
GPS front-end and tracking loop
SOP front-end and tracking loop
ISM
The value of URE multiplied by 1.5
ISM
[25]
ISM
Similar to the GPS maximum bias
Historical records. Currently used value is 105
Experimental campaign. Proposed value is 104
Historical records. Currently used value is 0
Experimental campaign. Proposed value is 0
mode. In particular, this step derives the following parameters
for each fault mode:
The variances of the fault-tolerant position components
(East, North, Up) for each fault mode.
The difference between the fault-tolerant position and
the all-in-view position and the variance of this difference.
The worst-case impact of the nominal biases
and fbnom;SOP;ig
fbnom;GPS;ig
NGPS
i¼1
NSOP
i¼1 on the position
estimate.
Step 5: Perform two sets of tests:
Solution separation tests:
- Compute the solution separation test thresholds from
the probability offalse alarm.
- Perform the test on all the components of the difference
between the fault-tolerant and all-in-view solutions
for each fault mode. If any test fails, exclusion
must be attempted.
A chi-squared test:
- A chi-squared test is performed on the measurement
residuals for the all-in-view solution with weight
matrix Cacc calculated in Step 1.
- The threshold is computed using the inverse chisquared
cumulative density function (cdf) and a
pre-defined probability of false alarm.
- If the chi-squared test fails, the PLs cannot be considered
valid and exclusion cannot be attempted. If
this test fails while none of the solution separation
tests fail, then the fault is most likely outside the
threat model. The chi-square test is a sanity check
for that purpose.
38
Step 6: Calculate the PLs if all of the solution separation
tests and the chi-squared test pass and formulate the
vertical positioning performance criteria:
1) Criterion 1: 95% accuracy parameter, which is the
achievable positioning accuracy in the vertical
domain 95% of the time. According to the Localizer
Performance with Vertical guidance (LPV)- 200
standard, the 95% accuracy must be limited to 4 m.
2) Criterion 2: 107 fault-free position error bound,
which is the achievable positioning accuracy in the
vertical domain 99.99999% of the fault-free time.
According to the LPV-200 standard, the 107 faultfree
position error bound must be limited to 10 m.
3) Criterion 3: Effective monitor threshold (EMT),
which is a parameter that takes into account the
faults with a prior greater than or equal to 105.
According to the LPV-200 standard, EMT must be
limited to 15 m.
Ifthe chi-squared test passes but any ofthe solution separation
tests fail, the following steps are performed instead.
Step 7: Exclude the faults by first determining the candidate
subset to exclude. This is achieved by performing a
search over all possible subsets to find the subset that
yields the highest discrepancy between the fault-tolerant
and all-in-view solution. Once the best candidate subset is
determined, an exclusion test is performed to account for
the wrong exclusion probability.
Step 8: Compute the PLs after exclusion. This step is
similar to Step 6 except that it accounts for the wrong
exclusion probability.
IEEE A&E SYSTEMS MAGAZINE
MAY 2023
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