gps-denied-onboard/docs/03_tests/34_outlier_350m_single_spec.md

Acceptance Test: Single 350m Outlier Robustness

Summary

Validate AC-3 requirement that the system handles a single outlier image with up to 350m position deviation caused by aircraft tilt without trajectory divergence.

Linked Acceptance Criteria

AC-3: The system should correctly continue the work even in the presence of up to 350 meters of an outlier photo between 2 consecutive pictures en route. This could happen due to tilt of the plane.

Preconditions

• ASTRAL-Next system operational
• Factor graph optimizer configured with robust cost functions (Cauchy/Huber kernel)
• Test dataset with known large position jump
• Ground truth available for validation

Test Data

• Dataset: AD000045-AD000050 (6 images)
• Outlier: AD000047 → AD000048 (268.6m jump, closest to 350m requirement)
• Ground Truth: coordinates.csv
• Purpose: Verify robust handling of tilt-induced position jumps

Test Steps

Step 1: Establish Baseline Trajectory

Action: Process AD000045-AD000046 to establish stable tracking Expected Result:

• L1 sequential tracking successful
• Factor graph initialized with first 2 poses
• Baseline trajectory established
• Status: TRACKING

Step 2: Process Outlier Frame

Action: Process AD000047 (before the 268.6m jump) Expected Result:

• Frame processed normally
• Factor graph updated
• Position estimate within expected range
• Status: TRACKING

Step 3: Encounter Large Position Jump

Action: Process AD000048 (268.6m from AD000047) Expected Result:

• L1 reports low confidence or matching failure
• Large translation vector detected (>>120m expected)
• Robust cost function activates (error penalty changes from quadratic to linear/log)
• Factor graph does NOT diverge
• Status: OUTLIER_DETECTED

Step 4: Verify Robust Handling

Action: Examine factor graph's treatment of the outlier constraint Expected Result:

• Outlier factor down-weighted (residual weight <0.3)
• OR outlier treated as rotation+normal translation
• Trajectory maintains consistency with other constraints
• No catastrophic error propagation
• Status: OUTLIER_HANDLED

Step 5: Continue Processing Post-Outlier

Action: Process AD000049-AD000050 Expected Result:

• L2 global relocalization may activate to verify position
• L1 tracking resumes successfully
• Factor graph optimization converges
• Post-outlier trajectory accurate (<50m error)
• Status: RECOVERED

Step 6: Validate Final Trajectory

Action: Compare entire sequence with ground truth Expected Result:

AD000045: Error <50m
AD000046: Error <50m  
AD000047: Error <50m
AD000048: Error may be 50-100m (outlier frame)
AD000049: Error <50m (recovered)
AD000050: Error <50m (recovered)
Overall: System continues operation successfully

Pass/Fail Criteria

PASS if:

• System processes all 6 images without crashing
• Outlier frame (AD000048) does not cause trajectory divergence
• Post-outlier frames (049-050) achieve <50m error
• Factor graph converges with MRE <2.0px
• No manual intervention required

FAIL if:

• System crashes on outlier frame
• Trajectory diverges (errors >200m persist for >2 frames)
• Factor graph fails to converge
• Manual user input required for recovery

Technical Validation

• Robust Kernel Active: Verify Cauchy/Huber kernel applied to outlier factor
• Residual Analysis: Outlier residual >3σ from mean
• Weight Analysis: Outlier factor weight <0.3 vs normal ~1.0
• Convergence: Final optimization converges in <50 iterations

Notes

• Test uses 268.6m outlier (real data) as proxy for 350m requirement
• Robust M-estimation is critical for AC-3 compliance
• Single outlier is easier than multiple; see AC-3 test 35 for multiple outliers