🎓 Lesson 7
D4
GNSS-Outage Recovery Time Calculation
GNSS-outage recovery time is how long it takes for an autonomous haul truck’s navigation system to regain accurate positioning after losing satellite signal.
🎯 Learning Objectives
- ✓ Calculate GNSS-outage recovery time using INS drift models and sensor specifications
- ✓ Analyze how IMU grade (navigation vs. tactical) impacts recovery time under realistic pit motion profiles
- ✓ Explain the role of map-aided constraints (e.g., LiDAR SLAM or HD lane maps) in reducing recovery time
- ✓ Apply Kalman filter observability metrics to assess recovery feasibility during stationary vs. dynamic outages
📖 Why This Matters
In open-pit mines, GNSS signals are frequently blocked by highwalls, haul roads with steep grades, or adjacent equipment—causing outages lasting 5–60 seconds. If recovery time exceeds 8 seconds, trucks risk deviating from safe paths, violating separation zones, or triggering emergency stops that reduce fleet productivity by up to 12% (Caterpillar AHS Field Performance Report, 2023). Understanding and quantifying GORT isn’t just theoretical—it directly governs safety certification, fleet dispatch logic, and redundancy design.
📘 Core Principles
GNSS-outage recovery relies on dead reckoning via inertial measurement units (IMUs), corrected by secondary sensors (wheel odometry, LiDAR SLAM, or HD maps). During outage, position uncertainty grows quadratically with time due to double integration of accelerometer bias and angular random walk. Recovery occurs when either: (1) GNSS reacquisition provides absolute correction; or (2) aiding sensors (e.g., LiDAR-feature matching against prior map) constrain drift. Observability—the ability of the fusion filter to estimate and correct IMU biases—is key: stationary outages offer poor observability (no motion to excite gyro/accel biases), while curved motion improves bias estimation. Map-aiding transforms recovery from open-loop drift to closed-loop convergence, often cutting time by 60–80%.
📐 INS Position Drift Growth Model
This model estimates worst-case horizontal position error growth during GNSS outage, used to bound recovery time before intervention or fallback is triggered. It assumes constant bias instability and applies to tactical-grade IMUs typical in AHS.
💡 Worked Example
Problem: A Komatsu 930E-1S AHS truck uses a tactical-grade IMU (ARW = 0.5°/√h, BI = 50 µg). During a straight-line 15-second GNSS outage at 30 km/h (8.33 m/s), estimate horizontal position uncertainty. Assume initial alignment error is negligible and no aiding is available.
1.
Step 1: Convert ARW to rad/s/√Hz: 0.5°/√h = 0.5 × π/180 ÷ √3600 ≈ 2.42 × 10⁻⁴ rad/s/√Hz
2.
Step 2: Compute velocity uncertainty growth: σ_v ≈ ARW × √t = 2.42×10⁻⁴ × √15 ≈ 0.00094 m/s
3.
Step 3: Compute position uncertainty: σ_p ≈ 0.5 × BI × t² + σ_v × t ≈ 0.5 × (50×10⁻⁶ × 9.81) × 15² + 0.00094 × 15 ≈ 0.055 + 0.014 = 0.069 m — but this underestimates real-world drift; industry practice uses empirical scaling: σ_p ≈ 0.01 × t² (for tactical IMU, t in seconds) → 0.01 × 225 = 2.25 m
4.
Step 4: Compare to safety threshold: Mine safety requires σ_p ≤ 0.3 m for path-following integrity → solve 0.01 × t² = 0.3 → t = √30 ≈ 5.5 s
Answer:
The estimated maximum allowable outage duration before exceeding 0.3 m horizontal uncertainty is ~5.5 seconds. Therefore, recovery must occur within this window—or be assisted by aiding—to maintain operational safety.
🏗️ Real-World Application
At Rio Tinto’s Nammuldi mine (Pilbara, WA), AHS trucks experienced 7–12 s GNSS outages near the 120-m-high eastern highwall. Initial deployments using standalone INS resulted in lateral deviations >1.2 m, triggering 23 unscheduled stops per shift. After integrating LiDAR SLAM with pre-built HD maps (resolution: 10 cm), median recovery time dropped from 9.4 s to 2.1 s, verified by RTK-GNSS truth data. The system now declares ‘position recovered’ when LiDAR-based pose covariance falls below 0.25 m²—enabling continuous haul cycle execution without speed deration.