Navigation Calculator

Error Propagation & Mission Profile Analysis

Calculate position uncertainty propagation, sensor requirements, and mission feasibility for custom underwater navigation profiles with comprehensive error budgeting.

Mission Profile
Sensor Specifications

Final Position Error

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m

Max Error (95%)

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m

Meets Requirements

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Total Distance

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km
Position Uncertainty Propagation
Error Budget Breakdown
Sensor Contribution Analysis
Sensor Requirements Summary
Parameter Current Value Required for Target Status
INS Drift Rate -- -- --
DVL Update Rate -- -- --
LBL Coverage -- -- --
LBL Accuracy -- -- --

Navigation Error Budgeting

Error Propagation Model

Position error grows over time due to sensor noise and bias drift. The total error is a combination of INS drift, sensor aiding effectiveness, and environmental factors:

σ_pos(t) = σ_INS(t) ⊕ σ_DVL(t) ⊕ σ_LBL(t) ⊕ σ_env(t) where ⊕ denotes RSS (root-sum-square) combination

INS Error Growth

Without aiding, INS position error grows approximately linearly with distance traveled due to velocity errors from gyro and accelerometer noise:

σ_INS(t) = σ₀ + (drift_rate × distance_traveled) drift_rate ≈ √(ARW_gyro² + bias_instability²) × velocity Typical values: - Tactical grade: 0.1-0.5% of distance - Navigation grade: 0.01-0.1% of distance

DVL Aiding

DVL provides velocity measurements that bound INS error growth. With regular DVL updates, position uncertainty is reset periodically:

σ_DVL = DVL_accuracy × velocity × Δt_update Effect: Limits position error growth rate, prevents unbounded drift

LBL Aiding

LBL provides direct position fixes that reset absolute position uncertainty:

After LBL fix: σ_pos ← σ_LBL (typically 2-5m) Coverage factor: effective_accuracy = σ_LBL / √(coverage_fraction)

Mission Feasibility

A mission is feasible if the predicted maximum position error remains within required accuracy bounds throughout the mission duration. Key considerations: