Long Baseline Acoustic Positioning System

Interactive transponder array design with real-time GDOP analysis and positioning accuracy visualization

About This Demo

Long Baseline (LBL) systems use seafloor-mounted acoustic transponders to provide absolute position fixes. The vehicle measures round-trip acoustic travel times to compute its position via multilateration. Positioning accuracy depends critically on transponder geometry - GDOP (Geometric Dilution of Precision) quantifies how measurement errors amplify into position errors. Configure the array and see GDOP in real-time.

Transponder Array Configuration

500 m
4
1.0 m
100 m

Array Presets

GDOP Heat Map & Vehicle Trajectory

GDOP vs Distance from Center

Position Error Ellipses

LBL Positioning Theory

Multilateration Principle

Position is computed from range measurements to multiple transponders with known locations:

Ri = √[(x - xi)² + (y - yi)² + (z - zi)²]

GDOP Calculation

GDOP quantifies how range errors magnify into position errors:

GDOP = √trace[(HTH)-1]

where H is the observation matrix with rows: [Δxi/Ri, Δyi/Ri, Δzi/Ri]

Position Accuracy

The actual positioning error depends on GDOP and range measurement noise:

σposition = GDOP × σrange