GDOP Calculator

Transponder Array Optimization & Geometry Analysis

Calculate Geometric Dilution of Precision (GDOP) for LBL acoustic positioning systems. Optimize transponder placement to minimize positioning uncertainty and maximize accuracy.

Analysis Parameters

No transponders configured. Click "Add Transponder" or choose a preset configuration.

Current GDOP

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HDOP (Horizontal)

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Position Error

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m

Transponders

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GDOP Heatmap & Transponder Geometry
GDOP Cross-Section (through vehicle position)
Position Error Ellipse

GDOP Theory

Geometric Dilution of Precision

GDOP quantifies how transponder geometry affects positioning accuracy. Lower GDOP values indicate better geometry and more accurate position fixes. GDOP multiplies the measurement error to produce position error.

Position Error = GDOP × Range Measurement Error

GDOP Calculation

For a 2D positioning problem with N transponders, GDOP is computed from the observation matrix H:

H[i] = [cos(θᵢ), sin(θᵢ)] where θᵢ = bearing to transponder i Q = (Hᵀ H)⁻¹ (covariance matrix) GDOP = √(trace(Q)) = √(Q₁₁ + Q₂₂)

Optimal Geometry Guidelines

Best GDOP values are achieved when:

GDOP < 2: Excellent geometry GDOP 2-3: Good geometry GDOP 3-5: Acceptable geometry GDOP > 5: Poor geometry (consider reconfiguration)

HDOP vs GDOP

HDOP (Horizontal Dilution of Precision) considers only horizontal position components, while GDOP includes all dimensions. For 2D underwater positioning, GDOP ≈ HDOP since we're solving for horizontal position only.