GPS Position Error (DOP)
Overall positioning error is the geometry factor (dilution of precision) multiplied by the per-satellite ranging error.
Formula
Variables
Example
GDOP 2.5, UERE 4 m: σ_pos ≈ 10 m
How it works
GPS does not measure your position directly; it measures ranges to several satellites and solves for position from the intersection of those range spheres. The UERE is the typical error in each pseudorange measurement, while GDOP tells you how strongly the satellite geometry amplifies that ranging error when converting it into a position estimate. Good satellite spread gives a low GDOP and keeps the final position error close to the raw ranging error; poor geometry can make the same measurement noise produce a much larger location error.
When to use it
Use this when estimating how accurate a GPS-derived position will be from a known satellite geometry and a known ranging error budget. It is especially useful in avionics, flight testing, and navigation performance analysis when comparing constellation geometry, receiver quality, and expected horizontal/3D accuracy.
Worked example, step by step
Given: GDOP = 3.1, UERE = 2.8 m Step 1: Write the formula σ_pos = GDOP × σ_UERE Step 2: Substitute the values σ_pos = 3.1 × 2.8 m Step 3: Calculate σ_pos = 8.68 m Step 4: Round suitably σ_pos ≈ 8.7 m Final answer: the expected position error is about 8.7 m
Common mistakes to avoid
- Using GDOP as if it were an error in meters rather than a dimensionless multiplier
- Confusing UERE with receiver-only error; UERE should include all range-error sources affecting the pseudorange measurement
- Applying the formula without checking that the GDOP value matches the position dimension being discussed, such as 3D position versus a specific horizontal metric
Did You Know?
Widely spread satellites give a low DOP and a sharp fix; satellites bunched together give a high DOP, so the same ranging accuracy can yield a far worse position.
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