SRV-28

GPS baseline precision

σ = a + b·D. Static GNSS: a in mm, b in ppm of the baseline D.

Reading speed

GNSSGPS baseline

Governing equation

\sigma=a+b\,D

where

a: Constant a (mm)
b: Scale b (ppm)
D: Baseline (km)
\sigma: Baseline σ (mm)

Lecture brief

Historical brief

From chain and theodolite through Bowditch’s compass-rule (1802) to GPS PDOP, surveying is the propagation of small errors across a network. These sheets close traverses, reduce stadia and state map scale. This sheet (SRV-28 — GPS baseline precision) is the form associated with GPS baseline. Working symbols: $a$ , $b$ , $D$ $\rightarrow$ $\sigma$ . Manufacturer specs quote a + b ppm. Ambiguity-fixed carrier phase on a short baseline sits near a few millimetres.

Purpose

Purpose: compute

\sigma

from

a

b

D

in Surveying via

\sigma=a+b\,D

σ = a + b·D. Static GNSS: a in mm, b in ppm of the baseline D. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 3.000\,\mathrm{mm}

b = 0.500\,\mathrm{ppm}

D = 8.000\,\mathrm{km}

, the governing relation

\sigma=a+b\,D

yields

\sigma = 7.00\,\mathrm{mm}

. Two receivers, a baseline, a growing σ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Constant a a3 mmScale b b0.5 ppmBaseline D8 km

Outputs

Baseline σ \sigma7.00 mm

Reading speed

Watch on YouTube

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Narration of this film

Two receivers, a baseline, a growing σ.

Manufacturer specs quote a + b ppm. Ambiguity-fixed carrier phase on a short baseline sits near a few millimetres.

Reading speed

Watch on YouTube