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

$D \in \left[0.1, 80\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\sigma=a+b\,D

$D \in \left[0.1, 80\right]$

$D = 0.1$ $\sigma = 3.05$

Along the curve

②

Domain of the variable — blue

D_{\min} = 0.1,\quad D_{\max} = 80

$D \in \left[0.1, 80\right]$

$D = 0.1$ $D = 0.1$

Along the curve

③

Response curve — green

\sigma=a+b\,D

$D \in \left[0.1, 80\right]$

$D = 0.1$ $\sigma = 3.05$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\sigma}{\mathrm{d}D}

$D \in \left[0.1, 80\right]$

$D = 0.603$ $\sigma^{\prime} = 0.5$

Along the curve

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