SRV-22

GPS position dilution PDOP

PDOP = √(σE²+σN²+σU²)/σUERE. Geometry multiplies the user-equivalent range error.

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GNSSPDOP

Governing equation

\mathrm{PDOP}=\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2}/\sigma_{\mathrm{UERE}}

where

\sigma_E: Easting σ (m)
\sigma_N: Northing σ (m)
\sigma_U: Up σ (m)
\sigma_{UERE}: UERE (m)
PDOP: PDOP (—)

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-22 — GPS position dilution PDOP) is the form associated with PDOP. Working symbols: $\sigma_E$ , $\sigma_N$ , $\sigma_U$ , $\sigma_{UERE}$ $\rightarrow$ $PDOP$ . The cofactor matrix of the satellite unit-vector design gives GDOP, PDOP, HDOP, VDOP. PDOP < 4 is healthy.

Purpose

Purpose: compute

PDOP

from

\sigma_E

\sigma_N

\sigma_U

\sigma_{UERE}

in Surveying via

\mathrm{PDOP}=\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2}/\sigma_{\mathrm{UERE}}

PDOP = √(σE²+σN²+σU²)/σUERE. Geometry multiplies the user-equivalent range error. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\sigma_E = 1.200\,\mathrm{m}

\sigma_N = 1.100\,\mathrm{m}

\sigma_U = 2.400\,\mathrm{m}

\sigma_{UERE} = 0.800\,\mathrm{m}

, the governing relation

\mathrm{PDOP}=\sqrt{\sigma_E^2+\sigma_N^2+\sigma_U^2}/\sigma_{\mathrm{UERE}}

yields

PDOP = 3.62\,\mathrm{—}

. A skyplot, a PDOP, a blown-up error ellipse. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Easting σ \sigma_E1.2 mNorthing σ \sigma_N1.1 mUp σ \sigma_U2.4 mUERE \sigma_{UERE}0.8 m

Outputs

PDOP PDOP3.62 —

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Narration of this film

A skyplot, a PDOP, a blown-up error ellipse.

The cofactor matrix of the satellite unit-vector design gives GDOP, PDOP, HDOP, VDOP. PDOP < 4 is healthy.

Reading speed

Watch on YouTube