Dilution of Precision (DOPs)

1. GLOBAL POSITIONING SYSTEM
Dilution of Precision (DOPs)
MAY 23, 2014
SUBMITTED TO: SIR. ALI MURAD KISANA
Institute of Geology, University of the Punjab
SUBMITTED BY: ATIQA IJAZ KHAN
Roll No: GEOL-02
MPhil Geomatics
2nd Semester
Session: 2013-2015

2. Global Positioning System (GPS)
GPS is an all-weather positioning system providing 24 hour world-wide coverage with at
least four satellites in view at any time (Milliken et al., 1990 and Wells et al., 1986). The
system has been fully operational since 1993.
GPS has become a standard surveying technique in most surveying practices. This could
be attributed to both the ease of use as well as reduction in hardware costs.
Dilution of Precision
An indicator of satellite geometry for a constellation of satellites used to determine a
position. It’s an amplification factor.
Positions with a lower DOP value generally constitute better measurement results than
those with higher DOP. A low DOP value indicates a higher probability of accuracy. DOP
only depends on the position of the satellites: how many satellites you can see, how high
they are in the sky, and the bearing towards them.
Factors determining the total GDOP (geometric DOP) for a set of satellites include:
1. PDOP (positional DOP),
2. HDOP (horizontal DOP),
3. VDOP (vertical DOP), and
4. TDOP (time DOP).
There individual formulas for each of them including GDOP are as follows:
Position Dilution of Precision (PDOP):
Measure accuracy in 3D – position. Also termed as Spherical DOP.
PDOP = (√σ2E + σ2N + σ2U ) / σ
Horizontal Dilution of Precision (HDOP):
Measure accuracy in 2D - position (Like, Latitude and Longitude)
𝐻𝐷𝑂𝑃 = (√ 𝜎2 𝐸 + 𝜎2 𝑁 ) / 𝜎

3. Vertical Dilution of Precision (VDOP):
Measure accuracy in 1D - position (Like, Height)
𝑉𝐷𝑂𝑃 = (𝜎U / 𝜎)
Time Dilution of Precision (TDOP):
Measure accuracy in Time.
𝑇𝐷𝑂𝑃 = (𝜎T / 𝜎)
Geometric Dilution of Precision (GDOP):
Measure accuracy in 3D – position and time.
GDOP = (√σ2E + σ2N + σ2U + σ2T ) / σ
Where,
σ2E = C0-Variance of East-components
σ2N = Co-Variance of North-components
σ2U = Co-Variance of Up-components
σ2T = Co-Variance of Time
σ = Collective standard deviation of pseudo-range, residual model, receiver noise,
satellite clock, ephemeris, multi-path, selective availability, and atmospheric error (in
terms of distance) OR UERE (User Equivalent Residual Error Matrix)
AND,
To obtain the position and time error variances, the covariance matrix of the
position and time correction errors is computed. This matrix has the form.
Where, Vx, Vy, Vz, and VT are the position and time variances and the off-diagonal
elements are functions of the correlations between the errors.
𝑐𝑜𝑣 (𝒙) = |
𝑉𝑥
𝑉𝑦
𝑉𝑧
𝑉𝑇
|

4. GENERAL EQUATIONS:
PDOP2 = HDOP2 + VDOP2
GDOP2 = PDOP2 + TDOP2
GENRALL VALUES RANGES:
PDOP = 4-5 is good while = 10 is poor
VDOP = 4-5
HDOP = 2-3
GDOP = <5
σ UERE for SPS user = 25 m
σ UERE with SA off for SPS users = 5 m
σ UERE for PPS users = <5 m
References
1. Information. (n.d.). How Accurate is your GPS ? Retrieved May 22, 2014, from
TRAKGPS, Anything, Anywhere, Anytime!: http://www.trakgps.com/en/
2. Langley, R. B. (1999, May 22). Innovation: Dilution of Precision. Retrieved May 22,
2014, from GPS World: www.gpsworld.com
3. STURZA, M. A. (1983). GPS Navigation Using Three Satellites and a Precise Clock .
Global Positioing System, 122-132. Retrieved May 23, 2014, from
http://3csysco.com/Pubs/GPSNavigationUsingThreeSatellitesandaPreciseClock.pdf
4. Webcourse. (n.d.). Module 2 : Global Positioning System Lecture 11 : Satellite geometry
and Accuracy measures. Retrieved May 22, 2014, from nptel.ac.in:
http://nptel.ac.in/courses/Webcourse-contents/IIT-
KANPUR/ModernSurveyingTech/lectureB_11/B_11_3GDOP.htm