Dilution of precision (navigation)

Dilution of precision ( DOP ), or geometric dilution of precision ( GDOP ), is used in satellite navigation and geomatics .

Introduction

The concept of dilution of precision (DOP) originated with users of the Loran-C navigation system . [1] The idea of ​​Geometric DOP is to state how the errors in the measurement will affect the final state estimate. This can be defined as: [2]

More recently, the term has come into use with the development and adoption of GPS. Neglecting ionospheric [3] and tropospheric [4] effects, the signal from satellites has a fixed precision. Therefore, the relative satellite-receiver geometry plays a major role in determining the precision of estimated positions and times. Due to the relative geometry of any given satellite to a receiver, the precision in the pseudorange of the satellite translated by a receiver.

The accuracy of multiple satellites in a receiver is a measure of the accuracy of the receiver. When visible satellites are close together in the sky, the geometry is said to be weak and the DOP value is high; DOP value is low. Consider two overlapping rings, or annuli , of different centers. If they overlap at right angles, the greatest extent of the overlap is much smaller than if they overlap in near parallel. Thus a low DOP value represents a better positional accuracy due to the wider angular separation between the satellites used to calculate a unit’s position.

DOP can be expressed as a number of separate measurements:

  • HDOP – horizontal dilution of precision
  • VDOP – vertical dilution of precision
  • PDOP – position (3D) dilution of precision
  • TDOP – time dilution of precision

These values ​​follow mathematically from the positions of the usable satellites. Signal receivers allow the display of these positions ( skyplot ) as well as the DOP values.

The term can also be applied to other locations. It can occur in electronic-counter-measures (electronic warfare) when computing the location of enemy emitters (radar jammers and radio communications devices). Using such an interferometry technique can provide certain geometric layouts where there are degrees of freedom that can not be accounted for due to inadequate configurations.

The effect of the geometry of the satellites on position error is called the geometric dilution of precision and it is roughly interpreted as the ratio of position error to the range error. Imagine that a square pyramid is formed by lines joining four satellites with the receiver at the tip of the pyramid. The GDOP is the lowest value of the pyramid; GDOP will be. Similarly, the better the value of satellites, the better the value of GDOP.

Meaning of DOP Values

DOP Value Rating Description
<1 Ideal Highest possible confidence level for all applications.
1-2 Excellent At this confidence level, positional measurements are considered accurate enough to meet all the most sensitive applications.
2-5 Good Represents a level that marks the minimum appropriate for making business decisions. Positional measurements could be used to make reliable in-route navigation suggestions to the user.
5-10 Moderate Positional measurements could be used for calculations, but the fix could be improved. A more open view of the sky is recommended.
10-20 Fair Represents a low confidence level. Positional measurements should be discarded or used only to indicate a very rough estimate of the current location.
> 20 Poor At this level, measurements are inaccurate by as much as 300 meters with a 6-meter accurate device (50 DOP × 6 meters) and should be discarded.

The DOP factors are functions of the diagonal elements of the covariance matrix of the parameters, expressed either in a global or a local geodetic frame.

References

Notes

  1. Jump up^ Richard B. Langley (May 1999). “Dilution of Precision” (PDF) . GPS World . Retrieved 2011-10-12 .
  2. Jump up^ Dudek, Gregory ; Jenkin, Michael (2000). Computational Principles of Mobile Robotics . Cambridge University Press . ISBN  0-521-56876-5 .
  3. Jump up^ Paul Kintner, Cornell University; Todd Humphreys; University of Texas-Austin; Joanna Hinks; Cornell University (July-August 2009). “GNSS and Ionospheric Scintillation: How to Survive the Next Solar Maximum” . Inside GNSS . Retrieved 2011-10-12 .
  4. Jump up^ GPS errors (Trimble tutorial)
  5. Jump up^ http://www.colorado.edu/geography/gcraft/notes/gps/gif/gdop.gif
  6. Jump up^ “Section 1.4.2 of Principles of Satellite Positioning ” . Archived from the original on December 1, 2008.

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