Dilution of Precision

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Dilution of Precision

Dilution of Precision (DOP), to German about reduction in accuracy is in satellite navigation systems a measure of the spread of the measured values. Since DOP depends on the relative position of the satellites to each other and to the observer, it is also called geometric dilution of precision (GDOP).

Overview

In satellite navigation systems, the distances to several satellites are determined by measuring the signal transit time to determine the position. The accuracy of the position determination depends on the position of the satellites to one another and to the observed location, as well as the accuracy of the time measurement or the transit time. Favorable angles between a satellite A, the location of the receiver, and a satellite B are 90 ° angles. If these angles are very small or around 180 °, the distance circles or spheres intersect at flat angles and reduce the measuring accuracy . The reciprocal value of the area or volume that the unit vectors span in the direction of the satellites determines the size of the DOP.

For a given satellite constellation at a certain location, DOP is a measure of how well this constellation is suitable for measurement. The value of one describes the best possible geometrical arrangement of the satellites, a value of about 6 is still good. DOP values ​​greater than 10 no longer permit evaluation.

The best possible value is 1.0. Values ​​less than 1.0 mean that the equation is over-determined; H. there are more equations than unknowns.

Grinding cut

Large and small DOP at B and B '

Similar to the reverse cut in geodesy , one speaks of dangerous locations ( dangerous intersection spheres ) between the surveying points concerned.

In the figure, two receivers at B and B 'receive signals from transmitters S1 and S2. At B 'the angle of the direction vectors of 135 ° in the plane causes a DOP of 2. The location uncertainty (red circle) is somewhat larger than the location error due to the signal propagation time measurement. At B the angle deviates only slightly from 180 °, DOP is greater than 10. Depending on the distance from the transmitter, the red error ellipse extends over a multiple of the area resulting from the signal inaccuracy.

DOP values

A distinction is made between the following DOP values:

VDOP Vertical DOP Vertical direction 1D
HDOP Horizontal DOP Horizontal direction 2D
PDOP Positional DOP Positional accuracy 3D
TDOP Time DOP Timing accuracy time
GDOP Geometric DOP Overall accuracy 3D and time

DOP values ​​are often provided by GPS receivers in the NMEA data set GSA in fields 15, 16 and 17.

GLONASS

Regional distribution of PDOP at GLONASS

accuracy

Relationship between true position (TP) and DOP of two satellite constellations S1 and S2

DOP itself is not a measure of the accuracy of the position determination. Instead, DOP influences the size of the spread of the measured values. A large DOP increases the spread of the measurements. Two experimentally determined positions S1 and S2 are shown in the graphic. A small DOP at S1 causes less scatter than at position S2. Due to systematic errors (for example deviations in the satellite ephemeris ) S1 and S2 are outside their error limits. Also because of systematic errors (for example due to deviations in the ionospheric correction), the true position is also outside the measurement fluctuations. The shift to the true position is called the offset . The offset and thus the absolute accuracy is in the order of 10 m with GPS .

See also

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