i. Probable Error Measures. The accuracy of 3D GPS measurements is commonly expressed by
the spherical error probable (SEP). The SEP represents the radius of a sphere with a 50 percent
confidence or probability level. This spheroid radial measure only approximates the actual 3D ellipsoid
representing the uncertainties in the geocentric coordinate system. A circular error probable (CEP)
statistic is commonly used in 2D horizontal positioning, particularly in military targeting. The CEP
represents the radius of a circle containing a 50 percent probability of position confidence.
5-17. Accuracy Comparisons. It is important that GPS measurements clearly identify the statistic
from which they are derived. A 100-meter or positional variance-covariance matrix is meaningless
unless it is identified as being either 2D or 3D, along with the applicable probability level. For example,
a PPS 16-meter 3-deviation accuracy is, by definition, an SEP (50 percent). This 16-meter SEP equates
to a 28-meter 3D, 95 percent confidence spheroid. If transformed to 2D accuracy, the SEP equates
roughly to a 10-meter CEP, a 12-meter RMS, a 2-meter 2-deviation RMS, or a 36-meter 3-deviation
RMS. Table 5-1 shows additional information on GPS measurement statistics. Additionally, absolute
GPS point-positioning accuracies are defined relative to an earth-centered coordinate system or datum.
This coordinate system differs significantly from local or construction datums. Nominal GPS accuracies
may also be published as design or tolerance limits, and accuracies achieved can differ significantly
from these values.
5-18. Dilution of Precision. The final positional accuracy of a point, determined using absolute GPS-S
techniques, is directly related to the geometric strength of the configuration of satellites observed during
the survey session. GPS errors resulting from satellite constellation geometry can be expressed in terms
of DOP. In mathematical terms, DOP is a scalar quantity used in an expression of a ratio of the
positioning accuracy. It is the ratio of the standard deviation of one coordinate to the measurement
accuracy. DOP represents the geometrical contribution of a certain scalar factor to the uncertainty (such
as standard deviation) of a GPS measurement. DOP values are a function of diagonal elements of the
covariance matrices of the adjusted parameters for the observed GPS signal. DOP values are used in
point formulations and determinations. In general terms, DOP is a scalar quantity of the contribution of
the configuration of satellite constellation geometry to the GPS accuracy or a measure of the strength of
the satellite constellation geometry. The more satellites that can be observed and used in the final
solution, the better the solution. Since DOP can be used as a measure of geometrical strength, it can also
be used to selectively choose four satellites in a particular constellation that will provide the best
solution.
EN0593
5-8
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