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.

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.

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.

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