The term accuracy is used to express the degree of closeness of a measurement, or the obtained solution, to the true value. The term precision, however, is used to describe the degree of closeness of repeated measurements of the same quantity to each other. In the absence of systematic errors, accuracy and precision would be equivalent [1]. For this reason, the two terms are used indiscriminately in many practical purposes. Accuracy can be measured by a statistical quantity called the standard deviation, assuming that the GPS measurements contain no systematic errors or blunders. The lower the standard deviation, the higher the accuracy.
For the 1-D case, for example, measuring the length of a line between two points, the accuracy is expressed by the so-called root mean square (rms). The rms is associated with a probability level of68.3%. For example, the accuracy of the static GPS surveying could be expressed as "5 mm + 1 ppm" (rms). This means that there is a 68.3% chance (or probability) that we get an error of less than or equal to "5 mm + 1 mm for every kilometer." In other words, if we measure a 10-km baseline, then there is a 68.3% chance that we get an error of less than or equal to 15 mm in the measured line.
Horizontal component (e.g., easting and northing) accuracy, a 2-D case, is expressed by either the circular error probable (CEP) or twice distance rms (2drms). CEP means that there is a 50% chance that the true horizontal position is located inside a circle of radius equal to the value of CEP [1]. The corresponding probability level of the 2drms varies from 95.4% to 98.2% depending on the relative values of the errors in the easting and northing components. The ratio of the 2drms to the CEP varies from 2.4 to 3. This means that an accuracy of 40m (CEP) is equivalent to 100m (2drms) for a ratio of 2.5.
The spherical error probable (SEP) is used to express the accuracy of the 3-D case. SEP means that there is a 50% chance that the true 3-D position is located inside a sphere of a radius equal to the value of SEP [1].
