2D position error in the Global Positioning System (GPS) depends on the Horizontal Dilution of Precision (HDOP) and User Equivalent Range Error UERE. The non-dimensional HDOP coefficient, determining the influence of satellite distribution on the positioning accuracy, can be calculated exactly for a given moment in time. However, the UERE value is a magnitude variable in time, especially due to errors in radio propagation (ionosphere and troposphere effects) and it cannot be precisely predicted. The variability of the UERE causes the actual measurements (despite an exact theoretical mathematical correlation between the HDOP value and the position error) to indicate that position errors differ for the same HDOP value.
The aim of this article is to determine the relation between the GPS position error and the HDOP value. It is possible only statistically, based on an analysis of an exceptionally large measurement sample. To this end, measurement results of a 10-day GPS measurement campaign (900,000 fixes) have been used. For HDOP values (in the range of 0.6–1.8), position errors were recorded and analysed to determine the statistical distribution of GPS position errors corresponding to various HDOP values.
The experimental study and statistical analyses showed that the most common HDOP values in the GPS system are magnitudes of: 0.7 (�� = 0•353) and 0.8 (�� = 0•432). Only 2.77% of fixes indicated an HDOP value larger than 1. Moreover, 95% of measurements featured a geometric coefficient of 0.973 – this is why it can be assumed that in optimal conditions (without local terrain obstacles), the GPS system is capable of providing values of HDOP ≤ 1, with a probability greater than 95% (2��). Obtaining a low HDOP value, which results in a low GPS position error value, calls for providing a high mean number of satellites (12 or more) and low variability in their number.