Mapping GPS positional errors with spatial linear mixed models

Abstract

Nowadays, GPS receivers are very reliable because of their good accuracy and precision; however, uncertainty is also inherent in geospatial data. Quality of GPS measurements can be influenced by atmospheric disturbances, multipathing, synchronization of clocks, satellite geometry, geographical features of the observed region, low broadcasting coverage, inadequate transmitting formats, or human or instrumental unknown errors. Assuming that the scenario and technical conditions that can influence the quality of GPS measurements are optimal, that functional and stochastic models that process the signals to a geodetic measurement are correct, and that all the GPS observables are taken in the same conditions, it is still possible to estimate the positional errors as the difference between the real coordinates and those measured by the GPS. In this paper, three spatial linear mixed models, one for each axis, are used for modelling real-time kinematic GPS accuracy and precision, of a multiple-reference-station network in dual-frequency with carrier phase measurements. Along the paper, the proposed models provide an estimate of the “accuracy” in terms of bias defined as the difference between real coordinates and measured coordinates after being processed and “precision” through the standard errors of the estimated differences. This is done using ten different transmitting formats. Mapping and quantifying these differences can be interesting for users and GPS professionals. The performance of these models is illustrated by mapping positional error estimates within the whole region of Navarre, Spain. Sampled data have been taken in 54 out of the 211 geodetic vertex points of this region. Maps show interesting error patterns depending on transmitting formats, the different axes, and the geographical characteristics of the region. Higher differences are found in regions with bad broadcasting coverage, due to the presence of mountains and high degree of humidity.