Stochastic model assessment of low-cost devices considering the impacts of multipath effects and atmospheric delays

Abstract

A proper stochastic model is urgently required in Global Navigation Satellite System (GNSS) data processing, whereas deficient knowledge of stochastic model often occurs, especially for low-cost devices such as low-cost receivers and smartphones. The stochastic modeling for low-cost devices considering the impacts of multipath effects and atmospheric delays is systematically studied in this paper. Firstly, two stochastic model assessment methods for low-cost devices are deduced. Secondly, the stochastic modeling including measurement precision and physical correlation for the low-cost receiver and smartphone is comprehensively investigated with single-differenced residuals by using different baseline lengths. The results show that the measurement precisions of short baseline and medium-long baseline for the low-cost receiver are worse than zero baseline due to the systematic errors. The code measurement precisions are similar between short baseline and medium-long baseline, whereas the phase measurement precisions of medium-long baseline are larger than short baseline. Moreover, the measurement precisions of the smartphone are much worse than the low-cost receiver and the C/N0-dependent function is more suitable for the smartphone measurements. For the physical correlation, the measurements of zero baseline are free of cross correlation, but the cross correlation can exist in short baseline and medium-long baseline. The phase measurements of the low-cost receiver are free of temporal correlation for zero baseline, but the code measurements show a certain temporal correlation. Meanwhile, the temporal correlations of the low-cost receiver can exist in short baseline and they are larger than zero baseline due to the multipath effects. In the medium-long baseline, the temporal correlations of code measurements are similar with short baseline both for the low-cost receiver and smartphone, whereas the temporal correlations of phase measurements become larger than short baseline. It can be concluded that the unmodeled errors such as multipath effects and atmospheric delays should be taken into account in the realistic stochastic model assessment including measurement precision and physical correlation for the low-cost devices. Meanwhile, different baseline lengths may consider the baseline-specific stochastic model better in realistic precise positioning.