Realistic stochastic modeling considering the PDOP and its application in real-time GNSS point positioning under challenging environments.

• The spatial distribution of satellites is considered into the stochastic modeling under challenging environments. • New realistic stochastic modeling considering the PDOP for positioning and navigation is systematically studied. • The proposed PDOP-based approach appropriately quantify the impact of each satellite on the spatial distribution. When the Global Navigation Satellite System (GNSS) is used for positioning under challenging environments, including the natural occlusions and man-made buildings, the signals are easily reflected, diffracted, and even blocked. A stochastic model that conforms to reality is the prerequisite for obtaining high-precision and high-reliability positioning results. However, existing stochastic models which use indicators such as elevation angle and carrier-to-noise ratio cannot reflect the actual situation of the station very well sometimes. Therefore, in this study, in addition to the accuracy of observations, we also consider the impact of the spatial distribution of satellites on positioning accuracy, i.e., position dilution of precision (PDOP). By combining with traditional weighting schemes, the PDOP is considered stochastic modeling. Specifically, different from the previous studies that use PDOP to determine the variance factors between different systems, a new approach is proposed to quantify the contribution of each satellite to PDOP so that the observation weight of each satellite in the system can be appropriately adjusted. The new approach highlights the satellites that contribute much to PDOP and increases the weight of these satellites. Both real static and kinematic data have been tested. The results show that the proposed method is helpful under challenging environments such as high occlusion environments. In civil navigation, the accuracy and reliability of code positioning are improved. [ABSTRACT FROM AUTHOR]