The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.