Precise estimation of horizontal displacement by combination of multi-GNSS (Galileo and GPS) observations via the LS-VCE method

In the present study, the role of the stochastic model in processing GNSS observations and determining the horizontal displacement parameters is investigated. Stochastic modeling has been evaluated using two approaches; (1) nominal weight and (2) estimated weight. The former is based on the experimental fixed values, meanwhile the latter is based on the least-square variance components estimation (LS-VCE) method, which is implemented for GNSS observations to estimate the components of variance of observations directly. In this research showed that the stochastic model plays an important role in detecting small displacements. For this purpose, a high-precision displacement simulator which can move accurately at short distances in one direction as well as on a horizontal plane was used. A simulated displacement motion experiment was performed. Derived displacements were compared with simulated (real) displacements along with their accuracy in two modes using only GPS and multi-GNSS as well as the two weighting modes provided. The results of the coordinate comparison show that the stochastic model based on the LS-VCE in the PPP method gives a difference of 0 and − 1.9 mm for the east–west and north–south components, while the use of nominal weight, a difference of − 1.9 and − 1.1 mm. Also, the maximum accuracy improvement in this case for these two coordinate components is 7.8 and 4 mm, respectively, also considering the combination of multi-GNSS observations, the accuracy of the coordinate components and the horizontal component in the weight estimation model has provided an improvement of 5.8 and 5.3 mm. In general, the combination of observations has increased the accuracy of the displacement component compared to the single system.