Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Abstract

ABSTRACT. The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Geodetic and Geodynamic Studies at Department of Geodesy and Geodetic Astronomy Wut

“…On this basis, it can be concluded that both the number of failure resolutions and the positioning error for the correct resolutions is significantly reduced in the case of the application of the NBSM model. Detailed test results are presented in the works (Prochniewicz, 2013;Prochniewicz, 2014;Prochniewicz et al, 2016).…”

“…Detailed form of the formula 1 for Network RTK instantaneous positioning model using double differences of dual-frequency GPS observations and ionospheric and geometric network corrections was presented in Prochniewicz (2014).…”

“…Based on the determined observation precision parameters, a stochastic model of GNSS observations was developed for Network RTK positioning, defined as Network-Based Stochastic Model (NBSM) (Prochniewicz, 2013;Prochniewicz, 2014;Prochniewicz et al, 2016). This model is dedicated, in particular, to instantaneous positioning, which is based solely on a single observation epoch.…”

Positioning and applications

“…In the reported studies a solution availability and accuracy were analysed using a new approach to account for the residual errors within the stochastic model of GNSS observations, called Network-Based Stochastic Model (NBSM) (Prochniewicz, 2014). This approach is based on the assumption that residual errors of observations remaining after applying network corrections can be described using the variances of those corrections.…”

“…Detailed mathematical formula and application algorithm of NBSM is presented in (Prochniewicz, 2014). Determination of the correction variance based on the network solution results in the variance estimation being performed independently for ionospheric and geometric corrections for each observation (for each satellite or for each double-difference).…”