Differential method’s adjustment for GNSS networks with limited access to satellite signals

: pp. 25-45
Department of Higher Geodesy and Astronomy of Lviv Polytechnic National University
Lviv Polytechnic National University

Purpose. Today various methods of automatic deformation’s monitoring of engineering buildings of hydroelectric power plants (HPPs) are widely used. Namely, the method of GNSS measurements. Like all geodetic methods to study deformations, the method of GNSS measurements has several advantages and disadvantages. Since hydro power plants in most cases are located in complex terrain, it leads to a limited passing signal to receivers, which worsens the results. In addition to these conditions, simultaneously measured by three or more receivers, vectors are burdened with systematic errors. Basically, modern methods of GNSS observations’ results’ processing allow us to resolve only random errors. It is therefore necessary to develop a method of balancing that would address the systematic component of the errors of the measured vectors. Methodology. Differential method’s adjustment for GNSS networks is proposed to reduce the influence of systematic errors on the results of observations. Instead of the correction equations for all vectors making the correction equations for differences simultaneously measured vectors is proposed for partial exclusion of systematic errors. Formed differential equations should not have common vectors. For vectors that are not included in the differential equation of the vectors classical correction equations are recorded. Accordingly, in the differential method two types of equations (correction equations of vectors and their differences) can be included. Results. The study the performance’s effectiveness of the proposed differential method in comparison with the classical parametric method was performed on three GNSS networks formed by a different number of points and the maximum length of the vectors up to 75 km. Vectors for these networks were determined from simultaneous measurements of the three GNSS receivers. To simulate the complex conditions of access to satellite signals (the cutoff angle of the satellites was 200 and the duration of observations was limited by 4 hours). The results of the adjustment by differential and classic parametric methods were compared with reference values of the coordinates of the points defined by the center SOPAC. Average and maximum errors for determining the points’ coordinates in general are 10–50 % less according to the results of a differential method of adjustment compared to the classical parametric method of adjustment and confirms the advantages of the differential method to correct systematic errors of the measurements. Obtained results from three networks show that the RMS error of the coordinates defined by classical parametric method, on average, by 60 % smaller than that determined their mistakes by the same method, and for differential method they are smaller only by 20 % average, which also confirms the high accuracy of the results obtained using a differential method. Scientific novelty and practical significance. On the basis of the conducted researches it is established that processing networks with the help proposed method can largely eliminate systematic errors and to obtain more reliable results than by using classic parametric method adjustment.

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