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Analysis of the precision of determination of aircraft coordinates using EGNOS+SDCM solution

Krasuski Kamil, Lalak Marta, Gołda Paweł, Ciećko Adam, Grunwald Grzegorz, Mrozik Magda, Kozuba Jarosław

Archives of Transport

2023

Vol. 67, iss. 3

105--117

This paper presents an algorithm for determining the precision parameter for aircraft position coordinates based on a combined GPS/EGNOS and GPS/SDCM solution. The proposed algorithm uses a weighted average model that combines a single GPS/EGNOS and GPS/SDCM position navigation solution to determine the resulting aircraft coordinates. The weighted mean model include the linear coefficients as a function of: the inverse of the number of tracked GPS satellites for which EGNOS and SDCM corrections have been generated, and the inverse of the geometric coefficient of the PDOP (Position Dilution of Precision). The corrections between the single GPS/EGNOS and GPS/SDCM solution to the aircraft's resultant coordinates are then calculated on this basis. Finally, the standard deviation for the aircraft resultant BLh (B-Latitude, L-Longitude, h-ellipsoidal height) coordinates is calculated as a measure of precision. The research experiment used recorded on-board GPS+SBAS data from two GNSS receivers mounted on a Diamond DA 20-C1 aircraft. The test flight was carried out on the Olsztyn-Suwałki-Olsztyn route. The calculations of aircraft position based on GPS/EGNOS and GPS/SDCM solution were performed in the RTKLIB v.2.4.3 program in the RTKPOST module. Next, aircraft resultant coordinates and standard deviations were computed in Scilab v.6.0.0 software package. Based on the tests performed, it was found that for the Trimble Alloy receiver, the standard deviation values for the ellipsoidal coordinates BLh of the aircraft do not exceed 1.77 m. However, for the Septentrio AsterRx2i receiver, the values of standard deviations for the aircraft's ellipsoidal BLh coordinates do not exceed 5.04 m. The use of linear coefficients as the inverse of the number of tracked GPS satellites with SBAS corrections in the GPS/EGNOS+GPS/SDCM positioning model resulted in a reduction in standard deviations of approximately 50-51% relative to the solution with linear coefficients calculated as the inverse of the PDOP parameter. In paper, the standard deviation was also obtained using arithmetic mean model. However the values of standard deviation from weighted mean model are lower than arithmetic mean model.

Analysis of the accuracy of EGNOS+SDCM positioning in aerial navigation

Mrozik Magda, Kozuba Jarosław, Krasuski Kamil, Ćwiklak Janusz, Bakuła Mieczysław, Ciećko Adam, Grunwald Grzegorz, Wierzbicki Damian

Archives of Transport

2022

Vol. 64, iss. 4

135--144

The article presents a modified scheme of determining the accuracy parameter of SBAS (Satellite Based Augmentation System) positioning with use of two supporting systems: EGNOS (European Geostationary Navigation Overlay Service) and SDCM (System of Differential Correction and Monitoring). The proposed scheme is based on the weighted mean model, which combines single solutions of EGNOS and SDCM positions in order to calculate the accuracy of positioning of the aerial vehicle. The applied algorithm has been tested in a flight experiment conducted in 2020 in north-eastern Poland. The phase of approach to landing of a Diamond DA 20-C1 aircraft at the EPOD airport (European Poland Olsztyn Dajtki) was subjected to numerical analysis. The Septentrio AsterRx2i geodesic receiver was installed on board of the aircraft to collect and record GPS (Global Positioning System) observations to calculate the navigation position of the aircraft. In addition, the EGNOS and SDCM corrections in the “*.ems” format were downloaded from the real time server data. The computations were realized in RTKPOST library of the RTKLIB v.2.4.3 software and also in SciLab application. Based on the conducted research, it was found that the accuracy of aircraft positioning from the EGNOS+SDCM solution ranged from -1.63 m to +3.35 m for the ellipsoidal coordinates BLh. Additionally, the accuracy of determination of the ellipsoidal height h was 1÷28% higher in the weighted mean model than in the arithmetic mean model. On the other hand, the accuracy of determination of the ellipsoidal height h was 1÷28% higher in the weighted mean model than for the single EGNOS solution. Additionally, the weighted mean model reduced the resultant error of the position RMS-3D by 1÷13% in comparison to the arithmetic mean model. The mathematical model used in this study proved to be effective in the analysis of the accuracy of SBAS positioning in aerial navigation.