Global Navigation Satellite System Positioning Under Interference Conditions

This paper contains a model of the flying object (FO) flight trajectory in the geocentric coordinate system and a model of FO position measurement errors using a Global Navigation Satellite System (GNSS) receiver under interference conditions. The size of the FO coordinate errors in the horizontal and vertical planes ranged from +20.0 m to -20.0 m. This paper's contribution is the creation of algorithms for processing GNSS signals under interference conditions based on the Savitzky-Golay filter and neural network. The simulation results confirmed that the Savitzky-Golay filter when applied in the GNSS receiver, can suppress FO position measurement errors. For example, if absolute FO position measurement errors due to GNSS interference were from 0.0 m to 5.0 m, and the mean square error of these errors was 0.441 m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, the Savitzky-Golay filter reduced them to a value from 0.0 m to 0.8 m, and the mean square error of these errors was equal was 0.0195 m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. In this case, the mean error value in the FO position after filtering with the Savitzky-Golay filter was 0.32 m, and the mean square error was 0.019 m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. Advanced machine learning techniques in the form of neural networks were also used to suppress errors from the output of the Savitzky-Golay filter. The simulation confirmed that if the FO position errors at the neural network's input ranged from 0 m to +0.8 m, the neural network reduced them to 0.0 m to 0.5 m. The mean FO position error value was 0.12 m, and the mean square error was 0.0089 m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. The results of this study may contribute to more precise and reliable FO navigation and improve the use of GNSS systems in interference conditions.