In the field of air navigation, there is a constant pursuit for new navigation solutions for precise GNSS (Global Navigation Satellite System) positioning of aircraft. This study aims to present the results of research on the development of a new method for improving the performance of PPP (Precise Point Positioning) positioning in the GPS (Global Positioning System) and GLONASS (Globalnaja Nawigacionnaja Sputnikovaya Sistema) systems for air navigation. The research method is based on a linear combination of individual position solutions from the GPS and GLONASS systems. The paper shows a computational scheme based on the linear combination for geocentric XYZ coordinates of an aircraft. The algorithm of the new research method uses the weighted mean method to determine the resultant aircraft position. The research method was tested on GPS and GLONASS kinematic data from an airborne experiment carried out with a Seneca Piper PA34-200T aircraft at the Mielec airport. A dual-frequency dual-system GPS/GLONASS receiver was placed on-board the plane, which made it possible to record GNSS observations, which were then used to calculate the aircraft’s position in CSRS-PPP software. The calculated XYZ position coordinates from the CSRS-PPP software were then used in the weighted mean model’s developed optimization algorithm. The measurement weights are a function of the number of GPS and GLONASS satellites and the inverse of the mean error square. The obtained coordinates of aircraft from the research model were verified with the RTK-OTF solution. As a result of the research, the presented solution’s accuracy is better by 11−87% for the model with a weighting scheme as a function of the inverse of the mean error square. Moreover, using the XYZ position from the RTKLIB program, the research method’s accuracy increases from 45% to 82% for the model with a weighting scheme as a function of the inverse of the square of mean error. The developed method demonstrates high efficiency for improving the performance of GPS and GLONASS solutions for the PPP measurement technology in air navigation.