This work considers the methods of optimal linear extrapolation of the flight path of the aircraft, which provide a minimum of the mean square of the forecast error with different amounts of a priori information. The research is based on the canonical decomposition of a vectorial random process. It is determined that the development of modern technologies entails increasing requirements for quality and accuracy of control. However, since the existing methods of linear extrapolation do not provide for the maximum accuracy of the forecast due to the inherent constraints on the random process that describe the motion of aircraft, this necessitates a further development and improvement of methods for extrapolation of aircraft trajectories. The peculiarity of the developed methods for extrapolation of aircraft trajectory is that they allow within the correlation model to fully take into account the properties of a real random process that describes the motion of aircraft at the landing approach stage. This provides for the maximum possible accuracy of linear extrapolation with a variety of information support conditions. These methods allow improving the safety of flights and the efficiency of aviation. Accordingly, new capabilities of aircraft and other sophisticated technical systems can be further considered.