Algorithms for aircraft track optimization in flexible routing

The authors consider the problem of optimization of aircraft flight tracks in air traffic management (ATM) on basis of flexible routing technologies which involve the use of satellite navigation systems (SNS). It is shown that in optimizing a trajectory it is necessary to take into account the accuracy of track holding in flight which depends on accuracy of the navigation system and external flight path disturbances, e.g. wind. For solving the problem of optimization the authors propose to use the theory of graphs. The technique of constructing a dynamic SNS accuracy field and representing it as a graph was developed. It is proposed that the SNS field could be characterized by geometric dilution of precision changing both in space and in time. Based on the theory of graphs (A-star algorithm) the technique of constructing a trajectory of optimal length under conditions of SNS accuracy variations and external flight path disturbances is proposed. The criterion of optimization based on minimizing the true track is offered. The cost function taking into account the track holding accuracy in navigating by SNS and effects of external flight disturbances is justified. The article represents the results of A-star algorithm application for optimal flight track construction under conditions of SNS accuracy field variation and presence of prohibited zones in the provide zone of airspace