Optimization of an aircraft flight trajectory in the GLONASS dynamic accuracy field

The authors consider the problem of optimization of aircraft flight trajectories in air traffic management (ATM) on the 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 during the flight which depends on the accuracy of the navigation system and external flight path disturbances, e.g. wind. For solving the task 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 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 with changing the SNS accuracy 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 presents the results of A-star algorithm application for constructing an optimal flight trajectory under conditions of SNS accuracy field variation and presence of prohibited zones in the provided airspace.

1. Skrypnik, O.N. (2019). Radio Navigation Systems for Airports and Airways. Springer Nature Singapure Pte Ltd, 226 p. DOI: 10.1007/978-981-13-7201-8

2. Russel, S.J. and Norvig P. (2003). Artificial Intelligence: A Modern Approach. Second edition, Pearson Education, Inc. 1408 p.

3. Vormer, F.G., Mulder, M., van Paassen, M.M. and Mulder, J.A. (2006). Optimization of Flexible Approach Trajectories Using Geneting Algorithm. Journal of Aircraft, vol. 43, no. 4, pp. 941–952. DOI:10.2514/1.13609

4. Fett, G.D. (2014). Aircraft route optimization using the A-STAR algorithm, Air force institute of technology, Thesis Degree of Master of Science in Operations Research, 68 p.

5. Veremey, E.I. and Sotnikova, M.V. (2016). Optimal Routing Based on Weather Forecast. International Journal of Open Information Technologies. Vol. 4, no. 3, pp. 55–61. Available at: https://pureportal.spbu.ru/ru/publications/% (accessed 10.06.2019). (in Russian)

6. Toratani, D. (2016). Study on Simultaneous Optimization Method for Trajectory and Sequence of Air Traffic Management. Doctoral Thesis, Yokohama National University, 101 p. DOI:10.13140/RG.2.2.27308.46727

7. Bonami, P., Olivares, A., Soler, M. and Staffetti, E. (2013). Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization. Journal of Guidance, Control, and Dynamics, vol. 36, no. 5, pp. 1267–1277. DOI: 10.2514/1.60492

8. Gardi, A., Sabatini, R. and Kistan, T. (2018). Multi-Objective 4D Trajectory Optimization for Integrated Avionics and Air Traffic Management Systems. IEEE Transactions on Aerospace and Electronic Systems, pp. 99–111. DOI: 10.1109/TAES.2018.2849238

9. Skrypnik, O.N. and Arefeva, N.G. (2017). Construction of an optimal flight trajectory in the GLONASS accuracy field. Coll. of papers of the 24th Saint Petersburg International Conference on Integrated Navigation Systems, ICINS, pp. 129–131. DOI:10.23919/icins.2017.7995606

10. Skrypnik, O.N., Arefyeva, N.G. and Arefyev, R.O. (2018). Optimization of an aircraft flight trajectory in the GLONASS dynamic accuracy field. The Civil Aviation High Technologies, vol. 21, no. 5, pp. 56–66. DOI:10.26467/2079-0619-2018-21-5-56-66 (in Russian)

11. Yarlykov, M.S. (1985). Statisticheskaya teoriya radionavigatsii [Statistical theory of radio navigation]. Moscow: Radio i svyaz, 345 p. (in Russian)