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A generalized stochastic method for estimating the characteristics of potential conflicts of a controlled air traffic. (English. Russian original) Zbl 1101.93072

Cybern. Syst. Anal. 41, No. 3, 385-396 (2005); translation from Kibern. Sist. Anal. 2005, No. 3, 81-93 (2005).
Summary: A generalized stochastic method is presented for evaluating conflict characteristics such as conflict probability, collision probability, integral estimate of conflict probability on the near-collision time interval, and mean time to a predicted conflict. Equations are obtained for finding these conflict characteristics with regard for the stochastic nature and time correlation of the deviation from a planned controlled-flight trajectory.

MSC:

93E03 Stochastic systems in control theory (general)
93C95 Application models in control theory
Full Text: DOI

References:

[1] J. K. Kuchar and L. C. Yang, ”A review of conflict detection and resolution modeling methods,” in: IEEE Trans. on Intelligent Transportation Systems, 1(4), 179–189 (2000). · doi:10.1109/6979.898217
[2] R. A. Paielli and H. Erzberger, ”Conflict probability estimation for free flight,” J. Guidance, Control and Dynamics, 20(3), 588–596 (1997). · Zbl 0890.90138 · doi:10.2514/2.4081
[3] H. A. P. Blom, G. J. Bakker, P. J. G. Blanker, J. Daams, M. H. C. Everdij, and M. B. Klompstra, ” Accident risk assessment for advanced ATM,” in: G. L. Donohue and A. G. Zellweger (eds.), Air Transportation Systems Engineering, AIAA (2001), pp. 463–480.
[4] ”Methodology for derivation of separation minima applied to the spacing between parallel tracks in ATS route structures,” ICAO Circular 120-AN/89/2, Montreal (1976).
[5] K. Blin, M. Akian, F. Bonnans, E. Hoffman, C. Martini, and K. Zenghal, ”A stochastic conflict detection model revisited,” in: AIAA Guidance, Navigation, and Control Conference, Denver, CO. Aug. (2000), http://www.eurocontrol.fr/projects/cospace/archive/gnc00.pdf.
[6] R. A. Paielli, ”Empirical test of conflict probability estimation,” USA/Europe Air Traffic Management R&D Seminar, Orlando, Dec. (1998), http://russp.org/CPEtest.pdf.
[7] V. I. Tikhonov and M. A. Mironov, Markovian Processes [in Russian], Sov. Radio, Moscow (1977). · Zbl 0478.60078
[8] I. N. Kovalenko, N. Yu. Kuznetsov, and V. M. Shurenkov, Random processes: A Reference Book [in Russian], Naukova Dumka, Kiev (1983). · Zbl 0525.60002
[9] I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). · Zbl 0734.60060
[10] A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Rusian], Nauka, Moscow (1968). · Zbl 0235.46001
[11] E. B. Dynkin, Markovian Processes [in Russian], Fizmatgiz, Moscow (1963).
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