Triple probability density distribution model in the task of aviation risk assessment
Abstract
The probability of an airplane deviation from pre-planned trajectory is a core of aviation safety analysis. We propose to use a mixture of three probability density distribution functions it the task of aviation risk assessment. Proposed model takes into account the effect of navigation system error, flight technical error, and occurrence of rare events. Univariate Generalized Error Distribution is used as a basic component of distribution functions, that configures the error distribution model from the normal error distribution to double exponential distribution function. Statistical fitting of training sample by proposed Triple Univariate Generalized Error Distribution (TUGED) is supported by Maximum Likelihood Method. Optimal set of parameters is estimated by sequential approximation method with defined level of accuracy. The developed density model has been used in risk assessment of airplane lateral deviation from runway centreline during take-off and landing phases of flight. The efficiency of the developed model is approved by Chi-square, Akaike’s, and Bayes information criteria. The results of TUGED fitting indicate better performance in comparison with double probability density distribution model. The risk of airplane veering off the runway is considered as the probability of a rare event occurrence and is estimated as an area under the TUGED.
Keyword : risk, airplane, aviation safety, probability density function, Triple Univariate Generalized Error Distribution, deviation, Maximum Likelihood Method, statistics
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Ayebo, A., & Kozubowski, T. (2003). An asymmetric generalization of Gaussian and Laplace laws. Journal of Probability and Statistical Science, 1(2) 187–210.
Cramer, M., & Rodriguez, L. (2013). Analysis of aircraft lateral path tracking accuracy and its implications for separation standards. Integrated Communications, Navigation and Surveillance Conference, ICNS (pp. 1–11). Herndon, VA, United States. https://doi.org/10.1109/ICNSurv.2013.6548526
Czyżycki, R. (2013). Using GED (Generalized Error Distribution) for modeling distribution of the rates of return. International Masaryk Conference for PhD Students and Young Researchers (pp. 1530–1535). Hradec Králové, The Czech Republic.
Fala, N., & Marais, K. (2016). Detecting safety events during approach in general aviation operations. 16th AIAA Aviation Technology, Integration, and Operations Conference (pp. 1–15). Washington, United States. https://doi.org/10.2514/6.2016-3914
Fujita, M. (2013). Iterative bayesian estimation of navigation performance modeled by a mixture of Gaussian and laplace distributions for the application of collision risk modeling. Transactions of the Japan Society for Aeronautical and Space Sciences, 56(5), 253–260. https://doi.org/10.2322/tjsass.56.253
Giller, G. (2013). A Generalized Error Distribution. SSRN (August 16, 2005). https://doi.org/10.2139/ssrn.2265027
ICAO. (1988). Review of the General Concept of Separation Panel (RGCSP) (Doc 9536). ICAO.
ICAO. (1998). Manual on airspace planning methodology for the determination of separation minima (Doc 9689, AN/953). ICAO.
ICAO. (2006). Procedures for Air Navigation Services. Aircraft Operation. Construction of Visual and Instrumental Flight Procedure, Vol. 2, (Doc 8168, OPS/611). ICAO.
ICAO. (2008a). Performance-based Navigation (PBN) (Doc 96131) Manual. ICAO.
ICAO. (2008b). Unified framework for collision risk modelling in support of the manual on airspace planning methodology with further applications (Doc 9689, 181 ed.). International Civil Avaition Organization.
Klein, V. (1980). Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain. NASA Technical Paper 1637 (61 p.).
Kutsenko, O., Ilnytska, S., & Konin, V. (2018). Investigation of the residual tropospheric error influence on the coordinate determination accuracy in a satellite landing system. Aviation, 22(4), 156–165. https://doi.org/10.3846/aviation.2018.7082
Kuzmenko, N., & Ostroumov, I. (2018). Performance analysis of positioning system by navigational aids in three dimensional space. 2018 IEEE 1st International Conference on System Analysis and Intelligent Computing, SAIC 2018 – Proceedings (pp. 101–104). IEEE. https://doi.org/10.1109/SAIC.2018.8516790
Markovsky, I., & Van Huffel, S. (2007). Overview of total least-squares methods. Signal Processing, 87(10), 2283–2302. https://doi.org/10.1016/j.sigpro.2007.04.004
Mitici, M., & Blom, H. (2019). Mathematical models for air traffic conflict and collision probability estimation. IEEE Transactions on Intelligent Transportation Systems, 20(3), 1052–1068. https://doi.org/10.1109/TITS.2018.2839344
Mori, R. (2011). Identifying the ratio of aircraft applying SLOP by statistical modeling of lateral deviation. Transactions of the Japan Society for Aeronautical and Space Sciences, 54(183), 30–36. https://doi.org/10.2322/tjsass.54.30
Nagaoka, S. (2008). A model for estimating the lateral overlap probability of aircraft with RNP alerting capability in parallel RNAV routes. ICAS Secretariat – 26th Congress of International Council of the Aeronautical Sciences 2008, ICAS 2008, 1 (pp. 3590–3597). Anchorage, AK, United States.
Naidu, V., & Durgarao, S. (2012). Estimation of aircraft height and lateral deviation with respect to runway using images from un-calibrated camera. National Conference on Signals and Image Processing, 1, 81–185.
Ostroumov, I., & Kuzmenko, N. (2018). Compatibility analysis of multi signal processing in apnt with current navigation infrastructure. Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika), 77(3). https://doi.org/10.1615/TelecomRadEng.v77.i3.30
Ostroumov, I., Kharchenko V., & Kuzmenko, N. (2019). An airspace analysis according to area navigation requirements. Aviation, 23(3), 36–42. https://doi.org/10.3846/aviation.2019.10302
Ostroumov, I. V., & Kuzmenko, N. S. (2019). Risk analysis of positioning by navigational aids. In Signal Processing Symposium: SPSympo-2019, International Conference of IEEE (pp. 92–95). Krakow, Poland. https://doi.org/10.1109/SPS.2019.8882003
Ryu, E., & Young, S. (2016). General aviation runway design evaluation based on aircraft deviations from runway center-line. 7th International Conference on Research in Air Transportation (pp. 1–4). Drexel University.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/aos/1176344136