Advances and Applications in Statistics
Volume 35, Issue 1, Pages 1 - 27
(July 2013)
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ESTIMATION OF NAVIGATION PERFORMANCE AND OFFSET BY THE EM ALGORITHM AND THE VARIATIONAL BAYESIAN METHODS
Masato Fujita
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Abstract: An offset procedure allows aircraft to fly several discrete nautical miles right of the course center line without informing air traffic control authority. On the other hand, an En-route Monitoring Agency (EMA) should monitor the navigation performance of aircraft, namely, the unintended deviation from their intended paths, for safety monitoring purposes. Only data available for the EMA are surveillance data collected for the purpose of normal air traffic control practices. They are the aircraft position data which are the sum of intended offset and unintended deviation.
This paper introduces Expectation-Maximization (EM) algorithms and variational Bayesian methods to estimate the proportion of offset and the distribution of navigation performance simultaneously from the surveillance data. A numerical experiment shows that both EM algorithms and variational Bayesian methods provide the ability to estimate the parameters of the distribution model in reasonably short time (in seconds). The estimation is accurate if the initial model parameter values or the parameters of prior distributions are appropriately set.
This paper also proposes the estimation of the offset for a single observation of an aircraft. |
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