A Novel Probability Density Estimating Method for Relative Altitudes of Civil

Abstract With the rapid development of civil aviation, the shortage of airspace resource is becoming one of the main limiting factors for air traffic transportation. Inspired by the ideas of reduced vertical separation minimum and reducing aircraft separation standard, this paper analyzes the distributing characteristics of civil aircraft tracks in cruising level space and presents a novel method for probability density estimation of civil aircraft tracks' relative altitudes in their cruising flight level spaces, and analyzes the distributing characteristics at their cruising altitude direction. The method is based on QAR data of enough random civil aircraft tracks from a domestic airline. First, we choose altitude data of each track's main cruise phase and calculate altitude values relative to the standard cruise altitude of respective cruising flight level, we call these processes as spatial alignment and the relative altitudes as relative-cruising altitudes or relative-cruise altitudes. Secondly, we do temporal alignment and figure out the relative altitude values of these tracks in panel data form. Then, we estimate the probability density of the relative altitude values using kernel density estimate method, with the least square cross-validation method choosing asymptotically optimal smoothing parameters. Finally, we figure out different confidence track bands, namely confidence interval limits, and do analysis. All the analysis results show that there is a great deal of airspace margin and space resource potential in each cruising levels. Hence there are a great possibility and expectation that the vertical separation minimum can be reduced again and add flight levels, which is beneficial to increase air traffic capacity and relieve traffic jams.