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The paired approach can effectively improve the efficiency of closely spaced parallel runways. The calculation of vertical overlap probability and frequency is an indispensable step in evaluating the vertical collision risk of the paired approach. As the existence of vertical overlap is closely related to the vertical position error, this paper presents a method to calculate vertical overlap probability based on the position error caused by pilot control. Firstly, a fuzzy correlation model is established and combined with Quick Access Recorder (QAR) data. The correlation rules between QAR parameters and vertical position error are mined, and the relevance is calculated according to the rules. The results show that the correlation between the control column position and the vertical position error is the strongest. According to the flight dynamics principle, the Vertical Attitude Adjustment Model (VAAM) of an aircraft during the approach process is then established. The Pilot Operating Model (POM), which describes different actions taken by pilots when they encounter different position errors, is also created by employing the concepts of the Markov decision process. The VAAM can restore the process of changing the attitude of the aircraft by the pilot operating column and can simulate the position error of the aircraft in the approach process when combined with the POM. Based on the previous simulated result and considering the overlap condition of the Interval Management (IM) aircraft overlap, the vertical overlap process in the paired approach can then be simulated. We employ MATLAB to carry out numerous simulations. Changing the accuracy of pilot operation in the simulations show that the lower the accuracy, the greater the overlap probability and frequency. However, when the accuracy is between 61% and 73% (61%-73% is the range of operational accuracy based on QAR data analysis), the vertical overlap probability and frequency are maintained at about 5% and 20 flights per hour, respectively.

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