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In the ground-based arrival time control operation, the measurement of the arrival time error and the speed advisory to cancel it are performed at specific waypoint(s). It is generally recognized that the arrival time accuracy depends on the accuracy of trajectory prediction and control and the availability of information about the aircraft intent. Additionally, the position of the waypoint also determines the arrival time accuracy. Therefore, in this study, the feasibility of waypoint position optimization to improve the arrival time accuracy of aircraft controlled by ground-based speed advisory and its effectiveness are discussed. The models of flight time uncertainty and the arrival time control window were developed using the actual track and numerical weather forecast data. An optimization problem was formulated that defined the arrival time uncertainty at the terminal point as the objective function and numerically solved using sequential quadratic programming. Through numerical investigations, the feasibility of the waypoint position optimization and its effectiveness were clearly demonstrated in comparison with uniform arrangement cases. It was also clarified that the advantage of the multiple waypoint application was enhanced when larger arrival time control windows were available.

In future air traffic plans [

Numerous studies concerning ground-based trajectory management have been devoted to clarifying its feasibility [

In this study, we aim to clarify the feasibility of waypoint position optimization to improve the arrival time accuracy of ground-based arrival time control. For this purpose, the uncertainty model of the ground-based trajectory prediction is derived using actual operation data and weather forecast data. Additionally, the arrival time control window models using the speed advisory are also derived. Through numerical analysis using these models, the feasibility of the optimum waypoint position and its effectiveness are investigated. The waypoint optimization is extended for the application of multiple waypoints, and its effectiveness is clarified.

Flight trajectories to Tokyo from the westward direction are particularly focused on in this study because they represent the heaviest traffic in Japan. The descent trajectory under consideration is shown in Figure

Flight route for analysis.

In this study, the secondary surveillance radar (SSR) Mode S [

Extracted trajectories: (a) lateral path, (b) vertical path, and (c) IAS altitude.

The wind forecast data were provided as the grid point value of the numerical weather forecast data by the Japan Meteorological Agency [

The flight time error arises from the difference between the intent GS and actual GS. The actual GS was provided in SSR Mode S data. However, no information concerning the flight intent was provided. In a time-based operation, the intent GS is determined according to the required arrival time, the intent TAS is determined according to the intent GS and forecast wind speed, and the intent IAS is calculated from the intent TAS. Therefore, in this study, the intent GS was estimated from the IAS recorded in SSR Mode S data and weather forecast data. Because the aircraft in descent phases toward a destination airport was inferred to maintain a constant IAS, as mentioned above, the intent IAS was determined as the average IAS of each trajectory. Then, the intent IAS was translated into the intent TAS using the forecast temperature and pressure [

To imitate the descent trajectory shown in Figure

Summary of the mean deviation, STD, and RMS.

| | | | |
---|---|---|---|---|

20 | 657 | 1.28 | 3.09 | 3.34 |

40 | 532 | 2.51 | 6.19 | 6.68 |

60 | 435 | 3.93 | 9.53 | 10.3 |

80 | 372 | 5.04 | 13.94 | 14.81 |

100 | 289 | 5.14 | 18.07 | 18.75 |

120 | 151 | 4.24 | 20.64 | 21.00 |

Vertical profiles of extracted paths from an altitude of 30,000 ft.

Example of the flight time error calculation.

Mean deviation, STD, and RMS of the flight time error.

Histogram of the flight time error at 40 km.

Based on the IAS distribution shown in Figure

Mean deviation and STD of the tailwind speed.

Flight time profiles to the terminal point.

Arrival time control window models.

To clarify the feasibility of waypoint optimization, the introduction of only one waypoint was considered, and the flight time uncertainty at the terminal point was evaluated by changing its position. For clarity in the investigation, it was assumed that deceleration and acceleration occurred instantaneously and that the flight time error followed a normal distribution based on the central limit theorem.

As was demonstrated in the previous section, the flight time uncertainty increased in proportion to the flight distance. The distribution of the flight time error at the waypoint became like that shown in Figure

Transition of the flight time error distribution: (a) distribution at the waypoint; (b) reduced distribution at the terminal point after arrival time control; (c) distribution increase from the waypoint to the terminal point; and (d) distribution finally obtained at the terminal point.

As was expected from the above example, the arrival time uncertainty at the terminal point became the function of the metering waypoint position. Provided that the flight time followed a normal distribution, the STD of the arrival time at the terminal point was calculated as follows:

The behaviors of the STD at the terminal point in the cases of the average and +2

Arrival time STD at the terminal point.

To investigate the effectiveness of multiple waypoints, it is necessary to formulate a nonlinear optimization problem. The objective function is the STD estimated at the terminal point. This becomes a function of the number and positions of the waypoint expressed as follows:

Because the objective function in this formulation is nonlinear, sequential quadratic programming [

Arrival time STD at the terminal point with multiple waypoints.

Placement of multiple waypoints: (a) even placement and (b) optimized placement.

History of the arrival time STD.

The feasibility of waypoint optimization for the ground-based arrival time control operation and its effectiveness were investigated using flight time uncertainty and arrival time control window models developed using actual track data and weather forecast data. In this study, the STD at the terminal point was considered as the objective function of the optimization. The feasibility and basic characteristics of the waypoint optimization were demonstrated through analysis using one waypoint. To enhance its effectiveness for accuracy improvement at the terminal point, the application of multiple waypoints and the effect of the arrival time control window were numerically investigated. It was clarified that the simultaneous applications of multiple waypoints and the optimization of the waypoint position achieved a significant improvement of arrival time accuracy. It was also clarified that its effectiveness was enhanced when a larger arrival time control window was applied. From this result, it is expected that the waypoint optimization for arrival time accuracy improvement will become more effective when a more accurate trajectory prediction becomes available. Additionally, it is considered that the optimum waypoint placement also depends on the wind condition that determines the arrival time control window. It must be noted that the accuracy of the flight time uncertainty model is essential in this study. Further investigations of the uncertainty model are necessary.

In this fundamental study on waypoint optimization, many assumptions were made, for example, no difference among aircraft types, the trajectory prediction and control error independent of the weather condition, the normal distribution of the flight time error based on the central limit theorem, and instantaneous speed change. Additionally, only the case in which the nominal trajectory had the same reducible and extensible times to arrive at the terminal point was investigated to clarify the fundamental characteristics. For practical use, these assumptions must be mitigated, and various practical cases must be investigated in detail in future work. Although the flight trajectory considered in this study is just a part of a descent trajectory, because of the limitation of the available track data, the fundamental characteristics found in this study will also be applicable to the entire trajectory. Because the effectiveness of waypoint optimization will be enhanced in longer trajectories, some investigations on its application to cruise trajectories are necessary to demonstrate its worthiness for practical use. Furthermore, the concept of arrival time uncertainty management presented in this study is considered applicable to the time-based operation using RTA functionality, for example, the waypoint placement to minimize the possibility that the arrival time required from the ATC goes out from the ETA window of the RTA functionality.

The author declares no conflicts of interest.