## Estimated Time of Arrival (ETA) Prediction

**Hybrid System Modeling and Estimation for Estimated Time of Arrival Prediction in Terminal Airspace**

As the National Airspace System (NAS) has been facing the pressure of steadily increasing air travel demand, air traffic congestion and flight delays around airports have become major issues in air traffic management. To mitigate such issues, a new framework known as the Next Generation Air Transportation System (NextGen) has been proposed. Under NextGen, a key requirement for safe and efficient air traffic flow management in terminal airspace is accurate knowledge of the aircraft’s states (e.g., position, velocity, and flight mode) and accurate prediction of the aircraft’s estimated time of arrival (ETA). Using the accurate state information of the aircraft, more efficient airborne spacing with reduced separation thresholds can be achieved, and thereby, air traffic flow near an airport can be effectively managed within its capacity. In addition, the accurate prediction of ETA can play an important role in enhancing the efficiency of airport surface operations, since it can reduce unnecessary delays in taxi times caused by inaccurate ETA of arrival aircraft.

Many trajectory prediction algorithms have been developed using kinematic models due to their simplicity. Since these models cannot accurately capture the maneuver uncertainty of the aircraft, they could cause large errors and only work for short look-ahead times. To improve the prediction accuracy, there have been efforts to incorporate flight intent information into prediction models. However, only short-term flight intents have been exploited in the intent-based prediction models, and therefore, their prediction accuracy is degraded for long look-ahead times.

Due to the development of advanced flight data communication systems, long-term flight intent information such as flight plans or airline procedures have become available for more accurate trajectory prediction. In particular, the long-term flight intent information can benefit the trajectory prediction of the aircraft during the descent phase. This is because the aircraft is subject to strictly follow its flight procedure during descent for safe and efficient terminal airspace operation. This implies that a more accurate prediction model can be developed which can exploit the flight plan information explicitly, and thereby predict future trajectories more accurately.

In this research, we propose a stochastic hybrid system model to describe the behavior of an aircraft along its flight plan (with the focus on the descent phase as related to ETA computation) since the aircraft’s behavior is composed of both discrete transitions between a number of flight modes (discrete states) and continuous motion corresponding to a specific flight mode (continuous states). In each flight mode, we derive a nonlinear dynamic model of the aircraft’s continuous motion and also derive a wind model to incorporate the effects of wind disturbance on the aircraft’s motion. Then, we model the discrete transitions between the flight modes by using the continuous state-dependent transition probabilities. This is reasonable since the flight mode changes along a given flight plan are triggered when some conditions on the continuous states (e.g., position and velocity) are satisfied. Based on the obtained stochastic hybrid system model containing the nonlinear continuous dynamics and multiple flight modes with continuous state-dependent transitions, we then develop an algorithm for both aircraft tracking and ETA prediction based on the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm. The proposed algorithm first estimates the aircraft’s continuous and discrete states using available measurements (aircraft tracking) and then propagates the estimates using the stochastic hybrid system model to predict the future trajectory and compute the corresponding ETA (ETA prediction).

The proposed aircraft tracking and ETA prediction algorithm is demonstrated with a continuous descend approach (CDA) case at the Louisville International Airport. The operational procedures and trigger conditions (i.e., guard conditions) corresponding to each mode are summarized in Table 1 (also see Fig. 1 for the nominal trajectory along the CDA procedure).

Table 1 Nominal flight profile of a Boeing 767 following a CDA procedure

Fig. 1 Nominal trajectory of a Boeing 767 along a CDA procedure

For comparison, we consider an algorithm consisting of the IMM and dead reckoning which have been extensively used for the aircraft tracking (i.e., hybrid state estimation) and ETA prediction, respectively. We denote this algorithm as “IMM-DR”. It is shown that the proposed algorithm produces more accurate state estimates and predicts more accurate ETA compared to the IMM-DR approach in in Fig. 2 and Table 2. The proposed algorithm can be applied to the conventional approach (standard stair-case descending) case by appropriately modeling the procedure.

Fig. 2 Comparison of tracking accuracy: root-mean-square values of state estimation error (100 runs)

Table 2 Comparison of ETA prediction accuracy: ETA error for 100 runs

**Publications**

**J. Wei, J. Lee, and I. Hwang, "Estimated Time of Arrival Prediction based on State-Dependent Transition Hybrid Estimation Algorithm," In the Proceedings of the AIAA Guidance, Navigation, and Control Conference, Kissimmee, FL, Jan. 2015.**

**J. Lee, S. Lee, and I. Hwang, "Hybrid System Modeling and Estimation for Estimated Time of Arrival Prediction in Terminal Airspace," Journal of Guidance, Control and Dynamics, (submitted on April 15, 2015)**

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