Aircraft takeoff weight estimation based on optimal control theory and statistical learning

Accurate estimation of aircraft takeoff weight (TOW) is essential for air traffic management, emissions modeling, and trajectory optimization, yet this information is rarely available in operational surveillance data. Existing statistical approaches achieve high accuracy but depend on extensive proprietary feature sets and large, region-specific training datasets, which limits their generalizability. This paper introduces a physics-based methodology that combines nonlinear optimal control with statistical learning to estimate TOW from only a small number of openly available flight parameters. Using the OpenAP performance model and the OpenAP.top trajectory optimizer, we generate a synthetic fuel-optimal dataset spanning 36 aircraft types over systematically varied takeoff weights, flight distances, and air temperatures. This dataset provides a controlled and physically consistent basis for training TOW estimation models without relying on sensitive data. Two regression approaches are evaluated across four compact feature sets built from two to four inputs: altitude, distance, true airspeed, and temperature. Validated against about 390,000 real flights from the EUROCONTROL Performance Review Commission 2024 Data Challenge, the aircraft type-specific models achieve a global mean absolute percentage error (MAPE) of 6.19%. Purely statistical models trained on the challenge dataset reach 4.12% MAPE, but their accuracy degrades substantially for underrepresented aircraft types, reflecting overfitting to dataset biases. Sensitivity analyses show that temperature provides modest gains (0.03–3.7% MAPE reduction), while removing wind information increases error by at most 2.75% MAPE. Two-feature models using only altitude and distance remain competitive, with MAPE increasing by just 0–6.4% when weather data is unavailable. The methodology represents a practical tradeoff: although it does not match the numerical accuracy of models trained directly on operational data, it offers stronger reproducibility, transparency, and broader applicability, requiring only two to four open-source features, supporting aircraft types with limited or no labeled real-world data, and providing ready-to-use linear coefficients for quick approximate estimation without any software dependency.