Accurate calculation of aircraft fuel consumption plays an irreplaceable role in flight operations, optimization, and pollutant accounting. Calculating aircraft fuel consumption accurately is tricky because it changes based on different flying conditions and physical factors. Utilizing flight surveillance data, this study developed a comprehensive mathematical framework and established a link between flight dynamics and fuel consumption, providing a set of high-precision, high-resolution fuel calculation methods. It also allows other practitioners to select data sources according to specific needs through this framework. The methodology begins by addressing the functional aspects of interval fuel consumption. We apply spectral transformation techniques to mine Automatic Dependent Surveillance-Broadcast (ADS-B) data, identifying key aspects of the flight profile and establishing their theoretical relationships with fuel consumption. Subsequently, a deep neural network with tunable parameters is used to fit this multivariate function, facilitating high-precision calculations of interval fuel consumption. Furthermore, a second-order smooth monotonic interpolation method was constructed along with a novel estimation method for instantaneous fuel consumption. Numerical results have validated the effectiveness of the model. Using ADS-B and Aircraft Communications Addressing and Reporting System (ACARS) data from 2023 for testing, the average error of interval fuel consumption can be reduced to as low as $3.31\%$, and the error in the integral sense of instantaneous fuel consumption is $8.86\%$. These results establish this model as the state of the art, achieving the lowest estimation errors in aircraft fuel consumption calculations to date.

翻译：飞机燃油消耗的精确计算在飞行运营、优化及污染物核算中具有不可替代的作用。由于燃油消耗随飞行条件与物理因素的变化而呈现复杂特性，实现其精确计算具有挑战性。本研究利用飞行监视数据，构建了一套综合数学框架，建立了飞行动力学与燃油消耗之间的关联关系，提供了一套高精度、高分辨率的燃油计算方法。该框架还可支持其他实践者根据具体需求选择数据源。方法首先处理区间燃油消耗的函数特性：应用谱变换技术挖掘广播式自动相关监视（ADS-B）数据，识别飞行剖面的关键特征，并建立其与燃油消耗的理论关联。随后采用参数可调的深度神经网络对该多元函数进行拟合，从而实现区间燃油消耗的高精度计算。此外，本研究构建了二阶光滑单调插值方法，并提出了一种创新的瞬时燃油消耗估计算法。数值结果验证了模型的有效性：使用2023年的ADS-B与飞机通信寻址与报告系统（ACARS）数据进行测试，区间燃油消耗的平均误差可降至$3.31\%$，瞬时燃油消耗在积分意义上的误差为$8.86\%$。这些结果表明该模型达到了当前最优水平，实现了迄今飞机燃油消耗计算中最低的估算误差。