Prediction of aircraft trajectory and the associated fuel consumption using covariance bidirectional extreme learning machines

Accurate prediction of the aircraft trajectory and associated fuel consumption has become an important research topic owing to the increasing importance of air traffic management. Currently, trajectory prediction and fuel estimation are usually accomplished via complex mathematical energy-balance methods. In these methods, the prediction error could get increased due to the possible usage of global values and outdated database, resulting from that most of the information regarding aircraft operations is unavailable. In this paper, we propose a covariance bidirectional extreme learning machine (CovB-ELM) for predicting aircraft trajectories and estimating fuel consumption. The selection of randomly generated parameters for the hidden unit, such as the input weight and bias, to improve the accuracy and numerical stability of the extreme learning machine (ELM), is an open problem. The fundamental idea behind the proposed method is to maximise the covariance between the hidden unit and network errors through partially updating the hidden-unit parameters randomly generated in bidirectional ELM so that the output weight norm value is minimised and the convergence gets improved. The merits of the proposed CovB-ELM are demonstrated by the experiments involving regression problems and international airline historically flight data, which suggests that the CovB-ELM outperforms, in terms of generalisation performance, several existing methods, e.g., airline mathematical approach, backpropagation neural network, and constructive ELM methods.