Fuel Quantity Estimation of Aircraft Supplementary Tank Using Markov Chain Monte Carlo Method

Abstract

This paper presents an aircraft fuel quantity estimation method using the Markov Chain Monte Carlo (MCMC) method. Using the proposed method, fuel quantity uncertainty of an aircraft supplementary tank can be estimated when the roll and pitch attitudes of an aircraft change. Through reflecting uncertainties, the conservative bound of fuel quantity estimation results can be found, which is necessary for a reliable aircraft operation. The first step of the estimation process is a mathematical modeling of the fuel quantity in a supplementary tank. In the model, the fuel quantity is represented as a multivariate polynomial function of sensor output (i.e., frequency), aircraft roll and pitch angles. The parameter of the mathematical model is then estimated using the MCMC method. As an estimation result, the probability density function of the fuel quantity is provided, which accounts for the uncertainties caused from the developed mathematical model and measured data. The lower bound in the estimation result can be utilized as a conservative fuel quantity value for a reliable operation. To validate the proposed fuel quantity estimation approach, a test with known fuel quantity is performed.