Aero-engine health degradation estimation based on an underdetermined extended Kalman filter and convergence proof

In order to improve the reliability of aero-engine, reduce maintenance cost, and promote aircraft safety, lots of attention is paid to health monitoring of aero-engine. The aero-engine gas components involve flow and efficiency parameters, which are key health parameters to obtain the aero-engine' performance degradation. A challenge has to be faced is that these health parameters needed to know are more than the available sensors, which cannot be estimated by the ordinary estimator like Kalman Filter (KF) and Extended Kalman Filter (EKF). In this paper, a system approach is raised to use model tuning parameter to solve the estimation problem mentioned before. To implement it, an underdetermined EKF estimator is constructed from previous achievement and applied to an aero-engine for health state estimation, to address the problem that there are fewer sensor data available with more unknown health parameters. And convergence proof of underdetermined EKF is also provided to make sure that the experimental result is deterministic rather than occasional, deducing that the convergence of this estimator can be verified with some mild constraints. It is found in this study that the covariance matrices Qk and Rk can meet the conditions of linear matrix inequality (LMI) by designing and setting specific ranges, leading to rapid convergence of the estimator. In addition, semi-physical experiments are shown to verify the feasibility of the proposed method.