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 $Q_k$ and $R_k$ 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.

为了提高航空发动机的可靠性，降低维修成本，促进飞行器安全，航空发动机的健康监测备受关注。航空发动机气体成分涉及流量和效率参数，这是获得航空发动机性能下降的关键健康参数。必须面临的一个挑战是，需要知道的这些健康参数不仅仅是可用的传感器，而这些传感器无法通过卡尔曼滤波器 (KF) 和扩展卡尔曼滤波器 (EKF) 等普通估计器来估计。在本文中，提出了一种系统方法来使用模型调整参数来解决前面提到的估计问题。为了实现它，一个欠定的 EKF 估计器是从以前的成就构建的，并应用于航空发动机的健康状态估计，以解决可用的传感器数据较少且健康参数未知的问题。并且还提供了欠定EKF的收敛证明，以确保实验结果是确定性的，而不是偶然的，推断该估计器的收敛性可以在一些温和的约束下得到验证。本研究发现协方差矩阵${问}_{ķ}$和$R_{ķ}$可以通过设计和设置特定的范围来满足线性矩阵不等式（LMI）的条件，从而导致估计量的快速收敛。此外，还通过半物理实验验证了所提方法的可行性。