Abstract: Aiming at the problem of turbojet engine component performance evaluation with inequality constraints，the least mean square (LMS) estimation and the truncated probability density function (PDF) are introduced into the normal extended kalman filter (EKF). The approaches of nonlinear filter with inequality constraints for turbojet engine health estimation are proposed. The constraint mean square error function is minimized and is solved with the Lagrange to inequality-constrained equations in least squares estimation algorithm. The prior inequality constraint is transformed into probability density function in the truncated PDF，and it is easy to obtain its mean and variance of normal distribution function. A series of simulations on a turbojet engine show that both of approaches (the LMS-EKF and the truncated PDF EKF) have better capabilities for the engine component health state estimating compared to the normal EKF one，and the truncated PDF EKF is with the best accuracy and least computational time.

Key words: Turbojet engine；Health estimation；Extended kalman filter；Inequality constraint；Truncated probability density function

摘要： 针对涡喷发动机在不等式约束条件下的部件性能估计问题，在标准扩展卡尔曼滤波方法的基础上引入了最小均方差和概率密度截断，提出了涡喷发动机健康状态的带约束非线性滤波估计方法。最小均方差的基本思想是求解最小化条件均方差函数，同时运用拉格朗日算子法将不等式约束引入待求方程，而概率密度截断求解则是将先验不等式约束条件转化为概率密度函数形式，并获得标准正态分布函数，其特点是均值和方差易于算得。以涡喷发动机为对象进行仿真验证，结果表明相比于标准扩展卡尔曼滤波方法，本文提出的最小均方差和概率密度截断的不等式约束的非线性滤波估计方法对部件性能估计精度高，而其中概率密度截断求解在保证精度的同时计算耗时更少。

关键词: 涡喷发动机；健康状态估计；扩展卡尔曼滤波；不等式约束；概率密度截断