Kalman filter and its different variants are commonly used as optimal methods for fault detection in various types of system components. In this paper, a newly introduced type of aforementioned filters, called modal Kalman filter, is extended and utilized in order to estimate the states of nonlinear systems, for sensor fault detection purposes, in a class of nonlinear certain systems. This method, in contrast to the extended Kalman filter, which employs only the linear term of Taylor expansion, retains higher-order terms; as a result, the estimation error will reduce accordingly. Practicality and effectivity of this method, and its superiority over Kalman filter, in terms of accuracy and promptness of sensor fault detection, are also verified with simulation results.

卡尔曼滤波器及其不同的变体通常用作各种类型系统组件中故障检测的最佳方法。在本文中，一种新型的上述滤波器（称为模态卡尔曼滤波器）得到了扩展和利用，以估计非线性系统的状态，用于传感器故障检测目的，属于一类非线性特定系统。与仅使用泰勒展开的线性项的扩展卡尔曼滤波器相反，该方法保留了高阶项。结果，估计误差将相应减小。仿真结果也验证了该方法的实用性和有效性，以及在传感器故障检测的准确性和迅速性方面优于卡尔曼滤波器的优势。