Unbiased State and Fault Estimation for Nonlinear Interconnected Systems Based on Second-Order Fault-Tolerant Kalman Filter
针对离散时间非线性互联系统，提出一种二阶容错卡尔曼滤波器，同时处理执行器故障和传感器故障，实现无偏最小方差估计，并通过仿真验证其容错性能。
For discrete-time nonlinear interconnected systems, this article proposes a new estimation technique, namely, second-order fault-tolerant Kalman filter associated with actuator fault and multisensor faults. Considering that the fault mechanisms of multiple interconnected subsystems are independent, actuator faults manifest as random loss of control effectiveness, while sensor faults manifest as bias faults. First, the second-order Taylor expansion is applied to approximate the nonlinear function dynamics for each subsystem. Then, in order to mitigate the impact of actuator faults and sensor faults on estimation performance and maintain data safety, a secure estimator based on active fault tolerance strategy is proposed. When a sensor fault is detected, the estimator can be updated in a timely manner based on fault information. Simultaneously, the sensor fault and system state can be estimated to achieve unbiased minimum variance estimation. Finally, through two simulation examples, the fault estimation strategy proposed is confirmed to have fault-tolerant performance and maintain good estimation performance.