Unbiased State and Fault Estimation for Nonlinear Interconnected Systems Based on Second-Order Fault-Tolerant Kalman Filter

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.