The joint optimal filtering and fault detection for multi-rate sensor fusion under unknown inputs

In multi-sensor fusion, it is hard to guarantee that all sensors have an identical sampling rate, especially in the distributive and/or heterogeneous case. Meanwhile, stochastic noise, unknown inputs (UIs), and faults may coexist in complex environment. To this end, we propose the problem of joint optimal filtering and fault detection (FD) for multi-rate sensor fusion subject to UIs, stochastic noise with known covariance, and faults imposed on the actuator and sensors. Furthermore, the new scheme of optimal multi-rate observer (MRO) is presented and applied to detect faults. The observer parameters are determined optimally in pursuit of the UI decoupling and maximizing noise attenuation under the causality constraint due to multi-rate nature. Finally, the output estimation error of the MRO is used as a residual signal for FD via a hypothesis test in which the threshold is adaptively designed according to the MRO parameters. One numerical example is given to show the effectiveness of our proposed method.