Fault detection for multi-rate sensor fusion under multiple uncertainties

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, system modelling may face the coexistence of multiple uncertainties including stochastic noise, unknown input (UI) and faults in complex environment. To this end, the authors propose the problem of fault detection for multi-rate sensor fusion systems subject to UI, stochastic noise with known covariance, and faults imposed on the actuator and sensors. Furthermore, the new form of multi-rate observer (MRO) is presented and lifted to the single-rate one with causality constraint for parameter design. Observer parameters are determined optimally in pursuit of the UI decoupling and maximum noise attenuation under the causality constraint. Differing from the traditional observer, the proposed MRO is time varying, that is, its parameters need recursive computation and hence has better adaptability to the effect of uncertainties. Finally, a multi-rate residual generator is constructed via a hypothesis test in which the threshold is adaptively designed. A numerical example is given to show the effectiveness of their proposed method.