Bias estimation for asynchronous multi-rate multi-sensor fusion with unknown inputs

In asynchronous multi-sensor fusion, it is hard to guarantee that all sensors work at the single sampling rate, especially in the distributive and heterogeneous case. Meanwhile, the time-varying sensor bias driven by unknown inputs (UIs) are likely to occur in complex environments when conducting the sensor registration. In this paper, a two-stage fusion scheme is proposed to estimate the state, the UI and the UI-driven bias for asynchronous multi-sensor fusion. By establishing the dynamic system model at each scale and deriving its corresponding equivalent UI-decoupled bias dynamic model, the proposed scheme is implemented in two stages. At the first stage, each sensor collects its own measurements and generates the local optimal estimates of the state and the bias which are later used to compute the local estimate of the UI via the least squares method. At the second stage, local estimates of the state and the UI are distributively fused via network consensus to obtain the consensus state and UI estimates which are fed back to refine the local bias estimate. Local estimators are designed via the orthogonal projection principle and the least squares method, and the fusion estimators are designed via the average consensus fusion rule weighted by matrices. Simulation experiments are given to show the effectiveness of the developed method.