State estimate for stochastic systems with dual unknown interference inputs

Stochastic system state estimation subject to the unknown interference input widely exists in many fields, such as the control, communication, signal processing, and fault diagnosis. However, the research results are mostly limited to the stochastic system in which only the dynamic state model or the measurement model concerns the individual unknown interference input, and the state model and the measurement model are both with the same unknown interference input. State estimate of the stochastic systems where the state model and the measurement model contain dual Unknown Interference inputs (dual-UI) with different physical meanings and mathematical definitions is concerned here. Firstly, the decoupling condition with the Unknown Interference input in the State model (S-UI) is shown, which introduces the decoupled system with the adjacent Measurement concerned Unknown Interference inputs (M-UI) appearing in the state model and the measurement model. Then, through defining the Differential term of the adjacent M-UI (M-UID), the equivalent system with only M-UID in the state model is obtained. Finally, considering the design freedom of the equivalent system, the decoupling filter in the minimum mean square error sense and the adaptive minimum upper filter with different applicable conditions are represented to obtain the optimal and sub-optimal state estimate, respectively. Two simulation cases verify the effectiveness and superiority compared with the traditional methods.