Estimators for autoregressive moving average signals with multiple sensors of different missing measurement rates

This study is concerned with the optimal linear estimation problems for multi-sensor autoregressive moving average (ARMA) signals with missing measurements, which can be converted into estimation problems of the state and white noise in the state space representation. The missing measurements from different sensors are described by a group of Bernoulli distributed random variables. Using the projection theory, the optimal linear estimators including filter, predictor and smoother for the state and white noise are derived in the linear minimum variance sense. Furthermore, the centralised optimal estimators for ARMA signals with multiple sensors of different missing measurement rates are obtained. The previous estimation algorithms under complete measurement data in references have lost the optimality when there are missing measurements of sensors. At last, the stability of the proposed estimators is analysed. Simulation results show the effectiveness of the proposed optimal linear estimators.