Fusion estimation for multi-sensor stochastic systems with unknown inputs and one-step random delays

This paper studies the distributed fusion filtering problem for multi-sensor stochastic systems with unknown inputs and one-step random delays. By defining some new variables, the original system with unknown inputs and random delays is equivalently transformed into a stochastic parameterized system. The time-delay is depicted by a Bernoulli distributed random variable. No prior information about unknown inputs is available. A Kalman-form distributed fusion filter (DFF) independent of unknown inputs is presented based on the linear unbiased minimum variance criterion. The filtering error cross-covariance matrices between any two local filters are derived. A simulation explains the effectiveness of the algorithms.