This paper investigates the problem of distributed ellipsoidal intersection (DEI) fusion estimation for linear time-varying multi-sensor complex systems with unknown input disturbances and measurement data transmission delays. For the problem with external unknown input disturbance signals, a non-informative prior distribution is used to model the problem. A set of independent random variables obeying Bernoulli distribution is also used to describe the situation of measurement data transmission delay caused by network channel congestion, and appropriate buffer areas are added at the link nodes to retrieve the delayed transmission data values. For multi-sensor systems with complex situations, a minimum mean square error (MMSE) local estimator is designed in a Bayesian framework based on the maximum a posteriori (MAP) estimation criterion. In order to deal with the unknown correlations among the local estimators and to select the fusion estimator with lower computational complexity, the fusion estimator is designed using ellipsoidal intersection (EI) fusion technique, and the consistency of the estimator is demonstrated. In this paper, the difference between DEI fusion and distributed covariance intersection (DCI) fusion and centralized fusion estimation is analyzed by a numerical example, and the superiority of the DEI fusion method is demonstrated.

For the state estimation problem of a multi-source localization nonlinear system with unknown and bounded noise, a distributed sequential ellipsoidal intersection fusion estimation algorithm based on the dual set-membership filtering method is proposed to ensure the reliability of the localization system. First, noise with unknown and bounded characteristics is modeled by using bounded ellipsoidal regions. At the same time, local estimators are designed at the sensor link nodes to filter out the noise interference in the localization system. The local estimator is designed using the dual set-membership filtering algorithm. It uses the dual principle to find the minimizing ellipsoid that can contain the nonlinear function by solving the optimization problem with semi-infinite constraints, and a first-order conditional gradient algorithm is used to solve the optimization problem with a low computational complexity. Meanwhile, the communication confusion among multiple sensors causes the problem of unknown correlation. The obtained estimates of local filters are fused at the fusion center by designing a distributed sequential ellipsoid intersection fusion estimation algorithm to obtain more accurate fusion localization results with lower computational cost. Finally, the stability and reliability of the proposed distributed fusion algorithm are verified by designing a simulation example of a multi-source nonlinear system.