A Study of Fusions of Multiple Estimates for Limit Cases

Decentralised estimation often sacrifices optimality for solution simplicity, while within the fusion under unknown correlation, a worst-case type of optimality is adopted. This paper studies the gap between the simple solution and the optimal one for special cases. Namely, symmetric configurations are considered for infinite number of estimates and also for infinite dimension of the state to be estimated. In these academic cases, the optimal solution is better than the simple one by low tens percent, if the size of circumscribing balls is considered. In practice, much lower gap can be expected.