Team optimal decentralized estimation by multiple agents with partial history sharing information structure

In this paper, we study the team optimal decentralized estimation with partial history sharing information structure. There exist N$$ N $$ agents that have their own observations and share partial history observations to each other. The main contributions include two aspects: One is to give the iterative equations of the common estimation, which is the conditional expectation of state with respect to the common information for all agents and the innovation of the local information for each agent; the other is to provide the structure of the team optimal decentralized estimation, that is, the linear combination of the common estimation and the innovation of the local information. The novelty lies in that the estimation can be obtained at one time by defining an augmented state. In particular, the result is reduced to the well-known centralized estimation when all the information is sharing for all the agents.