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This paper pertains to the analysis and design of decentralized estimationschemes that make use of limited communication. Briefly, these schemes equipthe sensors with scalar states that iteratively merge the measurements and thestate of other sensors to be used for state estimation. Contrarily to commonlyused distributed estimation schemes, the only information being exchanged arescalars, there is only one common time-scale for communication and estimation,and the retrieval of the state of the system and sensors is achieved infinite-time. We extend previous work to a more general setup and providenecessary and sufficient conditions required for the communication between thesensors that enable the use of limited communication decentralizedestimation~schemes. Additionally, we discuss the cases where the sensors arememoryless, and where the sensors might not have the capacity to discern thecontributions of other sensors. Based on these conditions and the fact thatcommunication channels incur a cost, we cast the problem of finding the minimumcost communication graph that enables limited communication decentralizedestimation schemes as an integer programming problem.

On the Limited Communication Analysis and Design for Decentralized Estimation