On the Limited Communication Analysis and Design for Decentralized Estimation
For control and estimation researchers, this work offers a theoretical foundation and optimization framework for designing communication-efficient decentralized estimation systems.
This paper extends limited communication decentralized estimation to a more general setup, providing necessary and sufficient conditions for sensor communication that enable finite-time state estimation with scalar exchanges. It formulates the minimum-cost communication graph problem as integer programming.
This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation~schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.