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This paper presents a new approach to distributed linear filtering andprediction. The problem under consideration consists of a random dynamicalsystem observed by a multi-agent network of sensors where the network issparse. Inspired by the consensus+innovations type of distributed estimationapproaches, this paper proposes a novel algorithm that fuses the concepts ofconsensus and innovations. The paper introduces a definition of distributedobservability, required by the proposed algorithm, which is a weaker assumptionthan that of global observability and connected network assumptions combinedtogether. Following first principles, the optimal gain matrices are designedsuch that the mean-squared error of estimation is minimized at each agent andthe distributed version of the algebraic Riccati equation is derived forcomputing the gains.

On observability and optimal gain design for distributed linear filtering and prediction