Distributed estimation of multi-agent systems with coupling in the measurements: Bulk algorithm and approximate Kalman-type filtering

We consider distributed estimation of a class of large population multi-agent systems where the agents have linear stochastic dynamics and are coupled via their partial observations. The measurements interference model is assumed to depend only on the empirical mean of agents states. In addition, a structural assumption is made on the agents' controls which are constrained to be linear constant feedbacks on a locally based state estimate. In previous work [19], we solved precisely the decentralized optimal estimation problem for a finite population of agents. In particular, we developed a non-sequential bulk estimation algorithm whereby at every time step, all past and present available measurements are considered. In this paper, a Kalman-type recursive approximate filtering approach using exchangeability arguments is presented and tested numerically.