control//state estimation//Kalman filter//distributed Kalman filter
A distributed Kalman filter is a state estimator spread over several agents, each with its own sensors and computer, that reach the estimate a central filter would compute by exchanging information only with their neighbours. It is the estimation half of a fleet working without a centre: drones over a disaster zone following the same fire front from different sides, ships of a convoy tracking the same contact, sensor nodes along a pipeline. The central solution is always simpler (every measurement goes to one Kalman filter), and it is chosen whenever the links and the single point of failure allow it (fleet architecture).
A distributed Kalman filter is a state estimator spread over several agents, each with its own sensors and computer, that reach the estimate a central filter would compute by exchanging information only with their neighbours. It is the estimation half of a fleet working without a centre: drones over a disaster zone following the same fire front from different sides, ships of a convoy tracking the same contact, sensor nodes along a pipeline. The central solution is always simpler (every measurement goes to one Kalman filter), and it is chosen whenever the links and the single point of failure allow it (fleet architecture).
The distributed version rests on the information filter. Written with the information matrix and vector, the fused estimate needs the sum over agents of what each one contributes, HiTRi−1HiH_i^{\mathsf T}R_i^{-1}H_iHiTRi−1Hi and HiTRi−1ziH_i^{\mathsf T}R_i^{-1}z_iHiTRi−1zi. A sum is NNN times an average, and an average is exactly what a consensus protocol computes: each agent repeatedly replaces its value by a weighted mix of its own and its neighbours', and all of them converge to the mean of the starting values. After enough rounds every agent multiplies by NNN and holds the central estimate, with nobody having seen all the data.
The price is time. Consensus needs several rounds of messages per filter step, and how many depends on how well the communication graph is connected (graph Laplacian); if the rounds do not fit in a step, the fusion is left half done and each agent weighs some sensors too much and others too little. Lost and late messages make it worse (communication constraints).
The classic danger is double counting. If agent A sends its estimate to B and B sends back its fused result, A receives its own information wearing another hat, believes it new, and each round shrinks the covariance without measuring anything. Exchanging raw information terms avoids it; when only finished estimates can be exchanged and their overlap is unknown, they are fused conservatively (covariance intersection).
Maturity differs sharply along the family. Fusing several radars in air traffic control is industry, and centralized; track-to-track fusion between sensors is a consolidated niche in surveillance (multi-target tracking); consensus Kalman filters are mostly research.