Decentralized game-theoretic filters

Both continuous-time and discrete-time optimal decentralized game-theoretic filters (DGF) involving a K node interconnected network, where there is a sensor at each node, are derived. In the continuous-time case, a disturbance attenuation problem is solved to obtain the optimal DGF. In a contrasting approach, the solution to a stochastic formulation based on minimizing the expected value of an exponential of a sum of quadratic estimation errors produces the discrete-time DGF. The solution to both approaches reduces to solving a continuous-time or discrete-time linear-quadratic differential game. For both cases, the global state estimate is computed by combining from all the nodes the local estimates and an additional data dependent vector at each node. Finally, a generalization of the continuous-time decentralized filter based on the disturbance attenuation problem is established when the system dynamics for local and global filters are assumed to be different.