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In the paper a state filtration in a decentralized discrete time Linear Quadratic Gaussian problem formulated for a multisensor system is considered. Local optimal control laws depend on global state estimates and are calculated by each node. In a classical centralized information pattern the global state estimators use measurements data from all nodes. In a decentralized system the global state estimates are computed at each node using local state estimates based on local measurements and values of previous controls, from other nodes.

A fusion hierarchical state filtration with k−step delay sharing pattern for a multisensor system is considered. A global state estimate depends on local state estimates determined by local nodes using local information. Local available information consists of local measurements and k−step delay global information - global estimate sent from a central node. Local estimates are transmitted to the central node to be fused. The synthesis of local and global filters is presented. It is shown that a fusion filtration with k−step delay sharing pattern is equivalent to the optimal centralized classical Kalman filtration when local measurements are transmitted to the center node and used to determine a global state estimate. It is proved that the k−step delay sharing pattern can reduce covariances of local state errors.

In the paper, fusion state hierarchical filtration for a multisensor system is considered. An optimal global Kalman filter is realized by a central node in the information form. The state estimate depends on local information that should be sent by local nodes. Two information structures are considered in the paper. In the first case local estimates are based on the local measurement information. It leads to distributed Kalman filter fusion that is well known in a literature. In the second case local node has additionally global information of the system with one step delay. A synthesis of local filters is presented. An advantage of this structure is discussed. [ABSTRACT FROM AUTHOR]

In the paper two filtration algorithms for distributed multisensor system are presented. The first one is derived for a linear dynamical system composed of local subsystems described by local state equations. Local estimates are sent to a central station to be fused and formed an optimal global estimate. The second algorithm is derived for a system observed by local nodes that determine estimates of the whole system using local information and periodically aggregated information from other nodes. Periodically local estimates are sent to the central station to be fused. Owing to this a reduced communication can be achieved. [ABSTRACT FROM AUTHOR]