Abstract 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.