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The asynchronous estimation fusion problem is investigated for an arbitrary number of sensors with arbitrary sampling rates. By constructing an augmented measurement equation at the fusion time instant, a centralized asynchronous fusion algorithm is developed based on the Kalman filter first without ignoring the correlation between the process noise and the augmented measurement noise. It is optimal in the minimum mean-squared error (MMSE) sense. A distributed asynchronous fusion algorithm is then proposed by reconstructing the optimal centralized fusion result with asynchronous local estimates and their error covariance matrices. It is equivalent to the centralized fusion algorithm under the full-rate communication assumption and outperforms the latter when at least one sensor communicates with the fusion center at a lower rate than its sampling rate. Compared with the existing distributed fusion algorithms for asynchronous sensors, the proposed distributed fusion algorithm avoids the complicated calculation of cross-covariance matrices between each pair of asynchronous local estimates. The communication burden can also be reduced since neither sensor measurement matrices nor local filtering gains need to be transmitted to the fusion center. Moreover all available local estimates are utilized as well as the fused one-step prediction. Some practical considerations of the proposed distributed fusion algorithm are also discussed. Performance of the proposed centralized and distributed fusion algorithms are illustrated through numerical simulations.