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This paper is concerned with the weighted observation fusion Kalman filtering problem for a class of multi-sensor fusion systems with random measurement delays and energy constraints. To reduce the energy consumptions, each sensor intermittently sends information to the fusion center in a random way. By using the full rank decomposition approach, the observation fusion equation is derived. Without resorting to the augmentation technique, optimal weighted observation fusion Kalman filter (WOFKF) is given, and it is proved that the performance of the WOFKF is equivalent to that of the centralized fusion Kalman filter. Simulations show the effectiveness of the proposed fusion methods. [ABSTRACT FROM AUTHOR]