This paper presents an adaptive determination method of the information sharing factors employed in the Federated Kalman filtering algorithm. This approach is based on eigenvalue decomposition of the covariance matrix of the estimated errors associated with individual sensors. The paper begins with a discussion of the structural features and information sharing principle of the Federated Kalman filtering approach. Following development of the new method, simulation results demonstrate its capability to provide a considerable improvement in robustness to changing plant conditions, at the cost of a minimal loss in accuracy under ideal plant behaviour.