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In this paper, distributed fusion filtering problem in multisensory dynamic system is considered. The approximation scheme for calculation of cross-covariances is presented, which are based on a correlation coefficient in steady-state. In addition, a new limiting cross-covariance method is also proposed, which gives the opportunity to save calculation times, and is computationally useful to implement the fusion filters in a real-time application. Numerical examples demonstrating the effectiveness of the proposed algorithm are presented.