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Networks consisting of several spatially distributed sensor nodes are useful in many applications. While distributed processing of information can be more robust and flexible than centralized filtering, it requires careful consideration of dependencies between local state estimates. This paper proposes an algorithm to keep track of dependencies in decentralized systems where no dedicated fusion center is present. Specifically, it addresses double counting of measurement information due to intermediate fusion results as well as correlations due to common process noise and common prior information. To limit the necessary amount of data, this paper introduces a method to bound correlations partially, leading to a more conservative fusion result while reducing the necessary amount of data. Simulation studies compare the performance and convergence rate of the proposed algorithm to other state-of-the-art methods.