Distributed Estimation using Square Root Decompositions of Dependent Information

Sensor networks allow robust and precise estimation by fusing estimates from several distributed sensor nodes. Because of the often limited communication resources, a trade-off between the amount of information communicated and the quality of the fusion result has to be made. On the one hand, obtaining the optimal fusion result often needs an infeasible amount of additional information, but on the other hand, conservative methods usually lead to more pessimistic results in comparison. This paper proposes a square root decomposition of the incorporated noise terms to reconstruct the cross-covariance matrices between sensor nodes. To save communication bandwidth, a residual is defined that allows bounding of the cross-covariance matrix with a reduced number of noise terms. The consistency of the proposed method is demonstrated by two simulation examples featuring a linear and a nonlinear setup and is compared with other state-of -the-art fusion methods.