Fully Decentralized Estimation Using Square-Root Decompositions

Abstract

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.

The Dark Side of Decentralized Target Tracking : Unknown Correlations and Communication Constraints

“…Consider the SSM in (3.1) but with a linear measurement model h(x k ) = H i,k x k for each agent. Recursive formulas for the update of R 12 are given by [143]…”

Decentralized Estimation Using Conservative Information Extraction

“…The authors of [52,61] utilize certain samples to represent the cross-correlations. Decentralized estimation using square-root decompositions of covariance matrices is suggested in [53]. Furthermore, different distributed Kalman filtering schemes are derived in [16,57], and in [50] an algorithm based on consensus convergence is developed.…”

Conservative Quantization of Covariance Matrices with Applications to Decentralized Information Fusion

“…The estimated error covariance matrix computed using the Bar-Shalom–Campo formulas is exact, i.e., holds [ 22 ]. The cross-covariance required by ( 25 ) and (26) can be tracked, e.g., using samples [ 41 ] to encode the cross-correlations or by a square-root decomposition [ 24 ] of the noise covariance matrices. Both approaches require additional data to be transmitted.…”

“…Optimal fusion algorithms [ 22 , 23 ] can be designed if cross-correlations between the estimates are also known. They typically require the transmission of additional information [ 24 ] or specific communication strategies [ 25 , 26 ]. In the case where correlations are unknown, conservative fusion algorithms compute a bound on the actual but unknown error covariance matrix of the fusion results.…”