Exact and Approximate Heterogeneous Bayesian Decentralized Data Fusion

Abstract

In Bayesian peer-to-peer decentralized data fusion for static and dynamic systems, the underlying estimated or communicated distributions are frequently assumed to be homogeneous between agents. This requires each agent to process and communicate the full global joint distribution, and thus leads to high computation and communication costs irrespective of relevancy to specific local objectives. This work considers a family of heterogeneous decentralized fusion problems, where we consider the set of problems in which either the communicated or the estimated distributions describe different, but overlapping, states of interest that are subsets of a larger full global joint state. We exploit the conditional independence structure of such problems and provide a rigorous derivation for a family of exact and approximate heterogeneous conditionally factorized channel filter methods. We further extend existing methods for approximate conservative filtering and decentralized fusion in heterogeneous dynamic problems. Numerical examples show more than 99.5% potential communication reduction for heterogeneous channel filter fusion, and a multi-target tracking simulation shows that these methods provide consistent estimates.

Conservative Filtering for Heterogeneous Decentralized Data Fusion in Dynamic Robotic Systems

“…For heterogeneous fusion, since robots only reason over parts of the global set of random variables, they cannot achieve the optimal estimate. Nevertheless, in [2], [10] an extended version of the original homogeneous CF is developed -the Heterogeneous State CF (HS-CF). In the HS-CF algorithm each CF maintains a distribution over only the common variables between any two communicating robots (as opposed to the full set of variables in the original CF), given the common data.…”

“…In previous work [2], [10] we define peer-to-peer Bayesian heterogeneous DDF as the process of fusing two non-*This work was not supported by any organization 1 Ofer Dagan and Nisar R. Ahmed are with the Smead Aerospace Engineering Sciences Department, University of Colorado Boulder, Boulder, CO 80309 USA ofer.dagan@colorado.edu; Nisar.Ahmed@colorado.edu equal, but overlapping, pdfs. 1 One of the main challenges of Bayesian DDF and more acutely of heterogeneous DDF is accounting for dependencies in the data gathered by the different robots.…”

“…Thus there is a need to look at heterogeneous fusion for robotics as a wider, non-application specific problem, and develop the necessary analysis tools and algorithms. For that reason, previous work [10] aimed at gaining insight into the heterogeneous fusion problem.…”

“…In [2], [10] it is shown that in order for the fused posterior to be conservative (doesn't underestimate the uncertainty) over all the robot's variables, conditional independence has to be maintained between non-mutual variables, given the common variables, e.g., in multi-robot SLAM, non-mutual position variables are independent given common landmark variables. An algorithm, named the Heterogeneous State Channel Filter (HS-CF) was developed, and shown to be conservative for static problems and for dynamic problems when a smoothing approach was applied.…”

“…The robots can then individually (locally) infer the posterior distribution over their random variables of interest via Bayes' rule p(χ i |Z i ) = p(χ i )p(Z i |χ i ), where Z i is the locally available data at robot i and p(χ i ) is the prior distribution. Note that if two robots i and j hold distributions over overlapping sets of variables, i.e., χ i ∩ χ j = ∅ and χ i \ χ j = ∅, where '\' is the set exclusion operation, [10] defines the resulting fusion process as an instance of heterogeneous fusion.…”