Exact and Approximate Heterogeneous Bayesian Decentralized Data Fusion

TL;DR

The work addresses the scalability bottleneck of Bayesian decentralized data fusion by introducing heterogeneous fusion rules that allow agents to fuse overlapping but non-identical state subsets. It formalizes exact BDF-fusion and approximate HS-fusion, leveraging conditional independence to reduce communication and computation, and extends the Channel Filter framework with Gaussian-information-space methods, including an information-augmented state smoother and conservative marginalization. Through static and dynamic multi-target tracking simulations, the methods demonstrate strong conservativeness and substantial data savings while maintaining consistent estimates, highlighting practical impact for large-scale autonomous sensing networks. Overall, the paper provides a rigorous probabilistic foundation, closed-form gaussian solutions, and practical algorithms for scalable heterogeneous DDF across dynamic networks.

Abstract

In Bayesian peer-to-peer decentralized data fusion, the underlying distributions held locally by autonomous agents are frequently assumed to be over the same set of variables (homogeneous). 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 formulates and studies heterogeneous decentralized fusion problems, defined as the set of problems in which either the communicated or the processed distributions describe different, but overlapping, random 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 of novel exact and approximate conditionally factorized heterogeneous fusion rules. We further develop a new version of the homogeneous Channel Filter algorithm to enable conservative heterogeneous fusion for smoothing and filtering scenarios in 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 while remaining computationally scalable.

Figures (8)

• Figure 1: (a) Static and (b) Partially dynamic Bayesian networks for two local random vectors $s^i, s^j$ (local measurement biases) and one common random vector $x$ (target state). In (a), $s^i$ and $s^j$ are conditionally independent given the static state $x$; in (b) the full time history $x_{1:k}$ is required for conditional independence.
• Figure 2: Progression of fusion rules derived in this paper, describing the set of rvs which needs to be: (i) communicated between any two agents in an undirected acyclic graph; (ii) inferred (estimated) by each agent, corresponding to computation load.
• Figure 3: Target tracking example. Full black arrows denote local measurements to targets $x^t$ and landmarks to estimate local biases $s^i$, red dashed arrows indicate bi-directional communication channel between agents. The undirected and a-cyclic chain topology can be seen.
• Figure 4: Diagram presenting the division of the full random state vector $\chi$ into smaller subsets.
• Figure 5: Information matrix visualisation showing conditional independence. (a) Before marginalization of time step $1$, local rv subsets are conditionally independent given common rv subsets, indicated by empty (zero) cells in the matrix. (b) Marginalizing $\chi_{C,1}^{ij}$ results in filling in the matrix or direct dependencies between local rv subsets. (c) Conservative filtering regains conditional independence by setting matrix cells to zero and deflating the matrix.