Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

TL;DR

This paper introduces a distributed Bayesian filtering algorithm for dynamic sensor networks that uses the logarithmic opinion pool and consensus methods, ensuring convergence and robustness in target tracking.

Contribution

It presents a novel distributed Bayesian filtering approach with proven convergence, stability, and robustness, applicable to heterogeneous sensor networks and cast into a Kalman information filter form.

Findings

Agents' likelihood estimates converge exponentially to the joint likelihood

Explicit bounds on time step size for convergence are provided

Numerical simulations validate the algorithm's performance and robustness

Abstract

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.