# Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

arXiv: https://arxiv.org/abs/1712.04062 · HTML: https://mlsanity.com/paper/1712.04062/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2017.

## Built on by (most cited first, 4 of 4)

- [Distributed Bayesian Learning of Dynamic States](https://mlsanity.com/paper/2212.02565/) (2022)
- [Policy Evaluation in Decentralized POMDPs with Belief Sharing](https://mlsanity.com/paper/2302.04151/) (2023)
- [H-TD2: Hybrid Temporal Difference Learning for Adaptive Urban Taxi Dispatch](https://mlsanity.com/paper/2105.02138/) (2021)
- [Learning Multimodal Confidence for Intention Recognition in Human-Robot Interaction](https://mlsanity.com/paper/2405.14116/) (2024)

## Abstract (arXiv)

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.