Distributed Density Filtering for Large-Scale Systems Using Mean-Filed Models

TL;DR

This paper introduces a decentralized density filtering method for large-scale systems, enabling agents to estimate global density using local observations and minimal communication, based on mean-field models and consensus algorithms.

Contribution

It extends previous centralized density filters to a distributed setting, allowing scalable, real-time density estimation with limited information exchange.

Findings

Distributed filter converges to centralized filter

Requires minimal communication between agents

Maintains stability and near-optimal performance

Abstract

This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information, such as sensor deployment and city traffic scheduling. This work is built upon our previous work [1] which presented a (centralized) density filter to estimate the dynamic density of large-scale systems through a novel integration of mean-field models, kernel density estimation (KDE), and infinite-dimensional Kalman filters. In this work, we further study how to decentralize the density filter such that each agent can estimate the global density only based on its local observation and communication with neighbors. This is achieved by noting that the global observation constructed by KDE is an average of the local kernels. Hence, dynamic average consensus algorithms are used for each agent to track the global observation in a distributed way. We present a distributed density filter which requires very little information exchange, and study its stability and optimality using the notion of input-to-state stability. Simulation results suggest that the distributed filter is able to converge to the centralized filter and remain close to it.