Distributed Invariant Unscented Kalman Filter based on Inverse Covariance Intersection with Intermittent Measurements

TL;DR

This paper introduces a novel distributed invariant Unscented Kalman Filter on Lie groups that effectively fuses local estimates with intermittent measurements, extending existing methods to more complex state spaces.

Contribution

It extends the distributed UKF framework to matrix Lie groups and incorporates inverse covariance intersection for the first time in this context.

Findings

Estimation error is proven to be bounded.

The method is robust to intermittent measurements.

Validated through extensive Monte-Carlo simulations.

Abstract

This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose a diffusion-based distributed invariant Unscented Kalman Filter using the inverse covariance intersection (DIUKF-ICI) method to address target tracking in 3D environments. Unlike existing distributed UKFs confined to vector spaces, our approach extends the distributed UKF framework to Lie groups, enabling local estimates to be fused with intermediate information from neighboring agents on Lie groups. To handle the unknown correlations across local estimates, we extend the ICI fusion strategy to matrix Lie groups for the first time and integrate it into the diffusion algorithm. We demonstrate that the estimation error of the proposed method is bounded. Additionally, the algorithm is fully distributed, robust against intermittent measurements, and adaptable to time-varying communication topologies. The effectiveness of the proposed method is validated through extensive Monte-Carlo simulations.