Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Zhian Ruan, Yizhi Zhou

TL;DR

A diffusion-based distributed invariant Unscented Kalman Filter using the inverse covariance intersection (DIUKF-ICI) method to address target tracking in 3D environments and is fully distributed, robust against intermittent measurements, and adaptable to time-varying communication topologies.

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.

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

TL;DR

A diffusion-based distributed invariant Unscented Kalman Filter using the inverse covariance intersection (DIUKF-ICI) method to address target tracking in 3D environments and is fully distributed, robust against intermittent measurements, and adaptable to time-varying communication topologies.

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.
Paper Structure (12 sections, 4 theorems, 27 equations, 2 figures, 3 tables, 2 algorithms)

This paper contains 12 sections, 4 theorems, 27 equations, 2 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Matrix Lie Group
  4. Unscented Kalman Filter on Lie Group
  5. System Model and Problem Statement
  6. Distributed Invariant Unscented Kalman Filter Based on ICI
  7. Incremental update
  8. Diffusion update
  9. Performance Analysis
  10. Numerical Studies
  11. Conclusion
  12. acknowledgement

Key Result

Lemma 1

Given assumption ass_1, each $\log\left(\check {\mathbf X}_j^t(\check {\mathbf X}_i^t)^{-1}\right)$, $\text{for} \,j\in\mathcal{N}_i^t$, can be treated as an estimate of ${\bm\xi}_i^t$, and ${\bm\xi}_j^t$ is the corresponding estimate error with error covariance ${\check{\mathbf P}_j^t}$.

Figures (2)

  • Figure 1: Estimation results of DIUKF-ICI on different trajectories at 70% communication rate
  • Figure 2: PRMSE and ORMSE of trajectory 1 under different communications

Theorems & Definitions (8)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • Remark 2
  • Lemma 3
  • Theorem IV.1
  • proof