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Geometric Data Fusion for Collaborative Attitude Estimation

Yixiao Ge, Behzad Zamani, Pieter van Goor, Jochen Trumpf, Robert Mahony

TL;DR

The work tackles collaborative attitude estimation for multi-agent systems on $SO(3)$ using a bottom-up approach where each agent runs a local EKF and fuses relative measurements from neighbors via Convex Combination Ellipsoid (CCE) fusion. It introduces geometric covariance handling on Lie groups through concentrated Gaussians, and provides a structured preprocessing, correction, and fusion pipeline to align distributions across agents. The main contributions are a complete geometry-aware data fusion workflow and its validation via Monte Carlo simulations under different relative-measurement models, demonstrating improved consistency and accuracy over baseline methods. This approach enables scalable, data-incest-resilient cooperative attitude estimation in distributed sensor networks with directional and relative-pose information.

Abstract

In this paper, we consider the collaborative attitude estimation problem for a multi-agent system. The agents are equipped with sensors that provide directional measurements and relative attitude measurements. We present a bottom-up approach where each agent runs an extended Kalman filter (EKF) locally using directional measurements and augments this with relative attitude measurements provided by neighbouring agents. The covariance estimates of the relative attitude measurements are geometrically corrected to compensate for relative attitude between the agent that makes the measurement and the agent that uses the measurement before being fused with the local estimate using the convex combination ellipsoid (CCE) method to avoid data incest. Simulations are undertaken to numerically evaluate the performance of the proposed algorithm.

Geometric Data Fusion for Collaborative Attitude Estimation

TL;DR

The work tackles collaborative attitude estimation for multi-agent systems on using a bottom-up approach where each agent runs a local EKF and fuses relative measurements from neighbors via Convex Combination Ellipsoid (CCE) fusion. It introduces geometric covariance handling on Lie groups through concentrated Gaussians, and provides a structured preprocessing, correction, and fusion pipeline to align distributions across agents. The main contributions are a complete geometry-aware data fusion workflow and its validation via Monte Carlo simulations under different relative-measurement models, demonstrating improved consistency and accuracy over baseline methods. This approach enables scalable, data-incest-resilient cooperative attitude estimation in distributed sensor networks with directional and relative-pose information.

Abstract

In this paper, we consider the collaborative attitude estimation problem for a multi-agent system. The agents are equipped with sensors that provide directional measurements and relative attitude measurements. We present a bottom-up approach where each agent runs an extended Kalman filter (EKF) locally using directional measurements and augments this with relative attitude measurements provided by neighbouring agents. The covariance estimates of the relative attitude measurements are geometrically corrected to compensate for relative attitude between the agent that makes the measurement and the agent that uses the measurement before being fused with the local estimate using the convex combination ellipsoid (CCE) method to avoid data incest. Simulations are undertaken to numerically evaluate the performance of the proposed algorithm.
Paper Structure (16 sections, 2 theorems, 43 equations, 4 figures)

This paper contains 16 sections, 2 theorems, 43 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Special orthogonal group $\mathbf{SO}(3)$
  4. Concentrated Gaussians on $\mathbf{SO}(3)$
  5. Problem Formulation
  6. Algorithm
  7. Predict and update
  8. Fusion using relative measurements:
  9. Geometric transformation of the measurement model:
  10. Preprocessing relative measurements:
  11. Geometric correction of distributions:
  12. Data Fusion
  13. Numerical experiment
  14. System implementation
  15. Result
  16. ...and 1 more sections

Key Result

Lemma 2.1

Given an arbitrary concentrated Gaussian distribution $p(X) = \mathbf{N}_{X_1}(\mu_1,\Sigma_1)$ on $\mathbf{SO}(3)$, then the zero-mean concentrated Gaussian distribution $q(X) = \mathbf{N}_{X_2}(0,\Sigma_2)$ with parameters minimises the Kullback-Leibler divergence $p(X)$ with respect to $q(X)$ up to second-order linearisation error.

Figures (4)

  • Figure 1: Illustration of the experimental setup to improve the estimate of agent $i$. The dotted lines represent each agent's measurements of known directions which are used to locally estimate their own states. The dashed line refers to the inter-agent measurement ${}^j y_i$ taken by agent $j$. The solid line represents the communication from agent $j$ to agent $i$.
  • Figure 2: Implementation structure of the estimators and the information flow on each agent.
  • Figure 3: Direct physical measurement of relative state \ref{['eq:measurement_1']}. Mean rotation error ($e:=\arccos((\mathop{\mathrm{tr}}\nolimits(R^{-1}\hat{R})-1)/2)$) with a shaded area representing the 25th and 75th percentiles.
  • Figure 4: Relative angle measurement \ref{['eq:measurementmodel_2']}.

Theorems & Definitions (3)

  • Lemma 2.1
  • proof
  • Corollary 2.2