Algebraic method for multisensor data fusion.

Area of Science:

• Statistics
• Information Theory
• Lie Group Theory

Background:

• Distributed sensor systems generate local estimates characterized by Gaussian posterior probability densities.
• These densities are assumed to reside within the Riemannian manifold of Gaussian distributions.
• Accurate fusion of these local estimates is crucial for reliable data interpretation.

Purpose of the Study:

• To develop a robust algebraic fusion method for combining local estimates from distributed sensors.
• To introduce a Lie algebraic structure for Gaussian probability densities to measure dissimilarity.
• To provide a theoretically convergent algorithm for mean fusion and an analytical form for fused covariance.

Main Methods:

• Characterization of local estimates using Gaussian posterior probability densities.
• Introduction of a Lie algebraic structure for the Gaussian submanifold with a fixed mean.
• Development of a geodesic projection-based algebraic fusion method using the norm as a loss function.

Main Results:

• A robust fixed-point iterative algorithm for mean fusion with theoretical convergence guarantees.
• An analytical form for the fused covariance matrix.
• Demonstration of the fusion method's effectiveness through numerical examples.

Conclusions:

• The proposed algebraic fusion method effectively integrates distributed sensor data characterized by Gaussian densities.
• The Lie algebraic approach provides a principled way to measure dissimilarity and achieve robust fusion.
• The method offers both theoretical convergence and practical analytical solutions for fused covariance.