Hankel and Toeplitz Rank-1 Decomposition of Arbitrary Matrices with Applications to Signal Direction-of-Arrival Estimation

2026-04-29 · Source: Machine Learning · Field: Technology & Digital — Robotics & Autonomous Systems, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new study introduces algorithms for optimal rank-1 Hankel and Toeplitz-structured approximations of arbitrary matrices, addressing problems in engineered systems like few-shot signal Direction-of-Arrival (DoA) estimation. These computationally efficient decomposition algorithms are developed for both L2 and L1-norm error formulations. The research derives analytically grounded small-sample-support DoA estimators, which are formally proven to be maximum-likelihood optimal under white Gaussian and Laplace noise for L2 and L1 norms, respectively. The estimators' efficacy is validated through extensive simulation studies and real-world data experiments, specifically in few-shot DoA inference scenarios.

Key takeaway

For Robotics Engineers developing autonomous systems requiring precise signal Direction-of-Arrival (DoA) estimation with limited data, consider integrating these new rank-1 Hankel and Toeplitz decomposition algorithms. Your choice between L2 and L1 norms should align with the expected noise characteristics of your environment (Gaussian for L2, Laplace for L1) to achieve maximum-likelihood optimal performance in few-shot inference scenarios.

Key insights

Optimal rank-1 Hankel/Toeplitz matrix decomposition improves few-shot signal DoA estimation.

Principles

• L2-norm is optimal for Gaussian noise.
• L1-norm is optimal for Laplace noise.

Method

Develops structured matrix decomposition algorithms for L2 and L1 norms, then derives small-sample-support DoA estimators.

In practice

• Apply to few-shot DoA estimation.
• Use in autonomous systems applications.

Topics

• Hankel Decomposition
• Toeplitz Decomposition
• Rank-1 Approximation
• Direction-of-Arrival Estimation
• L2-norm Error

Best for: AI Scientist, Robotics Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.