This article rigorously details the ESPRIT algorithm, focusing on its central limit error scaling and optimal error scaling in spectral estimation contexts. Through systematic proofs, it lays out claims and demonstrates properties of matrices used within the algorithm. The work also introduces second-order eigenvector perturbation theory and Taylor expansions to refine error terms further. Finally, it reports on the construction of particular invertible matrices and unveils essential properties that enhance the algorithm's robustness while providing comprehensive references for further exploration.
The article provides a detailed exploration of the ESPRIT algorithm, showcasing its effectiveness in spectral estimation along with rigorous proofs of error scaling and perturbation theory.
Key contributions include the proof of central limit error scaling and optimal error scaling, providing foundational techniques for enhancing the robustness of spectral analysis.
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