The ESPRIT Algorithm and Central Limit Error Scaling

The ESPRIT algorithm starts by rearranging the noisy measurements into a Hankel or Toeplitz matrix. In this paper, we consider the Toeplitz version


This content originally appeared on HackerNoon and was authored by Algorithmic Bias (dot tech)

Abstract and 1 Introduction

1.1 ESPRIT algorithm and central limit error scaling

1.2 Contribution

1.3 Related work

1.4 Technical overview and 1.5 Organization

2 Proof of the central limit error scaling

3 Proof of the optimal error scaling

4 Second-order eigenvector perturbation theory

5 Strong eigenvector comparison

5.1 Construction of the “good” P

5.2 Taylor expansion with respect to the error terms

5.3 Error cancellation in the Taylor expansion

5.4 Proof of Theorem 5.1

A Preliminaries

B Vandermonde matrice

C Deferred proofs for Section 2

D Deferred proofs for Section 4

E Deferred proofs for Section 5

F Lower bound for spectral estimation

References

1.1 ESPRIT algorithm and central limit error scaling

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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This content originally appeared on HackerNoon and was authored by Algorithmic Bias (dot tech)


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