# Nonasymptotic Performance Analysis of Direct-Augmentation and Spatial-Smoothing ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrays

arXiv: https://arxiv.org/abs/2302.11209 · HTML: https://mlsanity.com/paper/2302.11209/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Bit Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/2412.12678/) (2024)

## Abstract (arXiv)

Direction augmentation (DA) and spatial smoothing (SS), followed by a subspace method such as ESPRIT or MUSIC, are two simple and successful approaches that enable localization of more uncorrelated sources than sensors with a proper sparse array. In this paper, we carry out nonasymptotic performance analyses of DA-ESPRIT and SS-ESPRIT in the practical finite-snapshot regime. We show that their absolute localization errors are bounded from above by C1fracmaxσ2, C2√L with overwhelming probability, where L is the snapshot number, σ2 is the Gaussian noise power, and C1,C2 are constants independent of L and σ2, if and only if they can do exact source localization with infinitely many snapshots. We also show that their resolution increases with the snapshot number, without a substantial limit. Numerical results corroborating our analysis are provided.