## Abstract

This paper considers the problem of three-dimensional (3-D, azimuth, elevation, and range) localization of a single source in the near-field using a single acoustic vector sensor (AVS). The existing multiple signal classification (MUSIC) or maximum likelihood estimation (MLE) methods, which require a 3-D search over the location parameter space, are computationally very expensive. A computationally simple method previously developed by Wu and Wong (IEEE Trans. Aerosp. Electron. Syst. 48(1):159–169, 2012), which we refer to as Eigen-value decomposition and Received Signal strength Indicator-based method (Eigen-RSSI), was able to estimate 3-D location parameters of a single source efficiently. However, it can only be applied to an extended AVS which consists of a pressure sensor separated from the velocity sensors by a certain distance. In this paper, we propose a uni-AVS MUSIC (U-MUSIC) approach for 3-D location parameter estimation based on a compact AVS structure. We decouple the 3-D localization problem into step-by-step estimation of azimuth, elevation, and range and derive closed-form solutions for these parameter estimates by which a complex 3-D search for the parameters can be avoided. We show that the proposed approach outperforms the existing Eigen-RSSI method when the sensor system is required to be mounted in a confined space.

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## Notes

This approximation discards the term \(1/\sqrt{1 + 1/(kr_{s})^{2}}\).

The Eigen-RSSI method also allows incorporation of path loss models other than the inverse square law.

The SNR at which the performance of localization estimates shows a drastic reduction or “breakdown.”

Note that in Figs. 1(a) and (b), the CRB increases with a decrease in SNR; however this trend is hard to observe in the figure as the value of CRB is much lower than the RMSE of the DOA estimation methods.

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Hari, V.N., Premkumar, A.B. & Zhong, X. A Decoupled Approach for Near-Field Source Localization Using a Single Acoustic Vector Sensor.
*Circuits Syst Signal Process* **32**, 843–859 (2013). https://doi.org/10.1007/s00034-012-9508-9

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DOI: https://doi.org/10.1007/s00034-012-9508-9

### Keywords

- Acoustic vector sensor
- Localization
- Near-field
- MUSIC
- DOA estimation