Achieving 3D Beamforming by Non-Synchronous Microphone Array Measurements
Abstract
:1. Introduction
2. Forward Model of Acoustic Imaging and Acoustic Measurement
2.1. Conventional Beamforming
2.2. Non-Synchronous Measurements Theory
- The 1st constraint: ensures that the rank of the reconstructed cross-spectral matrix is still equal to the number of the sources .
- The 2nd constraint: denotes the sampling operator that gets the elements in the diagonal block of a matrix, and the size is , which is identical to . ensures that the difference between and in the Frobenius norm is less than a given tolerance .
- The 3rd constraint: is a projection matrix. is the cross-spectral matrix of , where the projected matrix can be the smooth pressure [40] of the non-synchronous measured pressure . To ensure the acoustic field’s spatial continuity, is added here, and the difference in the cross-spectral matrix between and is required to be smaller than a given tolerance . The detailed discussion on this constraint is addressed in Section 2.2.
- The 4th constraint: ensures that both and are positive semi-definite matrixes.
2.3. Spatial Basis and Spatial Continuity of the Acoustic Field
3. Simulation Results
3.1. 3D Imaging by the Conventional Beamforming with a Planar Array
3.2. 3D Imaging by the Non-Synchronous Measurements with Orthogonal Moving Arrays
3.3. 3D Imaging by the Non-Synchronous Measurements with Non-Orthogonal Moving Arrays
4. Comparison between the Synchronous Measurements and Non-Synchronous Measurements
5. Experimental Verification
5.1. Experimental Setup
5.2. Experimental Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Yu, L.; Guo, Q.; Chu, N.; Wang, R. Achieving 3D Beamforming by Non-Synchronous Microphone Array Measurements. Sensors 2020, 20, 7308. https://doi.org/10.3390/s20247308
Yu L, Guo Q, Chu N, Wang R. Achieving 3D Beamforming by Non-Synchronous Microphone Array Measurements. Sensors. 2020; 20(24):7308. https://doi.org/10.3390/s20247308
Chicago/Turabian StyleYu, Liang, Qixin Guo, Ning Chu, and Rui Wang. 2020. "Achieving 3D Beamforming by Non-Synchronous Microphone Array Measurements" Sensors 20, no. 24: 7308. https://doi.org/10.3390/s20247308