An intrusive Gibbs sampling method for implementing the nonsynchronous measurements of microphone array.

Area of Science:

• Acoustics
• Signal Processing
• Computational Physics

Background:

• Nonsynchronous microphone array measurements offer a solution for achieving large arrays or high microphone density through sequential scanning.
• This technique overcomes the frequency limitations imposed by traditional array aperture and microphone density.

Purpose of the Study:

• To address the critical challenge of recovering missing phase information in nonsynchronous measurements.
• To investigate the problem as solving a system of equations within a Bayesian framework.

Main Methods:

• The intrusive Gibbs sampling method is proposed for source reconstruction.
• Convergence diagnostics for the Markov chain are illustrated using three distinct approaches.
• Acoustical source reconstruction error is analyzed concerning frequency range, signal-to-noise ratio, measurement distances, and sequential movement shift distance.

Main Results:

• The proposed Gibbs sampling method yields results comparable to the expectation maximization algorithm for nonsynchronous measurements.
• Numerical simulations demonstrate the convergence of the Markov chain.
• Experimental validation in a semi-anechoic chamber confirms the method's effectiveness.

Conclusions:

• The Bayesian approach with intrusive Gibbs sampling is an effective method for acoustical source reconstruction using nonsynchronous microphone array measurements.
• The study validates the proposed method's performance across various parameters and through experimental testing.