In-situ Microphone Channel Frequency Response Calibration Using Eigenvalue Decomposition

Acoustic sensor networks consisting of spatially distributed microphone array nodes offer great potential in various areas such as acoustic surveillance, digital agriculture, and smart cities. As for each node, available microphone array signal processing algorithms generally assume that the amplitude and phase frequency responses across channels are identical, which however does not necessarily hold in practice. State-of-the-art microphone channel frequency response calibration (MCFRC) methods translate the calibration task into the optimization of calibration filter coefficients and have shown notable performance. Unfortunately, these approaches either require microphone disassembly and reassembly operations, or pose constraints on array configuration and/or inter-microphone distance for an array node, which limits the wide application of those techniques to a great extent. To address this issue, an in-situ MCFRC method for array node with arbitrary configuration and inter-microphone distance is presented in this article. First, a single far-field sound source with known direction of arrival is employed to broadcast band-limited white noise as the calibration signal. Then, the auto-covariance matrix of channel outputs is analyzed using eigenvalue decomposition. We prove that there is an explicit relationship between the eigenvector corresponding to the largest eigenvalue and the steering vector distorted by amplitude and phase mismatches. Finally, the calibration filter can be directly designed. Detailed mathematical derivation is provided. Simulation results reveal that our approach presents a more general, convenient solution as well as better calibration performance as compared with existing MCFRC algorithms. Real-world experiments also verify its effectiveness.