Use of robust Capon beamformer for extracting audio signals

The need to extract a single audio signal of interest from a multi-source and noisy environment is common across many disciplines. Use of sensor arrays with adaptive beamforming is a preferred approach for obtaining high quality audio signals in many applications. One of such applications is applying the microphone array technology to extract signals of interest for the purpose of condition monitoring in an industrial site. In that work, we employed a so called Robust Capon Beamformer (RCB) to perform the signal extraction. The adaptive algorithm in RCB was originally developed to deal with the uncertainty existing in the signal model. This uncertainty is also known as signal mismatch. There is an important parameter called the error allowance in the algorithm to regulate the robustness of the beamformer. For an application of signal direction of arrival or localization, which RCB was originally proposed for, the appropriate value of the error allowance is purely defined by anticipated errors in steering vectors. For an application of audio signal extraction, however, the appropriate value of the error allowance has been found to be related also to other factors in the system, such as signal to noise ratio, signal direction of arrival, and the distance between the source and the array. In this paper, we examine the influence of those factors to the appropriate value of the error allowance in the context of machinery condition monitoring through numerical simulation, and provide an empirical formula for choosing the appropriate value of the error allowance in that context.