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In this paper, distributing physical microphones on two concentric hemispherical surfaces surrounding the virtual microphone is proposed to improve the coherence in practical applications. It is demonstrated that such a double-layer physical microphone arrangement outperforms the single-layer arrangement with the same number of physical microphones due to the added sound pressure gradient information obtained with microphones in two different layers. The simulation results in a diffuse field, and the experiment results in a reverberation room are presented to show that the upper limit frequencies below which the coherence is more than 0.9 is larger than the single-layer arrangement with the proposed double-layer arrangement. The upper limit frequency can be further increased by decreasing the distance between the two spherical surfaces and aligning the physical microphones radially for a better estimation of the radial sound pressure gradient. The findings are further supported with the experiment results obtained in a real car running on a typical asphalt road at a constant speed of 50\u2009km\/h.<\/jats:p>","DOI":"10.1121\/10.0036354","type":"journal-article","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T23:00:17Z","timestamp":1743634817000},"page":"2392-2403","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Enhancing the coherence between virtual and physical signals in virtual sensing with a double-layer microphone arrangement"],"prefix":"10.1121","volume":"157","author":[{"given":"Hang","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University , 22 Hankou Road, Nanjing 210093,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuping","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University , 22 Hankou Road, Nanjing 210093,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiancheng","family":"Tao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University , 22 Hankou Road, Nanjing 210093,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5181-1220","authenticated-orcid":false,"given":"Xiaojun","family":"Qiu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University , 22 Hankou Road, Nanjing 210093,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"231","published-online":{"date-parts":[[2025,4,2]]},"reference":[{"key":"2025040208265106400_c1","first-page":"1027","article-title":"A virtual microphone arrangement for local active sound control","year":"1992"},{"issue":"5","key":"2025040208265106400_c2","doi-asserted-by":"publisher","first-page":"2858","DOI":"10.1121\/1.5037363","article-title":"Estimation of the pressure at a listener's ears in an active headrest system using the remote microphone technique","volume":"143","year":"2018","journal-title":"J. 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