A traditional method to measure particle velocity is based on the finite difference (FD) approximation of pressure gradient by using a pair of well matched pressure microphones. This approach is known to be sensitive to sensor noise and mismatch. Recently, a double hot-wire sensor termed Microflown became available in light of micro-electro-mechanical system technology. This sensor eliminates the robustness issue of the conventional FD-based methods. In this paper, an alternative two-microphone approach termed the u-sensor is developed from the perspective of robust adaptive filtering. With two ordinary microphones, the proposed u-sensor does not require novel fabrication technology. In the method, plane wave and spherical wave models are employed in the formulation of a Kalman filter with process and measurement noise taken into account. Both numerical and experimental investigations were undertaken to validate the proposed u-sensor technique. The results have shown that the proposed approach attained better performance than the FD method, and comparable performance to a Microflown sensor.

Conventional near-field acoustical holography (NAH) is generally based on the free-field assumption, which can cause errors when interfering sources are present in practical environments. To cope with this problem, previous research suggested a combined pressure-velocity approach for NAH that provides certain advantages to rejection of interferences. This paper revisits this idea in a broader context of optimal array design and examines the feasibility of using unidirectional microphones in each channel of the array such that the robustness of inverse reconstruction is enhanced against interfering sources. As indicated in the simulation, the numerical noise in finite difference estimation of particle velocity can nullify the advantage of the well-conditioned velocity-based reconstruction. In the proposed approach, the characteristics of each array channel consisting of two microphones are tailored by taking into account not only the directivity, but also the robustness against self-noise. An objective function based on directivity index and white noise gain is exploited in a linear quadratic optimization of a two-element end-fire array. The proposed optimal array is validated in conjunction with the equivalent source model (ESM) -based NAH through numerical simulations, with an interfering source positioned behind the array. The results have shown the directive optimal array has yielded improved quality of images in comparison with conventional approaches in the presence of an interfering source and sensor noise.