This paper presents the modeling, numerical simulations and experimental results of a differential microphone array and its associated post-processing methods. This study combines the development of an array geometry and the definition of a post-processing method adapted to applications within an aircraft. The research originality lies in the considered array and post-processing method, based on the approximation of the pressure gradient by a differential microphone calculation and linear combination of the signals. As the targeted frequency range of interest is from 200 Hz up to 5000 Hz, a fourth-order linear array is chosen, in order to handle at the same time the space constraints due to the aircraft environment and the inter-microphone spacing linked to the frequency range. The frequency band target is used to drive the antenna geometry definition. An experimental proof of concept is tested in an anechoic room. Simulations and experimental results are compared to an analytical model. The comparison highlights the method advantages as well as the experimental limitations of the designed linear array. Then, a first localization test is performed and finally, a modification of the post-processing method is suggested, to improve the directivity of the array low frequency.