Localizing uniformly moving mono-frequent sources using an inverse 2.5D approach

Localizing linearly moving sound sources using microphone arrays is particularly challenging as the transient nature of the signal leads to relatively short observation periods. Commonly, a moving focus is used and most methods operate at least partially in the time domain. In contrast, here an inverse source localization algorithm for mono-frequent uniformly moving sources that acts entirely in the frequency domain is presented. For this, a 2.5D approach is utilized and a transfer function between sources and a microphone grid is derived. By solving a least squares problem using the data at the microphone grid, the unknown source distribution in the moving frame can be determined. For that the measured time signals need to be transformed into the frequency domain using a windowed discrete Fourier transform (DFT), which leads to effects such as spectral leakage that depends on the length of the time interval and the analysis window used. To include these effects in the numerical model, the calculation of the transfer matrix is modified using the Fourier transform of the analysis window. Currently, this approach is limited to mono-frequent sources as this allows a simplification of the calculation and reduces the computational effort. The least squares problem is solved using a Tikhonov regularization employing an L-curve approach to determine a suitable regularization parameter. As a moving source is considered, the Doppler effect allows to enhance the stability of the system by combining the transfer functions for multiple frequencies in the measured signals. The performance of the approach is validated using simulated data of a moving point source with or without a reflecting ground. Numerical experiments are performed to show the effect of the choice of frequencies in the receiver spectrum, the effect of the DFT, the frequency of the source, and the distance of source and receiver.