  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.
