Localizing broadband noise sources using the Loève spectrum and a 2.5D approach
2026-06-01 • Sound
Sound
AI summaryⓘ
The authors worked on improving how to locate moving sound sources using microphone arrays without having to fix the sound signal itself. They developed a new method that works in the frequency domain using longer data segments by directly modeling how the source's motion affects the sound for a still listener. Their previous method worked well for single tones, but here they explore how it applies to broad-band noisy sounds by analyzing statistical properties like power spectral density. They demonstrated a proof of concept using simulated data and a technique based on the Loève spectrum, though it currently only works for stationary signals with flat spectra and does not handle multiple correlated sources.
microphone arrayDoppler effectfrequency domainpower spectral densityLoève spectrumbroad-band stochastic sourcemulti-taper spectral estimationsignal localizationuniform motion2.5D acoustic modeling
Authors
Christian H. Kasess, Wolfgang Kreuzer, Holger Waubke
Abstract
The localization of moving sound sources using a microphone array is typically based on modifying the signal to compensate for the Doppler effect. In the time domain this compensation is done on a sample-by-sample basis. In the frequency domain short time segments need to be used in which the Doppler effect is assumed to be approximately constant and a discrete Fourier transform is done on each segment. In contrast, the authors developed an inverse 2.5D localization method for uniformly moving single-frequency sources that works in the spectral domain and allows for the use of longer windows. This was achieved by modifying the 2.5D forward model to directly compute the effect of the motion in the static observer position. The method does neither require to modify the measured signal nor does it require quasi-stationary of the measurements within the window used. Unfortunately, this approach is not directly suitable for broad-band stochastic sources, and in the present work we will investigate how the statistical properties of a uniformly moving stochastic source change when observed at a static observer. Using a 2.5D setting, the relation between the power spectral density of the moving source and the Loève spectrum, which is a generalization of the cross-spectral density at the static receivers, was derived. Based on simulated data with speeds up to 100 m\,s$^{-1}$, the work presented here provides a proof of concept for a method based on multi-taper estimates for the Loève spectrum to localize moving broad-band stochastic sources . Currently, the method requires a stationary source signal and that the spectral density is flat within a certain range around the frequency of interest. Also, correlations between sources are currently not considered.