🤖 AI Summary
This study addresses the challenge of accurately localizing uniformly moving broadband random noise sources, a task where conventional methods often fail due to their reliance on signal modification or short-time stationarity assumptions required for Doppler compensation. To overcome these limitations, this work proposes a novel frequency-domain localization approach that integrates Loève spectral theory with a 2.5D acoustic model. For the first time, Loève spectrum theory is applied to the localization of moving broadband sources, establishing a direct mapping between the power spectral density of a moving source and stationary receivers without requiring signal preprocessing or local stationarity assumptions. By incorporating multitaper spectral estimation, the method successfully localizes spectrally flat, stationary broadband sources in simulations involving source velocities up to 100 m/s, thereby surpassing the performance constraints of existing techniques.
📝 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.