Double-Cross-Correlation Processing for Blind Sampling-Rate and Time-Offset Estimation

Coherent processing of signals captured by a wireless acoustic sensor network (WASN) requires an estimation of unknown parameters such as the sampling-rate and sampling-time offset (SRO and STO) of asynchronous sensor clocks. Although some sophisticated techniques for blind parameter estimation have become available in this young field of research, further development of new methods is required especially regarding environmental robustness, online estimation, and computational efficiency. As the main contribution of this work, we therefore introduce a novel approach for blind SRO estimation in the spirit of both a recently available time-domain double-cross-correlation processor (DXCP) and the well-known generalized cross-correlation with phase transform (GCC-PhaT). For the proposed approach, called DXCP-PhaT, we specifically introduce secondary cross-quantities to restore ergodicity of the otherwise drifting cross-correlation function or cross-spectrum of asynchronous input signals, which is an important property for estimation. Based upon this theoretical contribution of the paper, we then derive the DXCP-PhaT algorithm in the STFT domain, which brings along a number of improvements over state-of-the-art: advanced accuracy in terms of SRO assessment, environmental robustness to larger microphone distances as of real sensor networks, realtime-applicability in terms of online architecture and reduced complexity, and eventually an extension with online STO estimation (up to the inherent ambiguity of digital STO and acoustic TDOA) reliant on SRO compensation. Those claims are confirmed by comprehensive experiments, both offline and online, on simulated data and real recordings from a Rasberry-Pi-based WASN.