Robust Trajectory Fitting for Joint Time-Delay and Sampling-Rate-Offset Estimation in Asynchronous Acoustic Sensor Networks

Wireless acoustic sensor networks assembled from commodity devices suffer from sampling rate offsets (SROs) of tens to hundreds of parts per million between nodes, which degrade all multichannel processing. Frame-wise generalized cross-correlation (GCC) peaks between two asynchronous nodes drift along a straight line whose intercept is the time difference of arrival (TDOA) and whose slope is the SRO. We analyze this trajectory observation model: we derive a closed-form accuracy prediction for the joint TDOA–SRO estimate, prove that the analysis window length has no first-order effect on SRO accuracy in the coherent regime, and quantify the decoherence penalty that bounds the usable window length as L ≲ c·fs/(ϵ·f²). We then propose a simple robust (Theil–Sen/Huber) trajectory fitter that resists reverberation-induced outlier peaks. Simulations with image-source reverberation and experiments with real speech (CMU Arctic) confirm the analysis (accuracy within 0.68–1.09 of the prediction) and show large gains over least-squares trajectory fitting and correlation-maximization SRO search under reverberation.