Estimation of TDOA for room reflections by iterative weighted l<inf>1</inf> constraint

dEchorate: a Calibrated Room Impulse Response Database for Echo-aware Signal Processing

“…(iii) By solving a simple Multi-Dimensional Scaling (MDS) problem [38][39][40], refined microphone and source positions are computed from echo timings. The non-convexity of the problem is alleviated by using a good initialization (obtained at the previous step), by the high SNR of the measurements and, later, by including additional image sources in the formulation.…”

Are Multiple Cross-Correlation Identities better than just Two? Improving the Estimate of Time Differences-of-Arrivals from Blind Audio Signals

“…Sound source localisation applications can be tackled by inferring the time-difference-of-arrivals (TDOAs) between a sound-emitting source and a set of microphones. Among the referred applications, one can surely list room-aware sound reproduction [1], room geometry's estimation [2]- [6], speech enhancement [7], [21] and de-reverberation [8]- [10]. Despite a broad spectrum of prior works estimate TDOAs from an known audio source [22]- [24], even when the signal emitted from the acoustic source is unknown, TDOAs can be inferred by comparing the signals received at two (or more) spatially separated microphones [10], [11], [14], [17], [18] using the notion of cross-corrlation identity (CCI) -see Fig.…”

“…1. This is the key theoretical tool, not only, to make the ordering of microphones irrelevant during the acquisition stage, but also to solve the problem as blind channel identification [10], [11], [14], [17], [18], robustly and reliably inferring TDOAs from an unknown audio source (see Sec. II).…”

“…Furthermore, each observed signal may contain multiple distorted or delayed replicas of the emitting source due to reflections or generic boundary effects related to the (closed) environment. Thus, robustly estimating TDOAs is surely a challenging problem and CCI-based approaches cast it as single-input/multioutput blind channel identification [10], [11], [14], [17], [18]. Such methods promotes robustness in the estimate from the methodological standpoint: using either energy-based regularization [11], sparsity [10], [17], [18] or positivity constraints [17], while also pre-conditioning the solution space [10].…”

“…In this paper, we posit that there is a much easier practical strategy to ensure robustness while inferring TDOAs: the possibility of exploiting a larger pool of microphones. In fact, it is surprising to observe that, in prior state-of-the-art methods based on CCI, experimental evidences are provided for the case N = 2 microphones only [10], [11], [14], [17], [18]. Despite such a number is the bare minimum to solve the problem, it remains elusive whether N > 2 can, by itself, boost the estimate of TDOAs in accuracy/robustness, without requiring any changes in the computational pipeline.…”