Multi-dimensional speaker localization (SL) aims to estimate the two- or three-dimensional locations of speakers. A recent advancement in multi-dimensional SL is the end-to-end deep neural networks (DNNs) with ad-hoc microphone arrays. This method transforms the SL problem into a classification problem, i.e. a problem of identifying the grids where speakers are located. However, the classification formulation has two closely connected weaknesses. Firstly, this approach introduces quantization error, which needs a large number of grids to mitigate the error. However, increasing the number of grids leads to the curse of dimensionality. To address the problems, we propose an efficient multi-dimensional SL algorithm, which has the following three novel contributions. First, we decouple the high-dimensional grid partitioning intoaxis partitioning, which substantially mitigates the curse-of-dimensionality. Particularly, for the multi-speaker localization problem, we employ a separator to circumvent the permutation ambiguity of the axis partitioning in the inference stage. Second, we introduce a comprehensiveunbiased label distributionscheme to further eliminate quantization errors. Finally, a set of data augmentation techniques are proposed, including coordinate transformation, stochastic node selection, and mixed training, to alleviate overfitting and sample imbalance problems. The proposed methods were evaluated on both simulated and real-world data, and the experimental results confirm the effectiveness.

Recently, an end-to-end two-dimensional sound source localization algorithm with ad-hoc microphone arrays formulates the sound source localization problem as a classification problem. The algorithm divides the target indoor space into a set of local areas, and predicts the local area where the speaker locates. However, the local areas are encoded by one-hot code, which may lose the connections between the local areas due to quantization errors. In this paper, we propose a new soft label coding method, named label smoothing, for the classification-based two-dimensional sound source location with ad-hoc microphone arrays. The core idea is to take the geometric connection between the classes into the label coding process. The first one is named static soft label coding (SSLC), which modifies the one-hot codes into soft codes based on the distances between the local areas. Because SSLC is handcrafted which may not be optimal, the second one, named dynamic soft label coding (DSLC), further rectifies SSLC, by learning the soft codes according to the statistics of the predictions produced by the classification-based localization model in the training stage. Experimental results show that the proposed methods can effectively improve the localization accuracy.