## 1 Introduction  
Speech enhancement is generally performed as a front-end signal processing procedure in a speech processing pipeline, whose primary objective is to improve the intelligibility and quality of target speech under noisy, reverberant conditions. A common example of an indoor acoustic environment is the so-called \"cocktail party\" scenario [1], where multiple speech sources are speaking at the same time. Unlike conventional approaches [1; 2; 3; 4; 5; 6; 7], contemporary research has treated speech enhancement as a supervised learning problem from the context of deep learning (DL) [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Among these works [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26] are those that outline DL-based speech enhancement methodologies, where convolutional and recurrent neural architectures have been utilized to combine spectral and spatial features for target speech enhancement, while the works outlined in [27; 28; 29; 30] utilize graph neural architectures to perform speech enhancement. Among the DL-based speech enhancement approaches, mask-based beamformers [8; 13] and neural spectro-spatial filtering [14; 15] are two prominent approaches which provide excellent performance even under high reverberation and low acoustic signal-to-noise ratio (SNR). While the mask-based beamforming approach outlined in [8] provides a DL-based time-varying (TV) beamformer to enhance the target speech, the neural spectro-spatial filtering approach presented in [14] performs complex spectral mapping (CSM), which involves the mapping of real and imaginary components of an input mixture spectrogram to those of a target speech spectrogram by a DL architecture. Despite their advantages, both these methods suffer from a common drawback due to their apparent failure to consider the random nature of the cardinality of the speech sources in motion, something which is attributed to the disappearance of existing sources as well as the appearance of new sources inside the acoustic environment. A failure to account for sources' appearances and disappearances directly impacts the performance of speech enhancement. The multi-sensor generalized labelled multi-Bernoulli (MS-GLMB) [6; 31; 32] filtering algorithm within the labelled random finite sets (RFS) framework offers a flexible mechanism by which to address the problem of the unknown and time-varying cardinality of the speech sources in a Bayesian setting and helps to resolve the space-time permutation ambiguity by jointly estimating the sources' positions and labels. The space-time permutation problem, also referred to as the data association problem, addresses the uncertainty about which measurement is associated to which source in space, as well as the uncertainty about associations between different measurements and sources across different time frames [6]. A solution to space-time permutation ambiguity leads to better source tracking and hence to improved target speech enhancement in the presence of reverberation, noise and motion of the sources. In this work, MS-GLMB filtering is applied within the dynamic speech enhancement framework during training time, in order to assist the deep neural architecture to learn, within each time frame, the mapping from a reverberant mixture of speech signals belonging to mobile sources located at different spatial positions to the desired mask specific to the target source. This approach differs from the approach in [26], as, during test time, the proposed neural architecture presented in this work directly predicts the desired source-specific mask from the input magnitude spectrogram, without the need for additional MS-GLMB filtering. The contemporary research works on MS-GLMB filtering-assisted speech enhancement do not focus on the use of multi-source tracking based on MS-GLMB filtering to create datasets for training DL architectures for target speech enhancement under reverberant conditions [6; 26; 31].