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This study introduces an advanced methodology for estimating the source term of multiple, variable-number biochemical hazard releases, where the exact count of sources is not predetermined. Focusing on environments monitored via a network of sensors, we tackle this challenge through a multi-source Bayesian filtering paradigm, employing the theory of random finite sets (RFS). Our novel approach leverages a modified particle filter-based probability hypothesis density (PHD) filter within the RFS framework, enabling simultaneous estimation of critical source characteristics (such as location, emission rate, and effective release height) and the quantification of source numbers. This method not only accurately estimates pertinent source parameters but is also adept at identifying the emergence of new sources and the cessation of existing ones within the monitored area. The efficacy of our approach is validated through extensive simulations, which mimic a range of scenarios with varying and unknown source counts, highlighting the proposed method's robustness and precision. [ABSTRACT FROM AUTHOR]