This paper develops a Bayesian estimation method to estimate source parameters of a biochemical source using a network of sensors. Based on existing models of continuous and instantaneous releases, a model of discrete and periodic releases is proposed, which has extra parameters such as the time interval between two successive releases. Different from existing source term estimation methods, based on the sensor characteristic of chemical sensors, the zero readings of sensors are exploited in our algorithm where the zero readings may be caused by the concentration being below the threshold of the sensors. Two types of Bayesian inference algorithms for key parameters of the sources are developed and their particle filtering implementation is discussed. The efficiency of the proposed algorithms for periodic release is demonstrated and verified by simulation where the algorithm with the exploitation of the zero readings significantly outperforms that without.