Nowadays, the prevalence of sensor networks has enabled tracking of the states of dynamic objects for a wide spectrum of applications from autonomous driving to environmental monitoring and urban planning. However, tracking realworld objects often faces two key challenges: First, due to the limitation of individual sensors, state estimation needs to be solved in a collaborative and distributed manner. Second, the objects' movement behavior model is unknown, and needs to be learned using sensor observations. In this work, for the first time, we formally formulate the problem of simultaneous state estimation and behavior learning in a sensor network. We then propose a simple yet effective solution to this new problem by extending the Gaussian process-based Bayes filters (GPBayesFilters) to an online, distributed setting. The effectiveness of the proposed method is evaluated on tracking objects with unknown movement behaviors using both synthetic data and data collected from a multi-robot platform.