Intelligent transportation systems have enormous potential for improving the quality of our lives. They rely on traffic monitoring and control infrastructures to enable an efficient management of mobility. A crucial task is the estimation or prediction of traffic flows by large-scale sensor networks, which is a topic that has been attracting increasing attention in recent years because of its relevance in traffic control over urban areas or freeways. In this paper, we propose an innovative stochastic method for vehicular traffic estimation based on a distributed reconstruction of the density field through the cooperation of smaller monitoring subnetworks. The method guarantees high accuracy (because of information sharing) and, at the same time, moderate computational cost (due to distributed processing). Moreover, subnetworks do not need to exchange sensitive information (e.g., raw data) but simply traffic beliefs. We evaluate the performance of the method on simulated single-lane road scenarios, highlighting the potential benefits of the cooperative approach. As an example of application, we consider a fragmented monitoring scenario characterized by several sensor failures and we show how the proposed approach can overcome the problem related to the sensor malfunctions leveraging on information shared with neighboring subnetworks.