Consensus for continuous belief functions

We study the belief consensus problem in networks of agents. Unlike previous work in the literature, where agents try to reach consensus on a scalar or vector, here we investigate how agents can reach a consensus on a continuous probability distribution. In our setting, the agents fuse functions instead of point estimates. The objective is that every agent ends up with the belief being the global Bayesian posterior. We show that to achieve the objective, the agents need to know the number of total agents in the network. In many scenarios, this number is not available and therefore the global Bayesian posterior is not achievable. In such cases, we have to resort to approximation methods. We confine ourselves to Gaussian cases and formulate the optimization problem for them. Then we propose two methods for the selection of weighting coefficients used for combining information from neighbors in the fusion process. We also provide results of simulation that demonstrate the performance of the methods.