This paper presents a decentralized solution to the cooperative localization of mobile robot teams. The problem is cast as inference on a dynamic Bayesian network (DBN) of Gaussian distribution, which is implemented incrementally by decomposing the DBN into a sequence of chain graphs connected by the interfaces. The proposed inference scheme can make use of the sparsity of the chain graphs and achieve efficient communication. In our decentralized formulation, the local sensor data at each robot are organized as potentials of the cliques of junction trees; message passing between robots updates the clique potentials to realize information sharing. Each robot can get optimal estimates of its own states. The method is optimal in the sense that it makes no approximations apart from the usual model liberalization. The performance of the proposed algorithm is evaluated with simulation experiments.

Novel lazy Lauritzen-Spiegelhalter (LS), lazy Hugin and lazy Shafer-Shenoy (SS) algorithms are devised for Gaussian Bayesian networks (BNs). In the lazy algorithms, the clique potentials and separator potentials are kept in combinable decomposed form instead of combined to be a single valuation in conventional junction tree algorithms. By employing decomposed form potentials, the independence relations between variables are explored online and the directed graph information is utilized in the message calculations. In the proposed algorithms, a consistent junction tree with the evidence entered can be obtained by a single round of message passing. The moments form parametrization of Gaussian distributions allows the deterministic relationships between variables. Preliminary analysis shows that the lazy LS algorithm and the lazy Hugin algorithm are more computationally efficient than the lazy SS algorithm, especially when there are multiple items of evidence to be incorporated.