Distributed Estimation for Multi-Subsystem With Coupled Constraints

The problem of distributed constraint-coupled estimation for multi-subsystem is addressed, in which there exist coupled linear equality constraints generated by cooperating neighbor subsystems (nodes). Our goal is to design a distributed estimator such that the state estimates obtained by each node can satisfy the all/global constraints based on the fact that each node only knows the local coupling constraints with its neighbors. To this end, the global constrained weighted least squares (GCWLS) optimization, as a centralized processing scheme, is presented firstly with its recursive implementation. Then, the distributed estimator of each node is constructed based on the structure of the above recursive centralized estimator and the basic idea of consensus iterative. Moreover, the sufficient conditions are established to guarantee that the iterative solution of the designed distributed estimator is able to converge to the centralized GCWLS estimates, which demonstrates that the local estimates obtained by the distributed estimator satisfy the all/global constraints. Finally, an example of collaborative navigation for formation airplanes is provided to demonstrate the effectiveness of the proposed estimator.