An empirical method to fuse partially overlapping state vectors for distributed state estimation

State fusion is a method for merging multiple estimates of the same state into a single fused estimate. Dealing with multiple estimates is one of the main concerns in distributed state estimation, where an estimated value of the desired state vector is computed in each node of a networked system. Most solutions for distributed state estimation currently available assume that every node computes an estimate of the (same) global state vector. This assumption is impractical for systems observing large-area processes, due to the sheer size of the process state. A feasible solution is one where each node estimates a part of the global state vector, allowing different nodes in the network to have overlapping state elements. Although such an approach should be accompanied by a corresponding state fusion method, existing solutions cannot be employed as they merely consider fusion of two different estimates with equal state representations. Therefore, an empirical solution is presented for fusing two state estimates that have partially overlapping state elements. A justification of the proposed fusion method is presented, along with an illustrative case study for observing the temperature profile of a large rod, though a formal derivation is future research.