Range-based Coordinate Alignment for Cooperative Mobile Sensor Network Localization

This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements. The network consists of target nodes, each of which has only access position information in a local fixed coordinate frame, and anchor nodes with GPS position information. To localize target nodes, we aim to align their coordinate frames, which leads to a non-convex optimization problem over a rotation group $\text{SO}(3)$. Then, we reformulate it as an optimization problem with a convex objective function over spherical surfaces. We explicitly design both iterative and recursive algorithms for localizing a target node with an anchor node, and extend to the case with multiple target nodes. Finally, the advantages of our algorithms against the literature are validated via simulations.