# Range-based Coordinate Alignment for Cooperative Mobile Sensor Network Localization

## TL;DR

This paper introduces a novel range-based coordinate alignment method for cooperative mobile sensor network localization, transforming a non-convex problem into a convex one and proposing algorithms validated through simulations.

## Contribution

It presents a new convex reformulation of the coordinate alignment problem and develops iterative and recursive algorithms for localizing target nodes in sensor networks.

## Key findings

- Algorithms outperform existing methods in simulations
- Effective in localizing multiple target nodes
- Convex reformulation simplifies the non-convex optimization problem

## Abstract

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.