Cooperative Magneto-Inductive Localization

Wireless localization is a key requirement for many applications. It concerns position estimation of mobile nodes (agents) relative to fixed nodes (anchors) from wireless channel measurements. Cooperative localization is an advanced concept that considers the joint estimation of multiple agent positions based on channel measurements of all agent-anchor links together with all agent-agent links. In this paper we present the first study of cooperative localization for magneto-inductive wireless sensor networks, which are of technological interest due to good material penetration and channel predictability. We demonstrate significant accuracy improvements (a factor of 3 for 10 cooperating agents) over the non-cooperative scheme. The evaluation uses the Cramér-Rao lower bound on the cooperative position estimation error, which is derived herein. To realize this accuracy, the maximum-likelihood estimate (MLE) must be computed by solving a high-dimensional least-squares problem, whereby convergence to local minima proves to be problematic. A proposed cooperative localization algorithm addresses this issue: first, preliminary estimates of the agent positions and orientations are computed, which then serve as initial values for a gradient search. In all our test cases, this method yields the MLE and the associated high accuracy (comprising the cooperation gain) from a single solver run. The preliminary estimates use novel closed-form MLE formulas of the distance, direction and orientation for single links between three-axis coils, which are given in detail.