Fundamental Limits of Rigid Body Localization

We consider a novel approach to formulate the Cram\'er-Rao Lower Bound (CRLB) for the rigid body localization (RBL) problem, which allows us to assess the fundamental accuracy limits on the estimation of the translation and rotation of a rigid body with respect to a known reference. To that end, we adopt an information-centric construction of the Fisher information matrix (FIM), which allows to capture the contribution of each measurement towards the FIM, both in terms of input measurement types, as well as of their error distributions. Taking advantage of this approach, we derive a generic framework for the CRLB formulation, which is applicable to any type of rigid body localization scenario, extending the conventional FIM formulation suitable for point targets to the case of a rigid body whose location include both translation vector and the rotation matrix (or alternative the rotation angles), with respect to a reference. Closed-form expressions for all CRLBs are given, including the bound incorporating an orthonormality constraint onto the rotation matrix. Numerical results illustrate that the derived expression correctly lower-bounds the errors of estimated localization parameters obtained via various related state-of-the-art (SotA) estimators, revealing their accuracies and suggesting that SotA RBL algorithms can still be improved.

A Robust Routing Protocol for 5G Mesh Networks

We consider a novel routing protocol suitable for ad-hoc networks with dynamically changing topologies, such as DECT 2020 NR (NR+) systems, which often lead to missing links between the nodes and thus, incomplete or inefficient routes. A key point of the proposed protocol is the combination of network discovery and matrix completion techniques, which allow the nodes to establish communication paths efficiently and reliably. Additionally, multihop localization is performed to estimate the location of the nodes without needing to broadcast each node's geographical position, thus preserving privacy during the routing process and enabling nodes in the network to independently find potentially missing paths in a decentralized manner instead of flooding the whole network. Simulation results illustrate the good performance of the proposed technique in terms of the average number of hops of the obtained routes in different scenarios, with different network densities and amounts of incompleteness.