  Relative localization (RL) is essential for the successful operation of micro
air vehicle (MAV) swarms. Achieving accurate 3-D RL in infrastructure-free and
GPS-denied environments with only distance information is a challenging problem
that has not been satisfactorily solved. In this work, based on the range-based
peer-to-peer RL using the ultra-wideband (UWB) ranging technique, we develop a
novel UWB-based cooperative relative localization (CRL) solution that
integrates the relative motion dynamics of each host-neighbor pair to build a
unified dynamic model and takes the distances between the neighbors as
\textit{bonus information}. Observability analysis using differential geometry
shows that the proposed CRL scheme can expand the observable subspace compared
to other alternatives using only direct distances between the host agent and
its neighbors. In addition, we apply the kernel-induced extended Kalman filter
(EKF) to the CRL state estimation problem with the novel-designed
Logarithmic-Versoria (LV) kernel to tackle heavy-tailed UWB noise. Sufficient
conditions for the convergence of the fixed-point iteration involved in the
estimation algorithm are also derived. Comparative Monte Carlo simulations
demonstrate that the proposed CRL scheme combined with the LV-kernel EKF
significantly improves the estimation accuracy owing to its robustness against
both measurement outliers and incorrect measurement covariance matrix
initialization. Moreover, with the LV kernel, the estimation is still
satisfactory when performing the fixed-point iteration only once for reduced
computational complexity.
