  Fifth generation~(5G) networks providing much higher bandwidth and faster
data rates will allow connecting vast number of static and mobile devices,
sensors, agents, users, machines, and vehicles, supporting Internet-of-Things
(IoT), real-time dynamic networks of mobile things. Positioning and location
awareness will become increasingly important, enabling deployment of new
services and contributing to significantly improving the overall performance of
the 5G~system. Many of the currently talked about solutions to positioning
in~5G are centralized, mostly requiring direct line-of-sight (LoS) to deployed
access nodes or anchors at the same time, which in turn requires high-density
deployments of anchors. But these LoS and centralized positioning solutions may
become unwieldy as the number of users and devices continues to grow without
limit in sight. As an alternative to the centralized solutions, this paper
discusses distributed localization in a 5G enabled IoT environment where many
low power devices, users, or agents are to locate themselves without global or
LoS access to anchors. Even though positioning is essentially a non-linear
problem (solving circle equations by trilateration or triangulation), we
discuss a cooperative \textit{linear} distributed iterative solution with only
local measurements, communication and computation needed at each agent.
Linearity is obtained by reparametrization of the agent location through
barycentric coordinate representations based on local neighborhood geometry
that may be computed in terms of certain Cayley-Menger determinants involving
relative local inter-agent distance measurements.
