Topological Object Localization in a Visual Light Communications Application

In this thesis, we develop a technique for object localization in an
up-link optical wireless system for, most generally, indoor
applications. In contrast to other works (e.g. [1]), wherein the
authors exploit measures such as the line of sight peak power (LOS),
the second power peak of the channel’s impulse response, and the delay
between these aforementioned measures to localize an actively
transmitting object, we instead localize a passively sensed object via
a hitherto, to the best of our knowledge, novel methodology. We employ
a device from a relatively new research sub-field of computational
mathematics called topological data analysis (TDA). In particular, we
employ a methodological framework called persistent homology(PH),
which in short, is useful for identifying topological structure, by
identifying “holes” within a data-set at several scales of analysis.
In particular, we utilize the “holes” identified by PH to provide a
count of the number objects in an optical wireless system. In general,
PH can provide an overall assessment of the global structure and
connectivity of a data-set. PH is also useful because, in addition to
the simple aforementioned qualitative guide, it can be utilized, given
certain permitting conditions, to localize and potentially provide a
complete geometric description of objects in an indoor application
while obviating the need for potentially expensive explicit shape
models of various objects within a room. In summary, this thesis
introduces a methodology for object localization, enumeration and
description in an up-link wireless optical system for indoor
applications with the aid of PH. We demonstrate the viability of our
approach through several standard simulations and assess the
implications of their outcomes for determining the character of a path
for future work.