  The gravitational interaction of antimatter and matter has never been
directly probed. ALPHA-g is a novel experiment that aims to perform the first
measurement of the antihydrogen gravitational mass. A fundamental requirement
for this new apparatus is a position sensitive particle detector around the
antihydrogen trap which provides information about antihydrogen annihilation
location. The proposed detector is a radial Time Projection Chamber, or
\textit{rTPC}, whose concept is being developed at TRIUMF. A simulation of the
detector and the development of the reconstruction software, used to determine
the antihydrogen annihilation point, is presented alongside with the expected
performance of the rTPC.
