  Meteoroid modelling of fireball data typically uses a one dimensional model
along a straight line triangulated trajectory. The assumption of a straight
line trajectory has been considered an acceptable simplification for fireballs,
but it has not been rigorously tested. The unique capability of the Desert
Fireball Network (DFN) to triangulate discrete observation times gives the
opportunity to investigate the deviation of a meteoroid's position to different
model fits.
  Here we assess the viability of a straight line assumption for fireball data
in two meteorite-dropping test cases observed by the Desert Fireball Network
(DFN) in Australia -- one over 21 seconds (\textit{DN151212\_03}), one under 5
seconds (\textit{DN160410\_03}). We show that a straight line is not valid for
these two meteorite dropping events and propose a three dimensional particle
filter to model meteoroid positions without any straight line constraints. The
single body equations in three dimensions, along with the luminosity equation,
are applied to the particle filter methodology described by \citet{Sansom2017}.
  Modelling fireball camera network data in three dimensions has not previously
been attempted.
  This allows the raw astrometric, line-of-sight observations to be
incorporated directly.
  In analysing these two DFN events, the triangulated positions based on a
straight line assumption result in the modelled meteoroid positions diverging
up to $3.09\, km$ from the calculated observed point (for
\textit{DN151212\_03}). Even for the more typical fireball event,
\textit{DN160410\_03}, we see a divergence of up to $360$\,m.
  As DFN observations are typically precise to $<100$\,m, it is apparent that
the assumption of a straight line is an oversimplification that will affect
orbit calculations and meteorite search regions for a significant fraction of
events.
