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 s (DN151212_03), one under 5 seconds (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 Sansom et al. (2017). 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 DN151212_03). Even for the more typical fireball event, 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.