In this paper, we propose a box particle filtering algorithm for state estimation in nonlinear systems whose model assumes two types of uncertainties: stochastic noise in the measurements and bounded errors affecting the system dynamics. These assumptions respond to situations frequently encountered in practice. The proposed method includes a new way to weight the box particles as well as a new resampling procedure based on repartitioning the box enclosing the updated state. The proposed box particle filtering algorithm is applied in a fault detection schema illustrated by a sensor network target tracking example.