This paper presents a novel method for solving nonlinear filtering problems. This approach is particularly appealing in practical situations involving imprecise stochastic measurements, thus resulting in very broad posterior densities. It relies on the concept of a box particle, which occupies a small and controllable rectangular region having a non-zero volume in the state space. Key advantages of the box particle filter (Box-PF) against the standard particle filter (PF) are in its reduced computational complexity and its suitability for distributed filtering. Indeed, in some applications where the sequential importance resampling (SIR) PF may require thousands of particles to achieve an accurate and reliable performance, the Box-PF can reach the same level of accuracy with just a few dozens of box particles.