An effective flowestimation method with particle filter based on Helmholtz decomposition theorem

This paper proposes a novel flow estimation method with a particle filter based on a Helmholtz decomposition theorem. The proposed method extends a model of the Helmholtz decomposition theorem and enables the decomposition of flows into rotational, divergent, and translational components. From the extended model, the proposed method defines a state transition model and an observation model of the particle filter. Furthermore, the proposed method derives an observation density of the particle filter from an energy function based on the Helmholtz decomposition theorem. By utilizing these novel approaches, the proposed method provides a solution to the problem in the traditional ones of not being able to realize an effective flow estimation with the particle filter based on rotation, divergence, and translation, which are important geometric features. Consequently, the proposed method can accurately estimate the flows.