Efficient particle filtering for stochastic Korteweg-de Vries equations

We propose an efficient algorithm to perform nonlinear data assimilation for Korteweg-de Vries solitons. In particular we develop a reduced particle filtering method to reduce the dimension of the problem. The method decomposes a solitonic pulse into a clean soliton and small radiative noise, and instead of inferring the complete pulse profile, we only infer the two soliton parameters with particle filter. Numerical examples are provided to demonstrate that the proposed method can provide rather accurate results, while being much more computationally affordable than a standard particle filter.