The statistical observation localized equivalent-weights particle filter in a simple nonlinear model

This paper presents an improved approach based on the equivalent-weights particle filter(EWPF)that uses the proposal density to effectively improve the traditional particle filter.The proposed approach uses historical data to calculate statistical observations instead of the future observations used in the EWPF’s proposal density and draws on the localization scheme used in the localized PF(LPF)to construct the localized EWPF.The new approach is called the statistical observation localized EWPF(LEWPF-Sobs);it uses statistical observations that are better adapted to the requirements of real-time assimilation and the localization function is used to calculate weights to reduce the effect of missing observations on the weights.This approach not only retains the advantages of the EWPF,but also improves the assimilation quality when using sparse observations.Numerical experiments performed with the Lorenz 96 model show that the statistical observation EWPF is better than the EWPF and EAKF when the model uses standard distribution observations.Comparisons of the statistical observation localized EWPF and LPF reveal the advantages of the new method,with fewer particles giving better results.In particular,the new improved filter performs better than the traditional algorithms when the observation network contains densely spaced measurements associated with model state nonlinearities.