Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a particle filter construction for a system that exhibits time-scale separation. The separation of time scales allows two simplifications that  exploit: 1) the use of the averaging principle for the dimensional reduction of the dynamics for each particle during the prediction step and 2) the factorization of the transition probability for the Rao-Blackllization of the update step. The resulting particle filter is faster and has smaller variance than the particle filter based on the original system. The method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions.
['Dror Givon', 'Panagiotis Stinis', 'Jonathan Weare']
I am writing a research paper on a idea Variance Reduction for Particle Filters of Systems With Time Scale Separation
[{"from": "human", "value": "I am writing a research paper on a idea Variance Reduction for Particle Filters of Systems With Time Scale Separation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present a particle filter construction for a system that exhibits time-scale separation. The separation of time scales allows two simplifications that  exploit: 1) the use of the averaging principle for the dimensional reduction of the dynamics for each particle during the prediction step and 2) the factorization of the transition probability for the Rao-Blackllization of the update step. The resulting particle filter is faster and has smaller variance than the particle filter based on the original system. The method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions."}]