A novel particle filter for high-dimensional systems using penalized perturbations

In order to efficiently perform inference on high-dimensional nonlinear non-Gaussian state-space models using particle filtering, it is critical that particles are generated from the optimal proposal distribution. However, finding a closed-form to the optimal proposal proves to be difficult in practice, as many application problems do not satisfy the requirement of conjugate state and observation equations. In this paper, we overcome this challenge by designing a novel method that introduces conjugate artificial noise into the system and optimally perturbs the particles in a way that balances a bias-variance tradeoff. Our method is validated through extensive numerical simulations applied to a gene regulatory network problem, and results show better performance than that of state-of-the-art methods, especially in cases where the state noise is heavy-tailed.