Sample Regenerating Particle Filter Combined With Unequal Weight Ensemble Kalman Filter for Nonlinear Systems

Abstract

We present an approach which combines the sample regenerating particle filter (SRGPF) and unequal weight ensemble Kalman filter (UwEnKF) to obtain a more accurate forecast for nonlinear dynamic systems. Ensemble Kalman filter assumes that the model errors and observation errors are Gaussian distributed. Particle filter has demonstrated its ability in solving nonlinear and non-Gaussian problems. The main difficulty for the particle filter is the curse of dimensionality, a very large number of particles is needed. We adopt the idea of the unequal weight ensemble Kalman filter to define a proposal density for the particle filter. In order to keep the diversity of particles, we do not apply resampling as the traditional particle filter does, instead we regenerate new samples based on a posterior distribution. The performance of the combined sample regenerating particle filter and unequal weight ensemble Kalman filter algorithm is evaluated using the Lorenz 63 model, the results show that the presented approach obtains a more accurate forecast than the ensemble Kalman filter and weighted ensemble Kalman filter under Gaussian noise with dense observations. It still performs well in case of sparse observations though more particles are required. Furthermore, for non-Gaussian noise, with an adequate number of particles, the performance of the approach is much better than the ensemble Kalman filter and more robust to noise with nonzero bias.

Keywords

• Particle filter
• Monte Carlo method
• nonlinear dynamic systems
• Lorenz function