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.
Highlights
Particle filter (PF) is a Monte Carlo method which calculates the state estimation based on the samples generated from the prior or proposal distribution and obtains the full posterior distribution by combining model states and observations using Bayes’ theorem
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
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
Summary
Particle filter (PF) is a Monte Carlo method which calculates the state estimation based on the samples generated from the prior (model) or proposal distribution and obtains the full posterior distribution by combining model states and observations using Bayes’ theorem. We consider different weights of ensemble members instead of giving them the same equal weight We do this to obtain a better approximation of mean and variance of state variables especially when the dynamic system is highly nonlinear or noise distribution is non-Gaussian. PF is used to update the weights of particles and calculate the mean and variance of the posterior distribution of states. Unlike the Kalman filter, which is used for linear system model and calculates the error covariance analytically, EnKF approximates the covariance using a set of ensemble members. The aim of resampling is to make every particle to have the same weight, so why don’t we choose the particles from the posterior distribution instead of from the sample set?. Our aim is to regenerate particles according to the known mean and variance of state variables to avoid sample
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