Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter (original) (raw)

Ensemble Particle Filter with Posterior Gaussian Resampling

2005

An ensemble particle filter was recently developed as a fully nonlinear filter of Bayesian conditional probability estimation, along with the well known ensemble Kalman filter. A Gaussian resampling method is proposed here to generate the posterior analysis ensemble in an effective and efficient way. As a result the ensemble particle filter has good stability and potential applicability to large-scale problems. The Lorenz model is used here to test the proposed method. Multi-modal probability distributions can appear either with state dependent stochastic model errors or nonlinear observations. Ensemble Kalman filter (EnKF)is known to have a difficulty in tracking state transitions accurately. Current implementations of EnKF have not taken non-Gaussian contributions into account. With the posterior Gaussian resampling method the ensemble particle filter can track state transitions more accurately. Moreover, it is applicable to systems with typical multi-modal behavior, provided that certain prior knowledge becomes available about the general structure of posterior probability distribution. A simple scenario is considered to illustrate this point based on Lorenz model attractors. The present work demonstrates that the proposed ensemble particle filter can provide an accurate estimation of multi-modal distribution and is potentially applicable to large-scale data assimilation problems.

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters

2011

Abstract: This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture.

Gaussian-mixture based ensemble Kalman filter

2015

The Ensemble Kalman Filter (EnKF) is a Kalman based particle filter which was introduced to solve large scale data assimilation problems where the state space is of very large dimensionality. It also achieves good results when applied to a target tracking problem, however, due to its Gaussian assumption for the prior density, the performance can be improved by introducing Gaussian mixtures. In this paper, a new derivation of the EnKF is presented which is based on a duality between Gaussian products and particle densities. A relaxation of the Gaussian assumption is then achieved by introducing a particle clustering into Gaussian Mixtures by means of the Expectation Maximization (EM) algorithm and to apply the EnKF on the clusters. The soft assignment of the EM allows all Gaussian components to contribute to each of the particles. It is shown that the EM-EnKF performs better than a standard particle filter while having less computation time.

Ensemble Kalman filters, Sequential Importance Resampling and beyond

2000

Data assimilation in high-resolution atmosphere or ocean models is complicated because of the nonlinearity of the prob - lem. Several methods to solve the problem have been presented, all having their own advantages and disadvantages. In this paper so-called particle methods are discussed, wit h emphasis on Sequential Importance Resampling (SIR) and a new variant of that method. Reference is

Robust Adaptive Gaussian Mixture Sigma Point Particle Filter

2017

This paper presents a new robust adaptive Gaussian mixture sigma-point particle filter by adopting the concept of robust adaptive estimation to the Gaussian mixture sigma-point particle filter. This method approximates state mean and covariance via Sigma-point transformation combined with new available measurement information. It enables the estimations of state mean and covariance to be adjusted via the equivalent weight function and adaptive factor, thus restraining the disturbances of singular measurements and kinematic model noise. It can also obtain efficient predict prior and posterior density functions via Gaussian mixture approximation to improve the filtering accuracy for nonlinear and non-Gaussian systems. Simulation results and comparison analysis demonstrate the proposed method can effectively restrain the disturbances of abnormal measurements and kinematic model noise on state estimate, leading to improved estimation accuracy.

A Localized Adaptive Particle Filter within an Operational NWP Framework

Monthly Weather Review, 2019

Particle filters are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naïve application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimension of many practical assimilation problems (known as the curse of dimensionality). The goal of this work is to develop a localized adaptive particle filter (LAPF), which follows closely the idea of the classical MCMC or bootstrap-type particle filter, but overcomes the problems of collapse and divergence based on localization in the spirit of the local ensemble transform Kalman filter (LETKF) and adaptivity with an adaptive Gaussian resampling or rejuvenation scheme in ensemble space. The particle filter has been implemented in the data assimilation system for the global f...