scholarly journals A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248266
Author(s):  
Ian Grooms ◽  
Gregor Robinson
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Ensemble Kalman Filter ◽  
Orthogonal Transformation ◽  
Hybrid Filter ◽  
Hybrid Particle ◽  
Particle Ensemble ◽  
Non Gaussian ◽  
Two Stages ◽  
Lorenz 96

A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-‘96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-‘96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.

scholarly journals Ensemble Variational Assimilation as a Probabilistic Estimator. Part II: The fully non-linear case

2018 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Objective Function ◽  
Ensemble Kalman Filter ◽  
The Other ◽  
Linear Case ◽  
Absolute Minimum ◽  
Strong Constraint ◽  
Variational Assimilation ◽  
Lorenz 96

Abstract. In Part II, the method of Ensemble Variational Assimilation (EnsVAR) is implemented in fully nonlinear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires to be used in association with the method of Quasi-Static Variational Assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of Ensemble Kalman Filter and Particle Filter. On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are signif- icantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need to resort to QSVA.

scholarly journals A Hybrid Particle–Ensemble Kalman Filter for Lagrangian Data Assimilation

2015 ◽  
Vol 143 (1) ◽  
pp. 195-211 ◽  
Author(s):  
Laura Slivinski ◽  
Elaine Spiller ◽  
Amit Apte ◽  
Björn Sandstede
Keyword(s):  
Kalman Filter ◽  
Velocity Field ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
High Dimensional ◽  
Salinity Field ◽  
Hybrid Particle ◽  
Highly Nonlinear ◽  
Particle Ensemble ◽  
Low Dimensional

Abstract Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean’s state (velocity field, salinity field, etc.). However, trajectories from these instruments are often highly nonlinear, leading to difficulties with widely used data assimilation algorithms such as the ensemble Kalman filter (EnKF). Additionally, the velocity field is often modeled as a high-dimensional variable, which precludes the use of more accurate methods such as the particle filter (PF). Here, a hybrid particle–ensemble Kalman filter is developed that applies the EnKF update to the potentially high-dimensional velocity variables, and the PF update to the relatively low-dimensional, highly nonlinear drifter position variable. This algorithm is tested with twin experiments on the linear shallow water equations. In experiments with infrequent observations, the hybrid filter consistently outperformed the EnKF, both by better capturing the Bayesian posterior and by better tracking the truth.

scholarly journals A Moment Matching Ensemble Filter for Nonlinear Non-Gaussian Data Assimilation

2011 ◽  
Vol 139 (12) ◽  
pp. 3964-3973 ◽  
Author(s):  
Jing Lei ◽  
Peter Bickel
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Ensemble Forecasting ◽  
Moment Matching ◽  
State Variables ◽  
Mean And Variance ◽  
Large Systems ◽  
Non Gaussian ◽  
Lorenz 96 ◽  
Gaussian Data

Abstract The ensemble Kalman filter is now an important component of ensemble forecasting. While using the linear relationship between the observation and state variables makes it applicable for large systems, relying on linearity introduces nonnegligible bias since the true distribution will never be Gaussian. This paper analyzes the bias of the ensemble Kalman filter from a statistical perspective and proposes a debiasing method called the nonlinear ensemble adjustment filter. This new filter transforms the forecast ensemble in a statistically principled manner so that the updated ensemble has the desired mean and variance. It is also easily localizable and, hence, potentially useful for large systems. Its performance is demonstrated and compared with other Kalman filter and particle filter variants through various experiments on the Lorenz-63 and Lorenz-96 systems. The results show that the new filter is stable and accurate for challenging situations such as nonlinear, high-dimensional systems with sparse observations.

Dynamic Target Tracking Based on Particle Filter in Actual Environment

2013 ◽  
Vol 683 ◽  
pp. 824-827
Author(s):  
Tian Ding Chen ◽  
Chao Lu ◽  
Jian Hu
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Target Tracking ◽  
Monitoring System ◽  
Filter Method ◽  
Complex Scene ◽  
Actual Environment ◽  
Dynamic Target ◽  
Gaussian System ◽  
Non Gaussian

With the development of science and technology, target tracking was applied to many aspects of people's life, such as missile navigation, tanks localization, the plot monitoring system, robot field operation. Particle filter method dealing with the nonlinear and non-Gaussian system was widely used due to the complexity of the actual environment. This paper uses the resampling technology to reduce the particle degradation appeared in our test. Meanwhile, it compared particle filter with Kalman filter to observe their accuracy .The experiment results show that particle filter is more suitable for complex scene, so particle filter is more practical and feasible on target tracking.

scholarly journals Convective-Scale Data Assimilation for the Weather Research and Forecasting Model Using the Local Particle Filter

2017 ◽  
Vol 145 (5) ◽  
pp. 1897-1918 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Ryan A. Sobash ◽  
Jeffrey L. Anderson
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Squall Line ◽  
Monte Carlo Data ◽  
Mixing Ratios ◽  
Convective Scale ◽  
Non Gaussian ◽  
Mean Square Errors

Abstract Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

scholarly journals A Zero-Velocity Update Method for Adaptive Particle Filtering

2020 ◽  
Vol 38 (2) ◽  
pp. 427-433
Author(s):  
Yuyang Guo ◽  
Xiangbo Xu ◽  
Miaoxin Ji
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Particle Filtering ◽  
State Space Model ◽  
Classical Particle ◽  
Measurement Unit ◽  
Correction Algorithm ◽  
Zero Velocity ◽  
Non Gaussian ◽  
Navigation Errors

Aiming at the low precision of Kalman filter in dealing with non-linear and non-Gaussian models and the serious particle degradation in standard particle filter, a zero-velocity correction algorithm of adaptive particle filter is proposed in this paper. In order to improve the efficiency of resampling, the adaptive threshold is combined with particle filter. In the process of resampling, the degradation co-efficient is introduced to judge the degree of particle degradation, and the particles are re-sampled to ensure the diversity of particles. In order to verify the effectiveness and feasibility of the proposed algorithm, a hardware platform based on the inertial measurement unit (IMU) is built, and the state space model of the system is established by using the data collected by IMU, and experiments are carried out. The experimental results show that, compared with Kalman filter and classical particle filter, the positioning accuracy of adaptive particle filter in zero-velocity range is improved by 40.6% and 19.4% respectively. The adaptive particle filter (APF) can correct navigation errors better and improve pedestrian trajectory accuracy.

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