scholarly journals Obstacles to High-Dimensional Particle Filtering

2008 ◽  
Vol 136 (12) ◽  
pp. 4629-4640 ◽  
Author(s):  
Chris Snyder ◽  
Thomas Bengtsson ◽  
Peter Bickel ◽  
Jeff Anderson
Keyword(s):  
Particle Filter ◽  
Particle Filtering ◽  
The State ◽  
Ensemble Size ◽  
Problem Size ◽  
Asymptotic Results ◽  
Gaussian Analysis ◽  
Non Gaussian ◽  
State Component ◽  
Size Scales

Abstract Particle filters are ensemble-based assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and non-Gaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ensemble size required for a successful particle filter scales exponentially with the problem size. For the simple example in which each component of the state vector is independent, Gaussian, and of unit variance and the observations are of each state component separately with independent, Gaussian errors, simulations indicate that the required ensemble size scales exponentially with the state dimension. In this example, the particle filter requires at least 1011 members when applied to a 200-dimensional state. Asymptotic results, following the work of Bengtsson, Bickel, and collaborators, are provided for two cases: one in which each prior state component is independent and identically distributed, and one in which both the prior pdf and the observation errors are Gaussian. The asymptotic theory reveals that, in both cases, the required ensemble size scales exponentially with the variance of the observation log likelihood rather than with the state dimension per se.

scholarly journals Review article: Comparison of local particle filters and new implementations

2018 ◽  
Vol 25 (4) ◽  
pp. 765-807 ◽  
Author(s):  
Alban Farchi ◽  
Marc Bocquet
Keyword(s):  
Data Assimilation ◽  
Particle Filter ◽  
Particle Filtering ◽  
Transport Theory ◽  
Optimal Transport ◽  
Curse Of Dimensionality ◽  
Local Analysis ◽  
Problem Size ◽  
Yield Data ◽  
Non Gaussian

Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential importance sampling, suited for nonlinear and non-Gaussian filtering problems. Unless the number of ensemble members scales exponentially with the problem size, particle filter (PF) algorithms experience weight degeneracy. This phenomenon is a manifestation of the curse of dimensionality that prevents the use of PF methods for high-dimensional data assimilation. The use of local analyses to counteract the curse of dimensionality was suggested early in the development of PF algorithms. However, implementing localisation in the PF is a challenge, because there is no simple and yet consistent way of gluing together locally updated particles across domains. In this article, we review the ideas related to localisation and the PF in the geosciences. We introduce a generic and theoretical classification of local particle filter (LPF) algorithms, with an emphasis on the advantages and drawbacks of each category. Alongside the classification, we suggest practical solutions to the difficulties of local particle filtering, which lead to new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz 40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms, even for a mildly nonlinear system.

scholarly journals Exploring Practical Estimates of the Ensemble Size Necessary for Particle Filters

2016 ◽  
Vol 144 (3) ◽  
pp. 861-875 ◽  
Author(s):  
Laura Slivinski ◽  
Chris Snyder
Keyword(s):  
Data Assimilation ◽  
Particle Filter ◽  
Particle Filtering ◽  
Particle Filters ◽  
A Priori ◽  
Asymptotic Relation ◽  
Dimensional System ◽  
Ensemble Size ◽  
Asymptotic Results ◽  
Low Dimensional

Abstract Particle filtering methods for data assimilation may suffer from the “curse of dimensionality,” where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of , a statistic that depends on observation-space quantities and that is related to the system dimension when the number of observations is large; for linear, Gaussian systems, the statistic can be computed from eigenvalues of an appropriately normalized covariance matrix. Tests with a low-dimensional system show that these asymptotic results remain useful when the system is nonlinear, with either the standard or optimal proposal implementation of the particle filter. This study explores approximations to the covariance matrices that facilitate computation in high-dimensional systems, as well as different methods to estimate the accumulated system noise covariance for the optimal proposal. Since may be approximated using an ensemble from a simpler data assimilation scheme, such as the ensemble Kalman filter, the asymptotic relations thus allow an estimate of the ensemble size required for a particle filter before its implementation. Finally, the improved performance of particle filters with the optimal proposal, relative to those using the standard proposal, in the same low-dimensional system is demonstrated.

scholarly journals Review article: Comparison of local particle filters and new implementations

2018 ◽  
Author(s):  
Alban Farchi ◽  
Marc Bocquet
Keyword(s):  
Data Assimilation ◽  
Particle Filter ◽  
Particle Filtering ◽  
Transport Theory ◽  
Optimal Transport ◽  
Curse Of Dimensionality ◽  
Local Analysis ◽  
Problem Size ◽  
Yield Data ◽  
Non Gaussian

Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential importance sampling, suited for nonlinear and non-Gaussian filtering problems. Unless the number of ensemble members scales exponentially with the problem size, particle filter (PF) algorithms lead to weight degeneracy. This phenomenon is a consequence of the curse of dimensionality that prevents one from using PF methods for high-dimensional data assimilation. The use of local analyses to counteract the curse of dimensionality was suggested early on. However, implementing localisation in the PF is a challenge because there is no simple and yet consistent way of gluing locally updated particles together across domains. In this article, we review the ideas related to localisation and the PF in the geosciences. We introduce a generic and theoretical classification of local particle filter (LPF) algorithms, with an emphasis on the advantages and drawbacks of each category. Alongside with the classification, we suggest practical solutions to the difficulties of local particle filtering, that lead to new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz 40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms.

Quasi-Monte Carlo Gaussian Particle Filtering Acceleration Using CUDA

2011 ◽  
Vol 130-134 ◽  
pp. 3311-3315
Author(s):  
Nai Gao Jin ◽  
Fei Mo Li ◽  
Zhao Xing Li
Keyword(s):  
Monte Carlo ◽  
Particle Filter ◽  
Particle Filtering ◽  
Parallel Implementation ◽  
Accurate Estimation ◽  
Quasi Monte Carlo ◽  
Speedup Ratio ◽  
Non Gaussian ◽  
Gpu Implementation ◽  
Number Of Particles

A CUDA accelerated Quasi-Monte Carlo Gaussian particle filter (QMC-GPF) is proposed to deal with real-time non-linear non-Gaussian problems. GPF is especially suitable for parallel implementation as a result of the elimination of resampling step. QMC-GPF is an efficient counterpart of GPF using QMC sampling method instead of MC. Since particles generated by QMC method provides the best-possible distribution in the sampling space, QMC-GPF can make more accurate estimation with the same number of particles compared with traditional particle filter. Experimental results show that our GPU implementation of QMC-GPF can achieve the maximum speedup ratio of 95 on NVIDIA GeForce GTX 460.

scholarly journals IMM Iterated Extended Particle Filter Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Wan ◽  
Shouyong Wang ◽  
Xing Qin
Keyword(s):  
Particle Filter ◽  
Density Function ◽  
The State ◽  
Arbitrary Distribution ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Maneuvering Target ◽  
Particle Filter Algorithm ◽  
Non Gaussian ◽  
Importance Density Function

In order to solve the tracking problem of radar maneuvering target in nonlinear system model and non-Gaussian noise background, this paper puts forward one interacting multiple model (IMM) iterated extended particle filter algorithm (IMM-IEHPF). The algorithm makes use of multiple modes to model the target motion form to track any maneuvering target and each mode uses iterated extended particle filter (IEHPF) to deal with the state estimation problem of nonlinear non-Gaussian system. IEHPF is an improved particle filter algorithm, which utilizes iterated extended filter (IEHF) to obtain the mean value and covariance of each particle and describes importance density function as a combination of Gaussian distribution. Then according to the function, draw particles to approximate the state posteriori density of each mode. Due to the high filter accuracy of IEHF and the adaptation of system noise with arbitrary distribution as well as strong robustness, the importance density function generated by this method is more approximate to the true sate posteriori density. Finally, a numerical example is included to illustrate the effectiveness of the proposed methods.

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.

Improved Particle Filter for Integrated Navigation System

2014 ◽  
Vol 543-547 ◽  
pp. 1278-1281 ◽  
Author(s):  
Zhun Jiao ◽  
Rong Zhang
Keyword(s):  
Monte Carlo ◽  
Particle Filter ◽  
Navigation System ◽  
Particle Filtering ◽  
Bayesian Filtering ◽  
Integrated Navigation ◽  
Proposal Distribution ◽  
Gaussian Distributions ◽  
Integrated Navigation System ◽  
Non Gaussian

As a new method for dealing with any nonlinear or non-Gaussian distributions, based on the Monte Carlo methods and Bayesian filtering, particle filters (PF) are favored by researchers and widely applied in many fields. Based on particle filtering, an improved particle filter (IPF) proposal distribution is presented. Evaluation of the weights is simplified and other improved techniques including the residual resampling step and Markov Chain Monte Carlo method are introduced for SINS/GPS integrated navigation system. The simulation results confirm that the improved particle filter outperforms the others.

scholarly journals State estimation and prediction using clustered particle filters

2016 ◽  
Vol 113 (51) ◽  
pp. 14609-14614 ◽  
Author(s):  
Yoonsang Lee ◽  
Andrew J. Majda
Keyword(s):  
Particle Filter ◽  
Particle Filtering ◽  
Particle Filters ◽  
Forecast Model ◽  
Coarse Grained ◽  
State Variables ◽  
High Quality ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
True Signal

Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors.

scholarly journals Simplified partial resampling method for state estimation usingparticle filter

2018 ◽  
Vol 7 (2.7) ◽  
pp. 243
Author(s):  
M Tirumala Reddy ◽  
Y Sri Ganesh ◽  
Ch Lakshmi Gayathri ◽  
T Megha Shyam ◽  
S Koteswar Rao ◽  
...  
Keyword(s):  
Particle Filter ◽  
State Estimation ◽  
Gaussian Noise ◽  
The State ◽  
Resampling Methods ◽  
Simple Pendulum ◽  
Filter Methods ◽  
Resampling Method ◽  
Paper Work ◽  
Non Gaussian

Particle filter methods are used in the estimation and tracking of the objects for non-linear and non-gaussian noise conditions. In this paper work the object estimation using partial resampling methods are discussed. On using partial resampling method resampling becomes faster. The performance of particle filter with partial resampling scheme is analyzed using the state estima-tion of a simple pendulum.

scholarly journals COMPARISON OF GPS SMOOTHENING METHODS BETWEEN EXTENDED KALMAN FILTER AND PARTICLE FILTER FOR UAV

2017 ◽  
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Particle Filtering ◽  
State Vector ◽  
The State ◽  
Gps Data ◽  
Extended Kalman Filtering

This paper presents a method for smoothing GPS data from a UAV using Extended Kalman filtering and particle filtering for navigation or position control. A key requirement for navigation and control of any autonomous flying or moving robot is availability of a robust attitude estimate. Consider a dynamic system such as a moving robot. The unknown parameters, e.g., the coordinates and the velocity, form the state vector. This time dependent vector may be predicted for any instant time by means of system equations. The predicted values can be improved or updated by observations containing information on some components of the state vector. The whole procedure is known as Kalman filtering. On the other hand, the particle filtering algorithm is to perform a recursive Bayesian filter by Monte Carlo simulations. The key is to represent the required posterior density function by a set of random samples, which is called particles with associated weights, and to compute estimates based on these samples as well as weights. We compare the two GPS smoothening methods: Extended Kalman Filter and Particle Filter for mobile robots applications. Validity of the smoothing methods is verified from the numerical simulation and the experiments. The numerical simulation and experimental results show the good GPS data smoothing performance using Extended Kalman filtering and particle filtering.

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