PARTICLE FILTERS IN A MULTISCALE ENVIRONMENT: WITH APPLICATION TO THE LORENZ-96 ATMOSPHERIC MODEL

The study of random dynamical systems involves understanding the evolution of state variables that contain uncertainties and that are usually hidden, or not directly observable. Therefore, state variables have to be estimated and updated based on system models using information from observational data, which themselves are noisy, in the sense that they contain uncertainties and disturbances due to imperfections in observational devices and disturbances in the environment within which data are being collected. The development of efficient data assimilation methods for integrating observational data in predicting the evolution of random state variables is thus an important aspect in the study of random dynamical systems. In this paper, we consider a particle filtering approach to nonlinear filtering in multiscale dynamical systems. Particle filtering methods [1–3] utilizes ensembles of particles to represent the conditional density of state variables using particle positions, distributed over a sample space. The distribution of an ensemble of particles is updated using observational data to obtain the best representation of the conditional density of the state variables of interest. On the other hand, homogenization theory [4, 5], allows us to estimate the coarse-grained (slow) dynamics of a multiscale system on a larger timescale without having to explicitly study the fast variable evolution on a small timescale. The results of filter convergence presented in [6] shows the convergence of the filter of the actual state variable to a homogenized solution to the original multiscale system, and thus we develop a particle filtering scheme for multiscale random dynamical systems that utilizes this convergence result. This particle filtering method is called the Homogenized Hybird Particle Filter, and it incorporates a multiscale computation scheme, the Heterogeneous Multiscale Method developed in [7], with the novel branching particle filter described in [8–10]. By incorporating a multiscale scheme based on homogenization of the original system, estimation of the coarse-grained dynamics using observational data is performed over a larger timescale, thus resulting in computational time and cost reduction in terms of the evolution of the state variables as well as functional evaluations for the filtering aspect. We describe the theory behind this combined scheme and its general algorithm, concluded with an application to the Lorenz-96 [11] atmospheric model that mimics midlatitude geophysical dynamics with microscopic convective processes.

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State estimation and prediction using clustered particle filters

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1617398113 ◽

2016 ◽

Vol 113 (51) ◽

pp. 14609-14614 ◽

Cited By ~ 14

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.

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Human motion classification using a particle filter approach: multiple model particle filtering applied to the micro-Doppler spectrum

International Journal of Microwave and Wireless Technologies ◽

10.1017/s1759078713000366 ◽

2013 ◽

Vol 5 (3) ◽

pp. 391-399 ◽

Cited By ~ 7

Author(s):

Stephan Groot ◽

Ronny Harmanny ◽

Hans Driessen ◽

Alexander Yarovoy

Keyword(s):

Particle Filter ◽

Particle Filtering ◽

Human Motion ◽

The Body ◽

Doppler Spectrum ◽

Multiple Model ◽

State Variables ◽

Measurement Models ◽

Human Movements ◽

Filter Approach

In this article, a novel motion model-based particle filter implementation is proposed to classify human motion and to estimate key state variables, such as motion type, i.e. running or walking, and the subject's height. Micro-Doppler spectrum is used as the observable information. The system and measurement models of human movements are built using three parameters (relative torso velocity, height of the body, and gait phase). The algorithm developed has been verified on simulated and experimental data.

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Applying sequential Monte Carlo methods into a distributed hydrologic model: lagged particle filtering approach with regularization

Hydrology and Earth System Sciences ◽

10.5194/hess-15-3237-2011 ◽

2011 ◽

Vol 15 (10) ◽

pp. 3237-3251 ◽

Cited By ~ 42

Author(s):

S. J. Noh ◽

Y. Tachikawa ◽

M. Shiiba ◽

S. Kim

Keyword(s):

Monte Carlo ◽

Data Assimilation ◽

Particle Filter ◽

Particle Filtering ◽

Sequential Monte Carlo ◽

Hydrologic Model ◽

State Variables ◽

Process Noise ◽

Distributed Hydrologic Model ◽

Filtering Approach

Abstract. Data assimilation techniques have received growing attention due to their capability to improve prediction. Among various data assimilation techniques, sequential Monte Carlo (SMC) methods, known as "particle filters", are a Bayesian learning process that has the capability to handle non-linear and non-Gaussian state-space models. In this paper, we propose an improved particle filtering approach to consider different response times of internal state variables in a hydrologic model. The proposed method adopts a lagged filtering approach to aggregate model response until the uncertainty of each hydrologic process is propagated. The regularization with an additional move step based on the Markov chain Monte Carlo (MCMC) methods is also implemented to preserve sample diversity under the lagged filtering approach. A distributed hydrologic model, water and energy transfer processes (WEP), is implemented for the sequential data assimilation through the updating of state variables. The lagged regularized particle filter (LRPF) and the sequential importance resampling (SIR) particle filter are implemented for hindcasting of streamflow at the Katsura catchment, Japan. Control state variables for filtering are soil moisture content and overland flow. Streamflow measurements are used for data assimilation. LRPF shows consistent forecasts regardless of the process noise assumption, while SIR has different values of optimal process noise and shows sensitive variation of confidential intervals, depending on the process noise. Improvement of LRPF forecasts compared to SIR is particularly found for rapidly varied high flows due to preservation of sample diversity from the kernel, even if particle impoverishment takes place.

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Particle Filters in a Multiscale Environment: Homogenized Hybrid Particle Filter

Journal of Applied Mechanics ◽

10.1115/1.4003167 ◽

2011 ◽

Vol 78 (6) ◽

Cited By ~ 12

Author(s):

Jun H. Park ◽

N. Sri Namachchivaya ◽

Hoong Chieh Yeong

Keyword(s):

Dynamical Systems ◽

Particle Filter ◽

Dimensional Reduction ◽

Nonlinear Filtering ◽

Particle Filters ◽

Random Dynamical Systems ◽

High Dimensional ◽

Recursive Procedure ◽

Hybrid Particle ◽

True State

State estimation of random dynamical systems with noisy observations has been an important problem in many areas of science and engineering. Efficient new algorithms to estimate the present and future state of a dynamic signal based upon corrupted, distorted, and possibly partial observations of the signal are required. Since the true state is usually hidden and evolves according to its own dynamics, the objective of this work is to get an optimal estimation of the true state via noisy observations. The theory of filtering provides a recursive procedure for estimating an evolving signal or state from a noisy observation process. We consider a particle filter approach for nonlinear filtering in multiscale dynamical systems. Particle filters represent the posterior conditional distribution of the state variables by a system of particles, which evolves and adapts recursively as new information becomes available. Particle filters suffer from computational inefficiency when applied to high dimensional problems. In practice, large numbers of particles may be required to provide adequate approximations in higher dimensional poblems. In several high dimensional applications, after a sequence of updates, the particle system will often collapse to a single point. With the help of rigorous dimensional reduction methods, particle filters could regain their versatility. Based on our theoretical developments (Park, J. H., Sri Namachchivaya, N., and Sowers, R. B., 2008, “A Problem in Stochastic Averaging of Nonlinear Filters,” Stochastics Dyn., 8(3), pp. 543–560; Park, J. H., Sowers, R. B., and Sri Namachchivaya, N., 2010, “Dimensional Reduction in Nonlinear Filtering,” Nonlinearity, 23(2), pp. 305–324), we devise an efficient particle filter algorithm, which is applicable to high dimensional multiscale nonlinear filtering problems. In this paper, we present the homogenized hybrid particle filtering method that combines homogenization of random dynamical systems, reduced order nonlinear filtering, and particle methods.

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Coarse-grained entropy in dynamical systems

Regular and Chaotic Dynamics ◽

10.1134/s1560354710510106 ◽

2010 ◽

Author(s):

G. Piftankin ◽

D. Treschev

Keyword(s):

Dynamical Systems ◽

Coarse Grained

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VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

Stochastics and Dynamics ◽

10.1142/s0219493709002634 ◽

2009 ◽

Vol 09 (02) ◽

pp. 205-215 ◽

Cited By ~ 2

Author(s):

XIANFENG MA ◽

ERCAI CHEN

Keyword(s):

Dynamical Systems ◽

Variational Principle ◽

Multifractal Analysis ◽

Weak Condition ◽

Random Dynamical Systems ◽

Topological Pressure ◽

Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

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Imitation of Demonstrations Using Bayesian Filtering With Nonparametric Data-Driven Models

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4037782 ◽

2017 ◽

Vol 140 (3) ◽

Cited By ~ 1

Author(s):

Nurali Virani ◽

Devesh K. Jha ◽

Zhenyuan Yuan ◽

Ishana Shekhawat ◽

Asok Ray

Keyword(s):

Particle Filtering ◽

Dynamic Models ◽

Training Data ◽

Data Driven ◽

Conditional Density ◽

Bayesian Filtering ◽

State Dependent ◽

State Evolution ◽

And Control ◽

Nonparametric Kernel

This paper addresses the problem of learning dynamic models of hybrid systems from demonstrations and then the problem of imitation of those demonstrations by using Bayesian filtering. A linear programming-based approach is used to develop nonparametric kernel-based conditional density estimation technique to infer accurate and concise dynamic models of system evolution from data. The training data for these models have been acquired from demonstrations by teleoperation. The trained data-driven models for mode-dependent state evolution and state-dependent mode evolution are then used online for imitation of demonstrated tasks via particle filtering. The results of simulation and experimental validation with a hexapod robot are reported to establish generalization of the proposed learning and control algorithms.

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