Sequential Importance Resampling Filter Research Articles

Comparison of Bayesian estimation methods for modeling flow transients in gas pipelines

The aim of this work was to investigate the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and sequential importance resampling (SIR) filter for real-time estimation of a hyperbolic partial differential equation (PDE) system describing the gas flow transients in pipelines. The numerical method of lines was used for solving the system of PDEs. The spatial discretization was based on a five-point, fourth-order finite difference approximation and the time integrations were done using the fourth-order Runge-Kutta scheme (RK4). The resulting nonlinear state-space model was used by the Bayesian filtering algorithms for estimation of the system states. Numerical experiments were conducted to compare the accuracy, robustness and computation time. The results indicated that the difference in terms of accuracy between the EKF and UKF was small and considering the computation time of the UKF and numerically robustness of calculating the Jacobian matrix, the use of EKF might be a better choice when fast solutions are required. The UKF outperformed the EKF and SIR filter when steep variations in the mass flow rate boundary conditions occurred together with low model uncertainty.

Estimation of Production Rates by Use of Transient Well-Flow Modeling and the Auxiliary Particle Filter: Full-Scale Applications

Summary In the current work, we demonstrate the use of a detailed transient multiphase well-flow model and the auxiliary sequential-importance resampling filter, for better representation of flow rates in petroleum wellbores (influx and/or outflux). The fundamentals of the methodology have been presented by the authors in a previous work, and the purpose of this paper is full-scale case studies. Performance, robustness, and flexibility are demonstrated with data sets from two different wells. The first case is an application to an inclined gas producer with two inflow reservoir zones. Observations consist of pressure and temperature at two locations in the well. Next, we present an application to an inclined water injector with nine outflow zones. Observations consist of data from a distributed temperature sensor (DTS) and one pressure observation at the end of the DTS rod. Estimate of zonal flow rates, including error bounds, lead to better well control and reservoir management, which again are important for improved recovery of oil from existing petroleum fields. The results presented in this paper clearly demonstrate the feasibility of automatic identification of reservoir flow-rate distribution from wellbore measurements.

Modified sequential importance resampling filter

In order to deal with the particle degeneracy and impoverishment problems existed in particle filters, a modified sequential importance resampling (MSIR) filter is proposed. In this filter, the resampling is translated into an evolutional process just like the biological evolution. A particle generator is constructed, which introduces the current measurement information (CMI) into the resampled particles. In the evolution, new particles are first produced through the particle generator, each of which is essentially an unbiased estimation of the current true state. Then, new and old particles are recombined for the sake of raising the diversity among the particles. Finally, those particles who have low quality are eliminated. Through the evolution, all the particles retained are regarded as the optimal ones, and these particles are utilized to update the current state. By using the proposed resampling approach, not only the CMI is incorporated into each resampled particle, but also the particle degeneracy and the loss of diversity among the particles are mitigated, resulting in the improved estimation accuracy. Simulation results show the superiorities of the proposed filter over the standard sequential importance resampling (SIR) filter, auxiliary particle filter and unscented Kalman particle filter.

Maximum likelihood parameter estimation for a high-dimensional system by particle-based filters

Particle-based filters are applied to estimate poorly-known parameters in an oceanic thermohaline circulation model. The model is a stochastic partial differential equation that conceptually represents the Atlantic meridional overturning circulation. It exhibits rapid transitions between strong (temperature-dominated) and weak (salinity-dominated) circulations, and its stability depends on a stochastic term in the equation.Accurate estimation of the variance of the random term is critical in characterizing the circulation system, and the Maximum Likelihood Estimation is utilized via particle-based filters to estimate the parameter. The performance of different types of particle-based filters such as the Sequential Importance Resampling filter, Ensemble Kalman filter, and Maximum entropy filter are compared by the results of parameter estimation of the intermediate ocean model. The results show that all the three filters correctly estimate the stochastic parameter and, more importantly, suggest that particle-based filters are a promising tool for parameter estimation for high-dimensional systems.

State-space estimation with a Bayesian filter in a coupled PDE system for transient gas flows

The accuracy of the first-principle models describing the evolution of gas dynamics in pipelines is sometimes limited by the lack of understanding of the gas transport phenomena. In this paper, a stochastic filtering approach is proposed based on a sequential Monte Carlo method to provide real-time estimates of the state in gas pipelines. After constructing a state-space model of the compressible single-phase flow based on the laws of conservation of mass and momentum, the optimal sequential importance resampling filter (SIR) is implemented. The state variables are updated with simulated measurements. The two-step Lax–Wendroff method is used for the discretization of the partial differential equations describing the gas model in both space and time to obtain finite-dimensional discrete-time state-space representations. The system states are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of the particle filter that provides real-time estimations of the system states. Simulation results for a coupled PDE system describing an unsteady isothermal gas flow demonstrate the effectiveness of the proposed method. A sensitivity analysis is conducted to examine the performance of the filter for different model and observation error covariances and observation intervals.

On simultaneous on-line state and parameter estimation in non-linear state-space models

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex multi-dimensional integrals that are not amenable to analytical solution. While basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for simultaneous estimation exist, it is well recognized that there is a need for making these on-line algorithms non-degenerate, fast and applicable to processes with missing measurements. To overcome the deficiencies in traditional algorithms, this work proposes a Bayesian approach to on-line state and parameter estimation. Its extension to handle missing data in real-time is also provided. The simultaneous estimation is performed by filtering an extended vector of states and parameters using an adaptive sequential-importance-resampling (SIR) filter with a kernel density estimation method. The approach uses an on-line optimization algorithm based on Kullback–Leibler (KL) divergence to allow adaptation of the SIR filter for combined state-parameter estimation. An optimal tuning rule to control the width of the kernel and the variance of the artificial noise added to the parameters is also proposed. The approach is illustrated through numerical examples.

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

Abstract This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

The impact of localization and observation averaging for convective‐scale data assimilation in a simple stochastic model

AbstractA simple stochastic model, based on a Poisson birth–death process, is proposed as a test bed for convective‐scale data assimilation methods. The simple model mimics the extreme nonlinearity and non‐Gaussianity associated with rapidly developing and intermittent convective storms. In this framework, we evaluate the Ensemble Transform Kalman Filter (ETKF) and Sequential Importance Resampling (SIR) filter, and assess the impact of two strategies to improve their performance and efficiency: localization and observation averaging. In their basic implementations, both filters perform poorly. The SIR filter rapidly collapses, then very gradually converges to the observations as random perturbations introduced by resampling occasionally improve the analysis. The ETKF rapidly assimilates the correct locations of convective storms, but has large errors due to creation of spurious clouds by nonlinear amplification of small data assimilation increments. Localization, i.e. assimilating only local observations to produce the analysis at a given grid point, dramatically improves the performance of the SIR filter, but does not reduce errors in the ETKF. Observation averaging, i.e. spatially smoothing the observations before assimilation and thus making the distribution more Gaussian, is also effective for the SIR filter, and improves convergence of the ETKF. Copyright © 2012 Royal Meteorological Society

Assimilating remote sensing observations of leaf area index and soil moisture for wheat yield estimates: An observing system simulation experiment

Observing system simulation experiments were used to investigate ensemble Bayesian state‐updating data assimilation of observations of leaf area index (LAI) and soil moisture (θ) for the purpose of improving single‐season wheat yield estimates with the Decision Support System for Agrotechnology Transfer (DSSAT) CropSim‐Ceres model. Assimilation was conducted in an energy‐limited environment and a water‐limited environment. Modeling uncertainty was prescribed to weather inputs, soil parameters and initial conditions, and cultivar parameters and through perturbations to model state transition equations. The ensemble Kalman filter and the sequential importance resampling filter were tested for the ability to attenuate effects of these types of uncertainty on yield estimates. LAI andθobservations were synthesized according to characteristics of existing remote sensing data, and effects of observation error were tested. Results indicate that the potential for assimilation to improve end‐of‐season yield estimates is low. Limitations are due to a lack of root zone soil moisture information, error in LAI observations, and a lack of correlation between leaf and grain growth.

Proposed hardware architectures of particle filter for object tracking

In this article, efficient hardware architectures for particle filter (PF) are presented. We propose three different architectures for Sequential Importance Resampling Filter (SIRF) implementation. The first architecture is a two-step sequential PF machine, where particle sampling, weight, and output calculations are carried out in parallel during the first step followed by sequential resampling in the second step. For the weight computation step, a piecewise linear function is used instead of the classical exponential function. This decreases the complexity of the architecture without degrading the results. The second architecture speeds up the resampling step via a parallel, rather than a serial, architecture. This second architecture targets a balance between hardware resources and the speed of operation. The third architecture implements the SIRF as a distributed PF composed of several processing elements and central unit. All the proposed architectures are captured using VHDL synthesized using Xilinx environment, and verified using the ModelSim simulator. Synthesis results confirmed the resource reduction and speed up advantages of our architectures.

Assessing the Performance of the Ensemble Kalman Filter for Land Surface Data Assimilation

Abstract The ensemble Kalman filter provides an easy-to-use, flexible, and efficient option for data assimilation problems. One of its attractive features in land surface applications is its ability to provide distributional information about variables, such as soil moisture, that can be highly skewed or even bimodal. The ensemble Kalman filter relies on normality approximations that improve its efficiency but can also compromise the accuracy of its distributional estimates. The effects of these approximations can be evaluated by comparing the conditional marginal distributions and moments estimated by the ensemble Kalman filter with those obtained from a sequential importance resampling (SIR) particle filter, which gives exact solutions for large ensemble sizes. Comparisons for two land surface examples indicate that the ensemble Kalman filter is generally able to reproduce nonnormal soil moisture behavior, including the skewness that occurs when the soil is either very wet or very dry. Its conditional mean estimates are very close to those generated by the SIR filter. Its higher-order conditional moments are somewhat less accurate than the means. Overall, the ensemble Kalman filter appears to provide a good approximation for nonlinear, nonnormal land surface problems, despite its dependence on normality assumptions.

Sequential weak constraint parameter estimation in an ecosystem model

A Sequential Importance Resampling filter (SIR) is applied to assimilate data of the Bermuda Atlantic Time-Series Study for the period December 1988 to January 1994 into a nine-compartment ecosystem model. The filter provides an opportunity to combine state and parameter estimations. We detected notable seasonality of some model parameters. A filtered solution is in close agreement with the data and is superior to that obtained with fixed model parameters. The seasonal dependence of the initial slope of the P– I curve is similar to other known estimates. The seasonality of the phytoplankton specific mortality rate obtained can point out that either the phytoplankton mortality parameterization has to be improved or the Chl:C ratio varies in time. Being of the same computational cost as the Ensemble Kalman filter, the data assimilation approach used can be implemented for on-line tuning and operational prediction the ecosystem dynamics with a coupled hydrodynamical–ecosystem model.

Sequential parameter estimation for stochastic systems

Abstract. The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.