Sequential Importance Resampling Particle Filter Research Articles

State of charge estimation of electrical vehicle battery by Using Box Particle Filter Signal Tracking Method

ABSTRACT This paper concentrates on the effective study of the online state of charge (SoC) estimation of lithium-ion batteries used in electric vehicles (EVs). Box Particle filters (BPF) are commonly used in the estimation of multivariate systems under noisy environments. In this study, a Joint-estimator is proposed which uses the forgetting factor recursive least square (FF-RLS) method for the 1-RC battery model online parameter estimation and the lithium-ion battery SoC is estimated using battery terminal voltage signal tracking with (BPF). The implemented method is compared with a Sequential Importance Resampling Particle Filter (SIR-PF) which shows that the proposed BPF has reduced the number of particles and computational time and maintained the efficiency comparable to the SIR-PF. The BPF performance is further evaluated at assorted voltage signal tracking accuracy, the number of boxes and the initial dimension of the boxes. The BPF method requires less number of boxes as compared to the SIR-PF with compatible efficiency. Therefore, BPF can be used as an alternative to the complex algorithms used in the SoC estimation in battery management systems (BMS) of electric vehicles.

Large Ensemble Particle Filter for Spatial Climate Reconstructions Using a Linear Inverse Model

AbstractProxy records that document the last 2000 years of climate provide evidence for the wide range of the natural climate variability from inter‐annual to secular timescales not captured by the short window of recent direct observations. Assessing climate models ability to reproduce such natural variations is crucial to understand climate sensitivity and impacts of future climate change. Paleoclimate data assimilation (PDA) offers a powerful way to extend the short instrumental period by optimally combining the physics described by General Circulation Climate Models (GCMs) with information from available proxy records while taking into account their uncertainties. Here we present a new PDA approach based on a sequential importance resampling (SIR) Particle filter (PF) that uses Linear Inverse Modeling (LIM) as an emulator of several CMIP‐class GCMs. We examine in a perfect‐model framework the skill of the various LIMs to forecast the dynamics of the surface temperatures and provide spatial field reconstructions over the last millennium in a SIR PF. Our results show that the LIMs allow for skillful ensemble forecasts at 1‐year lead‐time based on GCMs dynamical knowledge with best prediction in the tropics and the North Atlantic. The PDA further provides a set of physically consistent spatial fields allowing robust uncertainty quantification related to climate models biases and proxy spatial sampling. Our results indicate that the LIM yields dynamical memory improving climate variability reconstructions and support the use of the LIM as a GCM‐emulator in real reconstruction to propagate large ensembles of particles at low cost in SIR PF.

A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements

The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73%and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.

Particles resampling scheme using regularized optimal transport for sequential Monte Carlo filters

SummaryA resampling method is presented for improving the performance of particle filters by using adaptive numbers of the resampling particles. The proposed method replaces the resampling step of a sequential importance resampling particle filter with regularized optimal transport that makes use of the transport plan to warp a posteriori weights into desired weights. The basis of the method is the same as an ensemble transform particle filter that uses the linear transformation step in the resampling of particles. However, the linear transformation step in ensemble transform particle filter is computationally expensive and needs relaxation matching between the two samples for robust processing. Furthermore, its performance can be degraded if the number of the effective particles becomes below the required number of particles, which represents the needed particle number of importance sampling. Therefore, in this paper, a regularized optimal transport method is used to deal with computational load reduction and relaxation matching in the resampling step by using a modified Sinkhorn‐Knopp algorithm that considers the process iteration rate convergence. In order to maintain the proper number of the effective particles for states estimation, Kullback‐Leibler distance sampling method is also implemented in the resampling process. The proposed method is evaluated by theoretical analysis including simple simulations compared with the conventional resampling methods. According to the simulations, the proposed method indicates that estimation accuracy is better than conventional methods with small number of the effective particles.

Simulation and Assimilation of Passive Microwave Data Using a Snowpack Model Coupled to a Calibrated Radiative Transfer Model Over Northeastern Canada

AbstractOver northern snowmelt‐dominated basins, the snow water equivalent (SWE) is of primary interest for hydrological forecasting. This paper evaluates first the performance of a detailed multilayer snowpack model (Crocus), driven by meteorological predictions generated by the Canadian Global Environmental Multiscale model, for hydrological applications. Simulations were compared to daily snow depth and SWE measurements over Québec, northeastern Canada (56–45°N), for 2012–2016, highlighting an overestimation of the annual maximum snow depth (35%) and of the annual maximum SWE (16%), which is not accurate enough for hydrological applications. To improve SWE simulations, a chain of models is implemented to simulate and to assimilate passive microwave satellite observations. The snowpack model is coupled to a microwave snow emission model (Dense Media Radiative Transfer‐Multilayers model, DMRT‐ML), and the comparison of simulated brightness temperatures (TBs) with surface‐based TB measurements (at 11, 19 and 37 GHz) shows best results when the snow stickiness parameter is set to 0.17 in DMRT‐ML. The overall root‐mean‐square error (RMSE) obtained by the calibrated coupling reaches 27 K, significantly better than the RMSE obtained by considering nonsticky spheres in DMRT‐ML (43.0 K). The relevance of TB assimilation is tested with synthetic observations to evaluate the information content of each frequency for SWE estimates. The assimilation scheme is a Sequential Importance Resampling Particle filter using an ensemble of perturbed meteorological forcing data. The results show a SWE RMSE reduced by 82% with TB assimilation compared to without assimilation.

On the assimilation of optical reflectances and snow depth observations into a detailed snowpack model

Abstract. This paper examines the ability of optical reflectance data assimilation to improve snow depth and snow water equivalent simulations from a chain of models with the SAFRAN meteorological model driving the detailed multilayer snowpack model Crocus now including a two-stream radiative transfer model for snow, TARTES. The direct use of reflectance data, allowed by TARTES, instead of higher level snow products, mitigates uncertainties due to commonly used retrieval algorithms.Data assimilation is performed with an ensemble-based method, the Sequential Importance Resampling Particle filter, to represent simulation uncertainties. In snowpack modeling, uncertainties of simulations are primarily assigned to meteorological forcings. Here, a method of stochastic perturbation based on an autoregressive model is implemented to explicitly simulate the consequences of these uncertainties on the snowpack estimates.Through twin experiments, the assimilation of synthetic spectral reflectances matching the MODerate resolution Imaging Spectroradiometer (MODIS) spectral bands is examined over five seasons at the Col du Lautaret, located in the French Alps. Overall, the assimilation of MODIS-like data reduces by 45 % the root mean square errors (RMSE) on snow depth and snow water equivalent. At this study site, the lack of MODIS data on cloudy days does not affect the assimilation performance significantly. The combined assimilation of MODIS-like reflectances and a few snow depth measurements throughout the 2010/2011 season further reduces RMSEs by roughly 70 %. This work suggests that the assimilation of optical reflectances has the potential to become an essential component of spatialized snowpack simulation and forecast systems. The assimilation of real MODIS data will be investigated in future works.

Testing particle filters on simple convective‐scale models Part l: A stochastic cloud model

Convective‐scale applications require data assimilation methods that can cope with nonlinear dynamics and the stochastic nature of convection. For this application, the particle filter is a promising data assimilation method because it estimates the probability density function (PDF) of the atmospheric state and not only its first two moments. However, in order to represent PDFs with a small number of particles, the particle filter is usually combined with another data assimilation technique. In this article we investigate a hybrid algorithm, the nudging proposal particle filter, which combines the sequential importance resampling particle filter with nudging.Analytic and experimental results on an idealized, nonlinear, one‐dimensional model are used to show that there exists a combination of the two methods such that the nudging proposal particle filter outperforms both of its components. In this article, a stochastic cloud model, represented through a birth–death process, serves as a first test model for the filter. The transition probability density can be calculated exactly for this model, thus providing insight into its contribution to the selection of particles during resampling. The functioning mechanism of the nudging proposal particle filter in its simplest form is investigated and the impact of the model parameters on the filter's behaviour highlighted.

Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods: ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF, which is a deterministic scheme of the ensemble Kalman filter (EnKF), performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.

영상 기반의 이차 칼만 필터를 이용한 객체 추적

In this paper, we propose a novel quadratic Kalman filter based object tracking algorithm using moving pictures. Quadratic Kalman filter, which is introduced recently, has not yet been applied to the problem of 3-dimensional (3-D) object tracking. Since the mapping of a position in 2-D moving pictures into a 3-D world involves non-linear transformation, appropriate algorithm must be chosen for object tracking. In this situation, the quadratic Kalman filter can achieve better accuracy than extended Kalman filter. Under the same conditions, we compare extended Kalman filter, unscented Kalman filter and sequential importance resampling particle filter together with the proposed scheme. In conculsion, the proposed scheme decreases the divergence rate by half compared with the scheme based on extended Kalman filter and improves the accuracy by about 1% in comparison with the one based on unscented Kalman filter.

A modified ensemble Kalman particle filter for non‐Gaussian systems with nonlinear measurement functions

AbstractThe ensemble Kalman particle filter (EnKPF) is a combination of two Bayesian‐based algorithms, namely, the ensemble Kalman filter (EnKF) and the sequential importance resampling particle filter (SIR‐PF). It was recently introduced to address non‐Gaussian features in data assimilation for highly nonlinear systems, by providing a continuous interpolation between the EnKF and SIR‐PF analysis schemes. In this paper, we first extend the EnKPF algorithm by modifying the formula for the computation of the covariance matrix, making it suitable for nonlinear measurement functions (we will call this extended algorithm nEnKPF). Further, a general form of the Kalman gain is introduced to the EnKPF to improve the performance of the nEnKPF when the measurement function is highly nonlinear (this improved algorithm is called mEnKPF). The Lorenz '63 model and Lorenz '96 model are used to test the two modified EnKPF algorithms. The experiments show that the mEnKPF and nEnKPF, given an affordable ensemble size, can perform better than the EnKF for the nonlinear systems with nonlinear observations. These results suggest a promising opportunity to develop a non‐Gaussian scheme for realistic numerical models.

Online adaptive motion model-based target tracking using local search algorithm

An adaptive tracker to address the problem of tracking objects which undergo abrupt and significant motion changes is introduced. Abrupt motion of objects is an issue which makes tracking a challenging task. To address this problem, a new adaptive motion model is proposed. The model is integrated into the sequential importance resampling particle filter (SIR PF), which is the most popular probabilistic tracking framework. In this model, in each time step, if necessary, the particles’ configurations are updated by using feedback information from the observation likelihood. In order to overcome the local-trap problem, local search algorithm with best improvement strategy is used to update particles’ configurations. Then, the motion model is updated online with respect to the configurations of the best particle in the current and previous time steps. By using this adaptive model, a more robust tracking is achieved to abrupt significant motion changes. The tracker is experimentally compared to other state-of-the-art trackers on BoBoT dataset. The experimental results confirm that the tracker outperforms the related trackers in many cases by having better PASCAL score. Furthermore, this tracker improves the accuracy of the conventional SIR PF approximately 15%.

Practical issues in state estimation using particle filters: Case studies with polymer reactors

In this paper, we compare Kalman update based filters with particle filters using simulations on polymerization processes. In particular, we compare the unscented Kalman filter (UKF) and the particle filter (PF) for the case of significant plant–model mismatch. The sequential importance resampling particle filter is shown to be less robust than the Kalman update-based filters. This issue is solved by bootstrapping the PF with the UKF, i.e., using the UKF as the proposal distribution; this retains its ability to estimate non-Gaussian distributions while providing robustness with respect to plant–model mismatch. Finally, we explore methods of obtaining a point estimate from the state distributions of the PF.

An exploration of the equivalent weights particle filter

AbstractParticle filters are fully nonlinear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high‐dimensional geophysical applications, the number of particles required by the sequential importance resampling (SIR) particle filter (in order to capture the high‐probability region of the posterior) is too large to make them usable. However particle filters can be formulated using proposal densities, which give greater freedom in how particles are sampled and allow for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high‐probability region of the posterior probability density function. This gives rise to the possibility of nonlinear data assimilation in large‐dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that, when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model. Copyright © 2012 Royal Meteorological Society

Measuring the uncertainty of RFID data based on particle filter and particle swarm optimization

The management of the uncertainties over data is an urgent problem of novel applications such as cyber-physical system, sensor network and RFID data management. In order to adapt the characteristics of evolving over time of sensor data in real-time location tracing service based on RFID, a measuring algorithm for the Uncertainty of RFID Data-PPMU (a particle filter and particle swarm optimization-based measuring uncertainty algorithm for RFID Data) is proposed in this paper. PPMU can change the number of samples adaptively on the basis of K---L distance to adapt the evolution of RFID data, and PPMU introduces an improved PSO (particle swarm optimization) method to enhance the efficiency of re-sampling phase of SIRPF (sequential importance re-sampling particle filter). Meanwhile, PPMU defines a fitness function base on Conventional Weighted Aggregation for PSO that balances the importance between the priori density and likelihood density to detect the most optimal samples among candidate sample sets. It provides a measurement with confidence factor for initial tuples in the probability RFID database. Experiments on real dataset show the proposed method can effectively measure the underlying uncertainty over RFID data. Compared with existing algorithms, PPMU can be further improved particle degradation and particle impoverishment problem.

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

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.

A novel system for robust lane detection and tracking

This paper presents a lane detection and tracking system based on a novel lane feature extraction approach and the Gaussian Sum Particle filter (GSPF). The proposed feature extraction approach is based on the fact that by zooming into the vanishing point of the lanes, the lane markings/boundaries will only move on the same straight lines they are on. Objects other than the lanes in the frame do not share this property and can be ignored during the model parameter estimation. This algorithm is able to iteratively refine various traditional feature maps and to operate with curved roads. The tracking part of the system is initialised by a deformable template matching algorithm. Three types of tracking algorithms are compared in our study: the original Sequential Importance Resampling (SIR) particle filter, the Gaussian Particle Filter (GPF) and the Gaussian Sum Particles Filter (GSPF). The GSPF achieves the best performance by integrating a novel likelihood function and an intuitive parameter selection process. Both the GSPF and GPF provide improved tracking performance and require less computational power than the SIR. It has also been found that the detection and tracking performance is enhanced significantly by incorporating the refined feature map.

Practical issues in the application of the particle filter for estimation of chemical processes

AbstractIn this work, we explore practical aspects of the application of particle filters to chemical processes, with special emphasis on polymerization processes. Particle filters are potentially better suited for estimation of these nonlinear processes than Kalman filter-based estimators, since they do not make the assumption that the process and measurement noise are Gaussian. We demonstrate the improved performance of particle filters over the extended Kalman filter and the unscented Kalman filter when the innovation sequences are non-Gaussian. Another potential advantage of the particle filter is that information on full distribution of the state is obtained, and not just the expectation of the state estimate. We provide results based on k-means clustering that indicate the best method of extracting a point estimate from the full state distribution. Finally, we show that in cases where there is high plant-model mismatch, e.g., when a reduced order model is used for estimation, the basic sequential importance resampling particle filter (SIR-PF) does not provide accurate estimates, while an unscented particle filter provides excellent estimates even under high structural plant-model mismatch.

A Fault Predication Algorithm Based on Artificial Immune Particle Filter

Degeneracy problem is an inevitable result of sequential importance re-sampling (SIR) particle filter, and a mass of degenerated particles will influence the tracking ability of particle filter seriously. As a result, SIR particle filter based predication algorithm can’t predict system faults accurately. Artificial immune algorithm is characterized by a global ability to search for optimum, so it is introduced into the particle filter, named artificial immune particle filter (AIPF). Particles are regarded as antibodies in AIPF and particles with large weight aberrance and are cloned, and then the better particles are selected for states evaluation. A fault predication algorithm based on AIPF is proposed to improve the predication accuracy, and simulation results have demonstrated the feasibility of the proposed algorithm.

A Strong Tracking Particle Filter with Application to Fault Prediction

Particle degeneracy and its poor ability to track saltatory states are two main problems when a particle filter is applied to fault prediction.The sequential importance re-sampling particle filter can abate the influence of particle degeneracy but will easily lead to another problem-sample impoverishment.The extended particle filter can resolve the problem of particle degeneracy to a certain extent but can not track the saltatory state.A strong tracking particle filter is put forward by introducing a strong tracking filter into a particle filter to resolve the above problems,in which the strong tracking filter is used to update particles and produce importance densities.As a result, the problems of particle degeneracy and sample impoverishment are ameliorated,and the tracking ability is improved. Simulation results demonstrate that the strong tracking particle filter is feasible and system fault can be predicted in time and correctly.

A Strong Tracking Particle Filter with Application to Fault Prediction

Particle degeneracy and its poor ability to track saltatory states are two main problems when a particle filter is applied to fault prediction.The sequential importance re-sampling particle filter can abate the influence of particle degeneracy but will easily lead to another problem-sample impoverishment.The extended particle filter can resolve the problem of particle degeneracy to a certain extent but can not track the saltatory state.A strong tracking particle filter is put forward by introducing a strong tracking filter into a particle filter to resolve the above problems,in which the strong tracking filter is used to update particles and produce importance densities.As a result, the problems of particle degeneracy and sample impoverishment are ameliorated,and the tracking ability is improved. Simulation results demonstrate that the strong tracking particle filter is feasible and system fault can be predicted in time and correctly.