Particle Filter Method Research Articles

Epidemiological model can forecast COVID-19 outbreaks from wastewater-based surveillance in rural communities

Wastewater has emerged as a crucial tool for infectious disease surveillance, offering a valuable means to bridge the equity gap between underserved communities and larger urban municipalities. However, using wastewater surveillance in a predictive manner remains a challenge. In this study, we tested if detecting SARS-CoV-2 in wastewater can forecast outbreaks in rural communities.Under the CDC National Wastewater Surveillance program, we monitored the SARS-CoV-2 in the wastewater of five rural communities and a small city in Idaho (USA). We then used a particle filter method coupled with a stochastic susceptible-exposed-infectious-recovered (SEIR) model to infer active case numbers using quantities of SARS-CoV-2 in wastewater.Our findings revealed that while high daily variations in wastewater viral load made real-time interpretation difficult, the SEIR model successfully factored out this noise, enabling accurate forecasts of the Omicron outbreak in five of the six towns shortly after initial increases in SARS-CoV-2 concentrations were detected in wastewater. The model predicted outbreaks with a lead time of 0 to 11 days (average of 6 days +/- 4) before the surge in reported clinical cases.This study not only underscores the viability of wastewater-based epidemiology (WBE) in rural communities—a demographic often overlooked in WBE research—but also demonstrates the potential of advanced epidemiological modeling to enhance the predictive power of wastewater data. Our work paves the way for more reliable and timely public health guidance, addressing a critical gap in the surveillance of infectious diseases in rural populations.

Bearing fault signal detection and prediction based on an improved particle filter method

Awareness and predicting bearing health are challenging because of uncertainties in the operating environment and noise in fault-signal measurements. Considering the sudden occurrence of bearing faults and their relatively brief duration over the bearing lifespan, this paper presents a fusion framework that combines an eighth-order polynomial model with a cuckoo search thought particle filter (CST-PF) method to estimate the failures occurrences. The fault characteristic signals are extracted from the amplitude spectrum within a specific frequency range and modeled by an eighth-order polynomial model. Cuckoo search (CS) is introduced to address the particle dilution in particle filter (PF). Furthermore, the proposed CST-PF refines the step size update equations and discovery probability for balancing the search speed and accuracy, thus enhancing the adaptability to bearing fault diagnosis and prediction. It ensures the parameter convergences in the prediction model by learning the fault characteristic signal during regular bearing operations, facilitating accurate predictions of subsequent failures. Validation results show that the eighth-order model accurately captures changes in fault characteristic signals throughout the bearing lifespan, with MAE and RMSE metrics surpassing those of traditional models. The CST-PF method demonstrates superior predictive ability compared to the Cuckoo search particle filter (CS-PF), traditional PF, and other PF variants.

Magneto-inductive positioning network based on magnetic energy density

The magneto-inductive positioning system (MPS) is considered a promising solution for realizing accurate positioning in challenging environments, particularly to support the development of emerging technologies. However, obtaining the position of magnetic beacons increases the system’s complexity and the sensor’s attitude error lowers the positioning performance. To solve the above problems, this paper proposes an improved magneto-inductive positioning network system (MPNS) based on magnetic energy density (MED). An orientation model without the sensor’s attitude is derived from MED. An incrementally deployed magneto-inductive positioning network is developed with the orientation model, which reduces the system complexity. An advanced resampling method of particle filter is employed in the MPNS to improve the positioning accuracy. The realized system displays the max error of no more than 0.13 m for the static target . The performance of MPNS that tracks moving targets is examined with simulation. The results exhibit that 99% of tracking errors are less than 0.25 m.

Intelligent enhanced particle filter with deep residual network surrogate for accurate groundwater pollution source characterization

Accurate groundwater pollution source characterization (GPSC) is crucial for environmental protection and water resource management. Although the particle filter (PF) algorithm is widely employed for GPSC, it suffers from particle degradation and loss of diversity. To address this challenge, this study proposes an intelligent enhanced particle filter (IEPF) method to enhance GPSC’s accuracy and efficiency. First, this method optimizes the resampling process by defining a weight threshold while introducing an information transmission mechanism. This mechanism enables low-weight particles to update their positions by leveraging information from high-weight particles and neighboring particles, thereby enhancing information exchange among particles and improving the algorithm’s global search capability. Crossover and mutation operations are introduced to further increase the particle diversity, effectively preventing particles from concentrating on local optimal solutions. Furthermore, this study employs a deep residual network (ResNet) as a surrogate model for the simulation model. The ResNet has strong feature learning and expression capabilities and efficiently captures nonlinear relationships in data, thus significantly improving computational efficiency while ensuring accuracy. The results demonstrate that the IEPF method significantly enhances GPSC accuracy. In summary, the proposed IEPF method combined with the ResNet surrogate model provides an efficient and accurate approach to GPSC, with considerable benefits for groundwater pollution management.

Life prediction of lithium battery based on particle filter and BP neural network

Abstract This paper focuses on using Particle Filter (PF) and Back Propagation (BP) neural networks for RUL prediction. This fusion strategy uses particle filtering (PF) for battery system state estimation and prediction while considering various types of noise and uncertainties to assess the system state comprehensively. Furthermore, the strategy employs a BP neural network to learn and combine historical data patterns with particle filtering estimation, improving prediction accuracy and reliability. This study validates the proposed fusion method by comparing it with the original PF and BP prediction methods using Toyota Motor Corporation and Stanford University datasets. The experimental results demonstrate its superior performance and higher prediction accuracy.

Crop Phenology Estimation in Rice Fields Using Sentinel-1 GRD SAR Data and Machine Learning-Aided Particle Filtering Approach

Abstract. Monitoring crop phenology is essential for managing field disasters, protecting the environment, and making decisions about agricultural productivity. Because of its high timeliness, high resolution, great penetration, and sensitivity to specific structural elements, synthetic aperture radar (SAR) is a valuable technique for crop phenology estimation. Particle filtering (PF) belongs to the family of dynamical approach and has the ability to predict crop phenology with SAR data in real time. The observation equation is a key factor affecting the accuracy of particle filtering estimation and depends on fitting. Compared to the common polynomial fitting (POLY), machine learning methods can automatically learn features and handle complex data structures, offering greater flexibility and generalization capabilities. Therefore, incorporating two ensemble learning algorithms consisting of support vector machine regression (SVR), random forest regression (RFR), respectively, we proposed two machine learning-aided particle filtering approaches (PF-SVR, PF-RFR) to estimate crop phenology. One year of time-series Sentinel-1 GRD SAR data in 2017 covering rice fields in Sevilla region in Spain was used for establishing the observation and prediction equations, and the other year of data in 2018 was used for validating the prediction accuracy of PF methods. Four polarization features (VV, VH, VH/VV and Radar Vegetation Index (RVI)) were exploited as the observations in modeling. Experimental results reveals that the machine learning-aided methods are superior than the PF-POLY method. The PF-SVR exhibited better performance than the PF-RFR and PF-POLY methods. The optimal outcome from PF-SVR yielded a root-mean-square error (RMSE) of 7.79, compared to 7.94 for PF-RFR and 9.1 for PF-POLY. Moreover, the results suggest that the RVI is generally more sensitive than other features to crop phenology and the performance of polarization features presented consistent among all methods, i.e., RVI＞VV＞VH＞VH/VV. Our findings offer valuable references for real-time crop phenology monitoring with SAR data.

Second-Order Central Difference Particle Filter Algorithm for State of Charge Estimation in Lithium-Ion Batteries

The estimation of the state of charge (SOC) in lithium-ion batteries is a crucial aspect of battery management systems, serving as a key indicator of the remaining available capacity. However, the inherent process and measurement noises created during battery operation pose significant challenges to the accuracy of SOC estimation. These noises can lead to inaccuracies and uncertainties in assessing the battery’s condition, potentially affecting its overall performance and lifespan. To address this problem, we propose a second-order central difference particle filter (SCDPF) method. This method leverages the latest observation data to enhance the accuracy and noise adaptability of SOC estimation. By employing an improved importance density function, we generate optimized particles that better represent the battery’s dynamic behavior. To validate the effectiveness of our proposed algorithm, we conducted comprehensive comparisons at both 25 °C and 0 °C under the new European driving cycle condition. The results demonstrate that the SCDPF algorithm exhibits a high accuracy and rapid convergence speed, with a maximum error which never exceeds 1.30%. Additionally, we compared the SOC estimations with both Gaussian and non-Gaussian noise to assess the robustness of our proposed algorithm. Overall, this study presents a novel approach to enhancing SOC estimation in lithium-ion batteries, addressing the challenges posed by the process itself and measurement noises.

An Adaptive Modeling Method for the Prognostics of Lithium-Ion Batteries on Capacity Degradation and Regeneration

Accurate prediction of remaining useful life (RUL) is crucial to the safety and reliability of the lithium-ion battery management system (BMS). However, the performance of a lithium-ion battery deteriorates nonlinearly and is heavily affected by capacity-regeneration phenomena during practical usage, which makes battery RUL prediction challenging. In this paper, a rest-time-based regeneration-phenomena-detection module is proposed and incorporated into the Coulombic efficiency-based degradation model. The model is estimated with the particle filter method to deal with the nonlinear uncertainty during the degradation and regeneration process. The discrete regeneration-detection results should be reflected by the model state instead of the model parameters during the particle filter-estimation process. To decouple the model state and model parameters during the estimation process, a dual-particle filtering estimation framework is proposed to update the model parameters and model state, respectively. A kernel smoothing method is adopted to further smooth the evolution of the model parameters, and the regeneration effects are imposed on the model states during the updating. Our proposed model and the dual-estimation framework were verified with the NASA battery datasets. The experimental results demonstrate that our proposed method is capable of modeling capacity-regeneration phenomena and provides a good RUL-prediction performance for lithium-ion batteries.

Time-varying dynamic modeling of micro-milling considering tool wear and the process parameter identification

Micro-milling technology is widely used in the manufacturing of micro three-dimensional complex parts in aerospace, mechanical equipment, biomedical devices, electronic components, and other fields due to its advantages of high machining accuracy, small size, and complex surface. Consequently, understanding its machining process is essential. This study proposes a time-varying dynamic micro-milling process model with the effects of tool runout, tool wear, and cutting status and explores the stable cutting domain of real-time machining. Considering the time-varying characteristics of the cutting process, combined with measured data and particle filtering method, the cutting force coefficients and tool wear parameters in the dynamic model at different times are identified. The dynamic equation of micro-milling is derived using a discrete method, and the stability of the cutting process is evaluated. Multiple cutting experiments are conducted on the Al6061, and the test data are compared with simulated values. The comparison results show that the accuracy of the proposed model in predicting the cutting state can reach 100%, and the average error of cutting force prediction is 7.72%. The research results can provide theoretical guidance for the safety evaluation of micro-milling and the selection of machining conditions.

Construction and Method Study of the State of Charge Model for Lithium-Ion Packs in Electric Vehicles Using Ternary Lithium Packs as an Example

Accurate and real-time estimation of pack system-level chips is essential for the performance and reliability of future electric vehicles. Firstly, this study constructed a model of a nickel manganese cobalt cell on the ground of the electrochemical process of the packs. Then, it used methods on the grounds of the unscented Kalman filter and unscented Kalman particle filter for system-level chip estimation and algorithm construction. Both algorithms are on the ground of Kalman filters and can handle nonlinear and uncertain system states. In comparative testing, it can be seen that the unscented Kalman filter algorithm can accurately evaluate the system-level chip of the nickel manganese cobalt cell under intermittent discharge conditions. The system-level chip was 0.53 at 1000 s and was reduced to 0.45 at 1500 s. These results demonstrate that the evaluation of the ternary lithium battery pack’s performance is time-dependent and indicate the accuracy of the algorithm used during this time period. These data should be considered in the broader context of the study for a comprehensive understanding of their meaning. In the later stage, the estimation error of the recursive least-squares unscented Kalman particle filter method for system-level chips began to significantly increase, gradually exceeding 1%, with a corresponding root-mean-square error of 0.002171. This indicates that the recursive least-squares optimization algorithm, the unscented Kalman particle filter algorithm, diminished its root mean square error by 27.59%. The unscented Kalman filter and unscented Kalman particle filter are effective in estimating the system-level chip of nickel manganese cobalt cells. However, UPF performs more robustly in handling complex situations, such as pack aging and temperature changes. This study provides a new perspective and method that has a high reference value for pack management systems. This helps to achieve more effective energy management and improve pack life, thereby enhancing the reliability and practicality of electric vehicles.

Sequential estimation of high temperatures of liquid metals by using particle filter methods

This work follows up our previous studies dedicated to the estimation of the transient temperature of niobium and 100c6 steel samples, in ranges that include solid and liquid phases, as well as phase changes. In the experimental setup, a metallic sample of few millimeters is aerodynamically levitated and then heated by a powerful laser, while a collimator focused on the sample collects the radiative flux that is split towards five pyrometers of different wavelengths. The measured spectral fluxes are used in an inverse analysis to estimate the sample temperature. Difficulties in the inverse problem solution related to the dependence of the sample emittance with temperature and wavelength could be overcome by reducing the number of model parameters using a simple linear variation of the emittance with respect to the wavelength. In this work the transient temperature of the sample is estimated sequentially by solving a state estimation problem with two algorithms of the particle filter method, namely: the Sampling Importance Resampling (SIR) and Auxiliary Sampling Importance Resampling (ASIR) algorithms. Results obtained with these algorithms and the radiative spectral fluxes exhibited small discrepancies with respect to the temperature measurements of a reference bichromatic pyrometer.

Multiple maneuvering target tracking based on hierarchical Dirichlet process and hidden Markov model

This paper is concerned with multiple maneuvering target tracking problems. Although the interacting multiple model (IMM) algorithm can be used for maneuvering targets tracking, the performance is limited as the motion mode set of the target is fixed in advance. In this paper, we address the problem of multiple maneuvering targets with unknown maneuvering models in cluttered environments. A finite hidden Markov model (HMM) is developed with truncated Hierarchical Dirichlet process (HDP) to recognize the unknown and changing motion modes. Further, the HDP-HMM is introduced into multiple hypothesis tracking (MHT) and probabilistic multiple hypothesis tracking (PMHT) approaches for multiple maneuvering targets tracking with data association uncertainty. To joint estimate the HDP-HMM parameters and target states, the particle learning and variational inference approaches are used, and the solutions of HDP-HMM-MHT and HDP-HMM-PMHT algorithms are obtained based on Rao-Blackwellized particle filter and variational Bayesian methods, respectively. As the changes of maneuver models can be learned using HDP, the multi-target tracking accuracy of the proposed algorithm is improved. Simulation results show that the proposed algorithms outperform the traditional IMM-MHT method with fixed model sets.

An improved adaptive weights correction-particle swarm optimization-unscented particle filter method for high-precision online state of charge estimation of lithium-ion batteries

An improved adaptive weights correction-particle swarm optimization-unscented particle filter method for high-precision online state of charge estimation of lithium-ion batteries

Remaining useful life prediction of ball screw based on integrating preload and precision

Ball screw remaining useful life (RUL) prediction is of great interest to industry and academia. However, the lack of a reliable prediction model limits accuracy. To address this, a hybrid method that combines physical-based and data-driven methods is proposed. A novel integrated index is developed to capture wear degradation by integrating the preload and precision parameters, and the optimum partitioning method is used for wear stage categorization. A physical-based method of a two-stage empirical model is constructed to characterize the randomness and nonlinearity of the degradation process. Model parameters are initialized and updated using particle filtering (PF) through a data-driven method for RUL prediction. To address discontinuous predictions in the empirical model, the random forest with PF (RF-PF) method is employed. The effectiveness of this approach is evaluated through experiments and comparisons with other methods.

Degradation prediction of proton exchange membrane fuel cells with model uncertainty quantification

This study presents a new approach for state of health (SOH) estimation and degradation trend prediction of proton exchange membrane fuel cells (PEMFCs) considering model uncertainty quantification. The model uncertainty is considered as completely unknown in this paper, and the Bayesian framework-based model uncertainty and state simultaneous estimation (Bayes-MUSE) method is proposed to quantify the model uncertainty from the perspective of the form of its effect on the system state transfer, and this method of quantifying model uncertainty is first applied to PEMFC long-term aging prediction and RUL estimation. The proposed Bayes-MUSE method is compared with extended Kalman filter (EKF), Unscented Kalman filter (UKF) and Unscented Particle filter (UPF) methods in terms of SOH estimation, noise immunity, aging prediction performance and RUL estimation using two aging test datasets, and the method is verified to have excellent noise immunity and the highest long-term aging prediction and RUL estimation accuracy. Compared with EKF, UKF and UPF methods, the proposed Bayes-MUSE method has a maximum improvement of 93.95% and 52.2% in RUL estimation accuracy of the two data sets under quasi-dynamic and static conditions, respectively.

A novel genetic marginalized particle filter method for state of charge and state of energy estimation adaptive to multi-temperature conditions of lithium-ion batteries

Power lithium-ion batteries are widely used in various fields, the battery management system (BMS) is the main object of battery energy management and safety monitoring, so the accurate collaboration of state of charge (SoC) and state of energy (SoE) is estimated to be essential for the BMS system. In this work, a novel genetic marginal particle filter (GMPF) algorithm to estimate SoC and SoE accurately. The forgetting factor recursive least square (FFRLS) algorithm is used to identify the second-order Thevenin equivalent model parameter, and the genetic algorithm is used to improve the re-sampling process of the traditional particle filtering (PF) algorithm, according to the Rao-Blackwell theory in statistical science, the marginalization of part of the linear state variables during the calculation of particle filtering, the distribution of the post-test is similar to a single Gaussian distribution. The GMPF algorithm is verified under the conditions of the hybrid pulse power characteristic (HPPC) and the Beijing bus dynamic stress test (BBDST) with 15 °C, 25 °C, and 35 °C respectively, and experimental results show that the improved GMPF algorithm can effectively realize the collaborative estimation of the SoC and SoE of power lithium-ion batteries. The mean absolute error of SoC and SoE estimation is always less than 1.56 %, the root-mean-square error is always less than 1.58 %. And the GMPF algorithm is suitable for temperature environments of 15 °C to 35 °C.

A Probabilistic Method-Based Smartphone GNSS Fault Detection and Exclusion System Utilizing PDR Step Length

A smartphone equipped with a Global Navigation Satellite System (GNSS) module can generate positional information for location-based services. However, GNSS signals are susceptible to fragility, multipath (MP), and Non-Line-Of-Sight (NLOS) interference, which can lead to a degradation in the accuracy of GNSS positioning on smartphones. Due to limitations in the smartphone’s antenna, GNSS signal strength is typically lower. Moreover, in urban areas, where smartphones rely on GNSS, MP and NLOS signals are the primary factors impeding accurate positioning. In this paper, with the goal of enhancing both the accuracy and robustness of smartphone GNSS positioning, we propose two methods. Firstly, an optimized particle filter method employing a Krill Herd Algorithm (KHA) is suggested for the integration of GNSS and Pedestrian Dead Reckoning (PDR). Secondly, a probabilistic approach is presented to identify faulty GNSS measurements using step distance information obtained from the PDR. Experimental tests were conducted using smartphones to evaluate the performance of the proposed method. The results demonstrate that both the KHA and fault detection methods effectively enhance the performance of integrated PDR and GNSS.

Analisis Metode Kalman Filter, Particle Filter dan Correlation Filter Untuk Pelacakan Objek

Object tracking is a challenging in computer vision. Object tracking is divided into two, which can be one object or several objects, depending on the object being observed. The process of tracking an object in the form of one object is to estimate the target in the next sequence based on information from the first frame given. In object tracking in the form of single object tracking, there are five steps that are often used in discriminatory methods, including motion models, feature extraction, observation models, model updates and integration methods. Although various algorithms of object tracking are proposed, there are still failures in the object tracking process caused by occlusion, non-rigid target deformation, and other factors. This study proposes the implementation of the Kalman filter, particle filter, and correlation filter methods for object tracking in video data. The results of the implementation of the three methods can track objects in traffic video data and the script circuit video. In object tracking calculations and method analysis, the kalman filter gets 96.89% where the kalman method is better in terms of accuracy compared to other methods. Meanwhile, in the average performance of computation time, the correlation method gets 26.69 FPS, where the correlation method is superior compared to other competitor methods.
 Keywords – Kalman Filter; Particle Filter; Correlation Filter; Object Tracking; Object Tracking in Video

A recursive inference method based on invertible neural network for multi-level model updating using video monitoring data

Likelihood-free inference methods have been widely adopted, but they face significant challenges in updating multi-level computational models that have hierarchically embedded sub-models. This difficulty arises from the lack of direct observations of the quantities of interest of the sub-models. In addition, recent advancements in sensing and image processing technologies allow for the collection of a substantial amount of video monitoring data through non-contact sensing techniques. The implicit and very complicated relationship between the uncertain model parameters and video monitoring data adds an additional layer of challenge to the updating of multi-level models. This paper overcomes these challenges by proposing an innovative Recursive Inference method based on Invertible Neural Networks (RINN) for multi-level models. The proposed RINN framework first compresses the high-dimensional video monitoring data into low-dimension latent-space data using a convolutional autoencoder. Using synthetic video monitoring data generated by considering various uncertainty sources in the computational simulation models, a likelihood-free inference model is then trained through a conditional invertible neural network (cINN) and a summary neural network. This model efficiently approximates the posterior distributions of uncertain model parameters without evaluating the computationally intractable likelihood function, given any latent-space data obtained from the autoencoder. To facilitate continuous monitoring and model updating over an extended monitoring period, this paper further proposes a recursive model updating strategy that integrates the cINN-based likelihood-free inference with the particle filtering method. The updating of a degradation model of a miter gate application is employed as an example throughout this paper to explain and demonstrate the efficacy of the proposed RINN framework. The results of the case study show that the RINN is able to effectively reduce uncertainty in the degradation model parameters through strain video monitoring data of a miter gate, and thereby increase the confidence in the remaining useful life (RUL) estimation using the updated degradation model.

A novel uncertainty evaluation method based on the particle filter and beta distribution for data with unknown distribution.

Uncertainty evaluation for unknown distribution data is a key problem to be solved in uncertainty evaluation theory. To evaluate the measurement uncertainty of data with unknown distributions, a novel uncertainty evaluation method based on the particle filter (PF) and beta distribution is proposed in this paper. A beta distribution with wide adaptability was adopted as the distribution type of measurement results, the parameters of the beta distribution were taken as the parameters to be estimated, and a state-space model was established. The PF method, suitable for non-Gaussian data, was utilized to obtain the estimates of the parameters of the beta distribution according to the measurement results. Finally, the best estimates of the measurement results and their uncertainty were calculated using the beta distribution parameters. Simulation results show that the proposed method is adaptive to accurately evaluate the measurement uncertainties of data, especially for non-Gaussian distribution data or asymmetrically distributed data. Multiple evaluation results show that the method has good robustness. The experimental results for the drift errors of a laser interferometer show that the uncertainty result of the proposed method is consistent with the Monte Carlo method. This method is suitable for a variety of distribution types that can be characterized through beta distribution and can solve the optimal estimation and uncertainty evaluation of most measurement results with unknown distribution types.