Particle Filter For Estimation Research Articles

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.

A hybrid residual correction method with auxiliary particle filter and conditional kernel density estimation for remaining useful life prediction

Predicting the remaining useful life (RUL) is crucial for prognosis and health management and provides an essential foundation for maintenance decisions. This study constructed a hybrid RUL prediction method based on residual correction to enhance prediction accuracy, minimize uncertainty, and mitigate errors caused by local fluctuations in the degeneration state within complex environments. This approach combined an auxiliary particle filter (APF), complementary ensemble empirical mode decomposition (CEEMD), and conditional kernel density estimation (CKDE). First, a Wiener degradation model was established, and the APF was used to acquire the initial state estimate of the equipment and residual difference between actual observations. Second, CEEMD was used to reconstruct the residual sequence and reduce interference. Subsequently, the nonparametric CKDE predicted the residual to correct the filter estimation. The corrected degeneration state value elucidated the local details of the system degradation process, and the point prediction of the RUL at the current time was obtained. The probability density distribution of the remaining life was estimated by substituting the modified degeneration state values into the kernel density estimation (KDE) model. Finally, the method was tested using an aircraft engine dataset. The results demonstrated the efficacy of the proposed method and its superiority over alternative approaches.

State of charge estimator based on tractable extended state observers for supercapacitor packs

A state of charge estimator (SOCE) is proposed for a single and a supercapacitor pack aimed at easy implementation and low computational cost extended state observers. This SOCE reduces modeling errors by implementing extended states using the classic supercapacitor equation. The proposed method involves a simple characterization of supercapacitors, which are tested using different discharge currents up to 40 [A] and subjected to added measurement noise. The proposed estimator is compared against different performance indexes, including the Unscented Kalman filter (UKF), unscented Kalman filter with parameter adaptation (PA), Extended Kalman Filter (EKF), Kalman filter with open-circuit voltage (OCV), Particle Filter (PF), and H-infinity estimator. This comparison was conducted using discharge profiles under different experimental conditions, where the SOCE herein proposed leads to the lowest error among all documented indexes and a performance improvement between 5.53 [%] and 99.90 [%]. Similarly, SOCE facilitates the characterization of the model inputs, reducing the preprocessing time while improving the execution time by 37 [%], and its estimation error by up to 86.77 [%]. These features enable the robust online implementation of embedded systems, improving SOC estimation.

A spawning particle filter for defocused moving target detection in GNSS-based passive radar

Global Navigation Satellite System (GNSS)-based passive radar (GBPR) has been widely used in remote sensing applications. However, for moving target detection (MTD), the quadratic phase error (QPE) introduced by the non-cooperative target motion is usually difficult to be compensated, as the low power level of the GBPR echo signal renders the estimation of the Doppler rate less effective. Consequently, the moving target in GBPR image is usually defocused, which aggravates the difficulty of target detection even further. In this paper, a spawning particle filter (SPF) is proposed for defocused MTD. Firstly, the measurement model and the likelihood ratio function (LRF) of the defocused point-like target image are deduced. Then, a spawning particle set is generated for subsequent target detection, with reference to traditional particles in particle filter (PF) as their parent. After that, based on the PF estimator, the SPF algorithm and its sequential Monte Carlo (SMC) implementation are proposed with a novel amplitude estimation method to decrease the target state dimension. Finally, the effectiveness of the proposed SPF is demonstrated by numerical simulations and preliminary experimental results, showing that the target range and Doppler can be estimated accurately.

Multidimensional Particle Filter for Long-Term Visual Teach and Repeat in Changing Environments

When a mobile robot is asked to navigate intelligently in an environment, it needs to estimate its own and the environment's state. One of the popular methods for robot state and position estimation is particle filtering (PF). Visual Teach and Repeat (VT&R) is a type of navigation that uses a camera to navigate the robot along the previously traversed path. Particle filters are usually used in VT&R to fuse data from odometry and camera to estimate the distance traveled along the path. However, in VT&R, there are other valuable states that the robot can benefit from, especially when moving through changing environments. We propose a multidimensional particle filter to estimate the robot state in VT&R navigation. Apart from the traveled distance, our particle filter estimates lateral and heading deviation from the taught path as well as the current appearance of the environment. This appearance is estimated using maps created across various environmental conditions recorded during the previous traversals. The joint state estimation is based on contrastive neural network architecture, allowing self-supervised learning. This architecture can process multiple images in parallel, alleviating the potential overhead caused by computing the particle filter over the maps simultaneously. We conducted experiments to show that the joint robot/environment state estimation improves navigation accuracy and robustness in a continual mapping setup. Unlike the other frameworks, which treat the robot position and environment appearance separately, our PF represents them as one multidimensional state, resulting in a more general uncertainty model for VT&R.

A comparative study of the unscented Kalman filter and particle filter estimation methods for the measurement of the road adhesion coefficient

Abstract. The measurement of the road adhesion coefficient is of great significance for the vehicle active safety control system and is one of the key technologies for future autonomous driving. With a focus on the problems of interference uncertainty and system nonlinearity in the estimation of the road adhesion coefficient, this work adopts a vehicle model with 7 degrees of freedom (7-DOF) and the Dugoff tire model and uses these models to estimate the road adhesion coefficient in real time based on the particle filter (PF) algorithm. The estimations using the PF algorithm are verified by selecting typical working conditions, and they are compared with estimations using the unscented Kalman filter (UKF) algorithm. Simulation results show that the road adhesion coefficient estimator error based on the UKF algorithm is less than 7 %, whereas the road adhesion coefficient estimator error based on the PF algorithm is less than 0.1 %. Thus, compared with the UKF algorithm, the PF algorithm has a higher accuracy and control effect with respect to estimating the road adhesion coefficient under different road conditions. In order to verify the robustness of the road adhesion coefficient estimator, an automobile test platform based on a four-wheel-hub-motor car is built. According to the experimental results, the estimator based on the PF algorithm can realize the road surface identification with an error of less than 1 %, which verifies the feasibility and effectiveness of the algorithm with respect to estimating the road adhesion coefficient and shows good robustness.

Temperature Control Unit—Modeling and Implementation of a Particle Filter on a Microcontroller

The paper discusses the possibilities of using particle filter estimation algorithms in embedded systems. For this purpose, the dedicated testing platform was built, which allowed for the determination of the estimation quality of a particle filter on a real system, and the microcontroller performance in that scenario. Tests were performed using the obsolete and not very efficient, although energy-saving, STM32F4 Discovery board—it has allowed for an in-depth analysis, and the results can be easily improved by switching to a modern platform. The quality of operations in open- and closed-loop systems was investigated based on the analysis of time simulations conducted for various mathematical models. These analyses made it possible to establish a correlation between the number of particles and the required calculation power. They have shown that it is possible to successfully implement and run a particle filter algorithm on an older and computationally limited device, as well as in real-time scenarios.

Nanoscale defect evaluation framework combining real-time transmission electron microscopy and integrated machine learning-particle filter estimation

Observation of dynamic processes by transmission electron microscopy (TEM) is an attractive technique to experimentally analyze materials’ nanoscale phenomena and understand the microstructure-properties relationships in nanoscale. Even if spatial and temporal resolutions of real-time TEM increase significantly, it is still difficult to say that the researchers quantitatively evaluate the dynamic behavior of defects. Images in TEM video are a two-dimensional projection of three-dimensional space phenomena, thus missing information must be existed that makes image’s uniquely accurate interpretation challenging. Therefore, even though they are still a clustering high-dimensional data and can be compressed to two-dimensional, conventional statistical methods for analyzing images may not be powerful enough to track nanoscale behavior by removing various artifacts associated with experiment; and automated and unbiased processing tools for such big-data are becoming mission-critical to discover knowledge about unforeseen behavior. We have developed a method to quantitative image analysis framework to resolve these problems, in which machine learning and particle filter estimation are uniquely combined. The quantitative and automated measurement of the dislocation velocity in an Fe-31Mn-3Al-3Si autunitic steel subjected to the tensile deformation was performed to validate the framework, and an intermittent motion of the dislocations was quantitatively analyzed. The framework is successfully classifying, identifying and tracking nanoscale objects; these are not able to be accurately implemented by the conventional mean-path based analysis.

Numerical simulation-aided particle filter-based damage prognosis using Lamb waves

Damage prognosis generally resorts to a damage evolution model and the current damage state to predict the future state and the remaining useful life (RUL). As a properly defined damage-sensitive statistical feature extracted from the Lamb waves can be used to online quantify the damage state, it is here exploited within a particle filter (PF) scheme to perform damage prognosis in structural health monitoring. An accurate mapping between the damage state and this feature would require a sufficient set of experimental Lamb waves collected in correspondence of different damage levels occurring during the run-to-failure process, which, however, is not usually available in real practice due to the high costs and the complex logistics involved in such experimental campaigns. In order to deal with this issue, this paper develops a new numerical simulation-aided particle filter-based damage prognosis framework, where the process equation is still built on the basis of available physical knowledge about the degradation process, whereas the measurement equation is built by means of a data-driven modeling approach using the features extracted from the numerically simulated Lamb waves. The PF framework serves as the state estimation tool which allows to identify the damage state and the parameters in the two equations. The future damage states and the RUL can finally be predicted by projecting the PF estimates in the future using the process equation. The proposed framework is demonstrated with reference to experimental studies of fatigue crack growth in aluminum lug structures with online Lamb wave monitoring.

Diffusion Particle Filtering on the Special Orthogonal Group Using Lie Algebra Statistics

In this paper, we introduce new distributed diffusion algorithms to track a sequence of hidden random matrices that evolve on the special orthogonal group. The algorithms are based on the Adapt-then-Combine and the Random Exchange methods, and diffuse Gaussian approximations of posterior densities computed in the Lie algebra of the special orthogonal group. Simulation results show that, in scenarios with nonlinear observation functions, the proposed algorithms perform closely to the centralized particle filter estimator and can outperform competing Extended Kalman Filters.

Predictive Monitoring of Shake Flask Cultures with Online Estimated Growth Models.

Simplicity renders shake flasks ideal for strain selection and substrate optimization in biotechnology. Uncertainty during initial experiments may, however, cause adverse growth conditions and mislead conclusions. Using growth models for online predictions of future biomass (BM) and the arrival of critical events like low dissolved oxygen (DO) levels or when to harvest is hence important to optimize protocols. Established knowledge that unfavorable metabolites of growing microorganisms interfere with the substrate suggests that growth dynamics and, as a consequence, the growth model parameters may vary in the course of an experiment. Predictive monitoring of shake flask cultures will therefore benefit from estimating growth model parameters in an online and adaptive manner. This paper evaluates a newly developed particle filter (PF) which is specifically tailored to the requirements of biotechnological shake flask experiments. By combining stationary accuracy with fast adaptation to change the proposed PF estimates time-varying growth model parameters from iteratively measured BM and DO sensor signals in an optimal manner. Such proposition of inferring time varying parameters of Gompertz and Logistic growth models is to our best knowledge novel and here for the first time assessed for predictive monitoring of Escherichia coli (E. coli) shake flask experiments. Assessments that mimic real-time predictions of BM and DO levels under previously untested growth conditions demonstrate the efficacy of the approach. After allowing for an initialization phase where the PF learns appropriate model parameters, we obtain accurate predictions of future BM and DO levels and important temporal characteristics like when to harvest. Statically parameterized growth models that represent the dynamics of a specific setting will in general provide poor characterizations of the dynamics when we change strain or substrate. The proposed approach is thus an important innovation for scientists working on strain characterization and substrate optimization as providing accurate forecasts will improve reproducibility and efficiency in early-stage bioprocess development.

Modeling brain connectivity dynamics in functional magnetic resonance imaging via particle filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that alterations in the interaction among brain areas can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition.

Emitter Location with Azimuth and Elevation Measurements Using a Single Aerial Platform for Electronic Support Missions.

Passive ground emitter geolocation techniques are essential to electronic warfare systems, as they provide threat warnings in hostile environments, while ensuring the electronic silence of the mission platform. Geolocation of enemy emitters indicates the position of and type of adversary troops, and allows for the use of guided munition against enemy targets. Three-dimensional geolocation solutions based on least squares and particle filter estimation, using only azimuth and elevation measurements, were considered. Three batch-processing and one instantaneous solution algorithms, i.e., using a single pulse or a single observation point, were developed and investigated. The performance of the proposed solutions was demonstrated by simulations. Results showed that the batch-processing solutions achieved acceptable accuracies with a sufficient number of observation points. The performance degraded with fewer observation points. The instantaneous geolocation solution improved performance with increasing observation points, i.e., working in the sequential mode, and therefore could approach the accuracy of the batch-processing solutions.

An equivalent circuit model for Vanadium Redox Batteries via hybrid extended Kalman filter and Particle filter methods

This paper proposes a model for parameter estimation of Vanadium Redox Flow Battery based on both the electrochemical model and the Equivalent Circuit Model. The equivalent circuit elements are found by a newly proposed optimization to minimized the error between the Thevenin and KVL-based impedance of the equivalent circuit. In contrast to most previously proposed circuit models, which are only introduced for constant current charging, the proposed method is applicable for all charging procedures, i.e., constant current, constant voltage, and constant current-constant voltage charging procedures. The proposed model is verified on a nine-cell VRFB stack by a sample constant current-constant voltage charging. As observed, in constant current charging mode, the terminal voltage model matches the measured data closely with low deviation; however, the terminal voltage model shows discrepancies with the measured data of VRFB in constant voltage charging. To improve the proposed circuit model's discrepancies in constant voltage mode, two Kalman filters, i.e., hybrid extended Kalman filter and particle filter estimation algorithms, are used in this study. The results show the accuracy of the proposed equivalent with an average deviation of 0.88% for terminal voltage model estimation by the extended KF-based method and the average deviation of 0.79% for the particle filter-based estimation method, while the initial equivalent circuit has an error of 7.21%. Further, the proposed procedure extended to estimate the state of charge of the battery. The results show an average deviation of 4.2% in estimating the battery state of charge using the PF method and 4.4% using the hybrid extended KF method, while the electrochemical SoC estimation method is taken as the reference. These two Kalman Filter based methods are more accurate compared to the average deviation of state of charge using the Coulomb counting method, which is 7.4%.

Stochastic modeling for tracking and prediction of gradual and transient battery performance degradation

As rechargeable battery-powered devices become a pervasive part of daily life, consumer standards for quality and reliability in these devices increase. One standard of particular interest is the ability to reliably track and predict the daily and lifetime capacity degradation of the batteries, over successive charge–discharge cycles. Tracking and predicting the degradation trend over batteries’ entire service lives can be challenging, not only due to the nonlinear degradation patterns subject to different usage conditions, but also because of the presence of transient regeneration events that can rapidly increase the battery's maximum capacity and affect degradation rates. Current methods in the literature commonly apply an exponential model in a Bayesian inference framework to track and predict global degradation trend, neglecting the transient behaviors and local fluctuations, hence leading to unsatisfactory performance. This paper presents a new customary model specifically designed to track the gradual battery degradation pattern, combined with a compound Poisson process-based model that aims to capture the transient behaviors. The integration of the two parts, forming a comprehensive degradation model, provides a more accurate description of capacity variation throughout battery's life cycle. During the model training phase, upon historical data, parameters involved in the two models are estimated through two Bayesian inference techniques: step-by-step estimation by a Particle Filter and batch estimation by a Markov Chain Monte Carlo algorithm, with their performance compared. The estimated parameters are then utilized for generating transient events and predicting future capacity degradation. NASA's lithium-ion battery data are analyzed to evaluate the effectiveness of the developed degradation model.

A Novel Gaussian Particle Swarms optimized Particle Filter Algorithm for the State of Charge Estimation of Lithium-ion Batteries

A gaussian particle swarm optimized particle filter estimation method, along with the second-order resistance-capacitance model, is proposed for the state of charge estimation of lithium-ion battery in electric vehicles. Based on the particle filter method, it exploits the strong optimality-seeking ability of the particle swarm algorithm, suppressing algorithm degradation and particle impoverishment by improving the importance distribution. This method also introduces normally distributed decay inertia weights to enhance the global search capability of the particle swarm optimization algorithm, which improves the convergence of this estimation method. As can be known from the experimental results that the proposed method has stronger robustness and higher filter efficiency with the estimation error steadily maintained within 0.89% in the constant current discharge experiment. This method is insensitive to the initial amount and distribution of particles, achieving adaptive and stable tracking in the state of charge for lithium-ion batteries.

SOC Estimation of a Rechargeable Li-Ion Battery Used in Fuel Cell Hybrid Electric Vehicles—Comparative Study of Accuracy and Robustness Performance Based on Statistical Criteria. Part II: SOC Estimators

The purpose of this paper is to analyze the accuracy of three state of charge (SOC) estimators of a rechargeable Li-ion SAFT battery based on two accurate Li-ion battery models, namely a linear RC equivalent electrical circuit (ECM) and a nonlinear Simscape generic model, developed in Part 1. The battery SOC of both Li-ion battery models is estimated using a linearized adaptive extended Kalman filter (AEKF), a nonlinear adaptive unscented Kalman filter (AUKF) and a nonlinear and non-Gaussian particle filter estimator (PFE). The result of MATLAB simulations shows the efficiency of all three SOC estimators, especially AEKF, followed in order of decreasing performance by AUKF and PFE. Besides, this result reveals a slight superiority of the SOC estimation accuracy when using the Simscape model for SOC estimator design. Overall, the performance of all three SOC estimators in terms of accuracy, convergence of response speed and robustness is excellent and is comparable to state of the art SOC estimation methods.

Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem

In the applied mathematical modelling of heat transfer systems, the heat transfer coefficient (HTC) is one of the most important parameters. This paper proposes a combination of the Method of Fundamental Solutions (MFS) with particle filter Sequential Importance Resampling (PF-SIR) to estimate the time-dependent HTC in two-dimensional transient inverse heat conduction problems from non-standard boundary integral measurements. These measurements ensure the unique solvability of the boundary coefficient identification problem. Numerical results show high performance on several test cases with both linear and nonlinear Robin boundary conditions, supporting the synergy between the MFS and simulation-based particle filter sequential analysis methods.

Estimation of Traffic Stream Density Using Connected Vehicle Data: Linear and Nonlinear Filtering Approaches.

The paper presents a nonlinear filtering approach to estimate the traffic stream density on signalized approaches based solely on connected vehicle (CV) data. Specifically, a particle filter (PF) is developed to produce reliable traffic density estimates using CV travel-time measurements. Traffic flow continuity is used to derive the state equation, whereas the measurement equation is derived from the hydrodynamic traffic flow relationship. Subsequently, the PF filtering approach is compared to linear estimation approaches; namely, a Kalman filter (KF) and an adaptive KF (AKF). Simulated data are used to evaluate the performance of the three estimation techniques on a signalized approach experiencing oversaturated conditions. Results demonstrate that the three techniques produce accurate estimates—with the KF, surprisingly, being the most accurate of the three techniques. A sensitivity of the estimation techniques to various factors including the CV level of market penetration, the initial conditions, and the number of particles in the PF is also presented. As expected, the study demonstrates that the accuracy of the PF estimation increases as the number of particles increases. Furthermore, the accuracy of the density estimate increases as the level of CV market penetration increases. The results indicate that the KF is least sensitive to the initial vehicle count estimate, while the PF is most sensitive to the initial condition. In conclusion, the study demonstrates that a simple linear estimation approach is best suited for the proposed application.

Semantic Localization System for Robots at Large Indoor Environments Based on Environmental Stimuli.

In this paper, we present a new procedure to solve the global localization of mobile robots called Environmental Stimulus Localization (ESL). We propose that the presence of common facts on the environment around the robot can be considered as stimuli for the procedure. The robust performance of our approach is supported by two concurrent particle filters. A primary particle filter estimates and tracks the robot position, while a secondary filter is fired by environmental stimuli, helps to reduce the influence of measurement errors and allows an earlier recovery from localization failures. We have successfully used this method in a 5000 m real indoor environment using as inputs the available environment information from a Geographical Information System (GIS) map, the robot’s odometry and the output of an algorithm for the perception of facts from the environment. We present a case study and the result of different tests, showing the performance of our method under the influence of errors in real applications.