Kalman Particle Filter Research Articles

Non-Line-of-Sight Positioning Method for Ultra-Wideband/Miniature Inertial Measurement Unit Integrated System Based on Extended Kalman Particle Filter

In the field of unmanned aerial vehicle (UAV) control, high-precision navigation algorithms are a research hotspot. To address the problem of poor localization caused by non-line-of-sight (NLOS) errors in ultra-wideband (UWB) systems, an UWB/MIMU integrated navigation method was developed, and a particle filter (PF) algorithm for data fusion was improved upon. The extended Kalman filter (EKF) was used to improve the method of constructing the importance density function (IDF) in the traditional PF, so that the particle sampling process fully considers the real-time measurement information, increases the sampling efficiency, weakens the particle degradation phenomenon, and reduces the UAV positioning error. We compared the positioning accuracy of the proposed extended Kalman particle filter (EKPF) algorithm with that of the EKF and unscented Kalman filter (UKF) algorithm used in traditional UWB/MIMU data fusion through simulation, and the results proved the effectiveness of the proposed algorithm through outdoor experiments. We found that, in NLOS environments, compared with pure UWB positioning, the accuracy of the EKPF algorithm in the X- and Y-directions was increased by 35% and 39%, respectively, and the positioning error in the Z-direction was considerably reduced, which proved the practicability of the proposed algorithm.

Parameter Identification of Maritime Vessel Rudder PMSM Based on Extended Kalman Particle Filter Algorithm

To address the issue of system parameter variations during the operation of a maritime light vessel rudder permanent magnet synchronous motor (PMSM), an extended Kalman particle filter (EKPF) algorithm that combines a particle filter (PF) with an extended Kalman filter (EKF) is proposed in this paper. This approach enables the online identification of motor resistance and inductance. For highly nonlinear problems that are challenging for traditional methods such as Kalman filtering, this algorithm is typically a statistical and effective estimation method that usually yields good results. Firstly, a standard linear discrete parameter identification model is established for a PMSM. Secondly, the PF algorithm based on Bayesian state estimation as a foundation for subsequent research is derived. Thirdly, the advantages and limitations of the PF algorithm are analyzed, addressing issues such as sample degeneracy, by integrating it with the Kalman filtering algorithm. Specifically, the EKPF algorithm for online parameter identification is employed. Finally, the identification model within MATLAB/Simulink is constructed and the simulation studies are executed to ascertain the viability of our suggested algorithm. The outcomes from these simulations indicate that the proposed EKPF algorithm identifies resistance and inductance values both swiftly and precisely, markedly boosting the robustness and enhancing the control efficacy of the PMSM.

Implementation of unknown parameter estimation procedure for hybrid and discrete non‐linear systems

AbstractThe application of the hybrid extended Kalman filter (HEKF), hybrid unscented Kalman filter (HUKF), hybrid particle filter (HPF), and hybrid extended Kalman particle filter (HEKPF) is discussed for hybrid non‐linear filter problems, when prediction equations are continuous‐time and the update equations are discrete‐time, and also the discrete extended Kalman filter (DEKF), discrete unscented Kalman filter (DUKF), discrete particle filter (DPF), and discrete extended Kalman particle filter (DEKPF) for discrete‐time non‐linear filter problems, when prediction equations and update equations are discrete‐time. In order to assess the performance of the filters, the authors consider the non‐linear dynamics for a re‐entry vehicle. The filters are used in two hybrid and discrete states to estimate the position, velocity, and drag parameter associated with the re‐entry vehicle. Theoretical topics concerning estimating the drag parameter of a vehicle in re‐entry phase have been dealt with. Drag parameter estimation is carried out using a combination of hybrid filters and discrete filters as an effective estimator and fixed value, forgetting factor, and Robbins‐Monro stochastic approximation methods as the noise covariance matrix adjuster of the parameter.

An active equalization strategy for series-connected lithium-ion battery packs based on a dual threshold trigger mechanism

It is well acknowledged to all that an active equalization strategy can overcome the inconsistency of lithium-ion cell's voltage and state of charge (SOC) in series-connected lithium-ion battery (LIB) pack in the electric vehicle application. In this regard, a novel dual threshold trigger mechanism based active equalization strategy (DTTM-based AES) is proposed to overcome the inherent inconsistency of cells and to improve the equalization efficiency for a series-connected LIB pack. First, a modified dual-layer inductor equalization circuit is constructed to make it possible for the energy transfer path optimization. Next, based on the designed dual threshold trigger mechanism provoked by battery voltage and SOC, an active equalization strategy is proposed, each single cell's SOC in the battery packs is estimated using the extended Kalman particle filter algorithm. Besides, on the basis of the modified equalization circuit, the improved particle swarm optimization is adopted to optimize the energy transfer path with aiming to reduce the equalization time. Lastly, the simulation and experimental results are provided to validate the proposed DTTM-based AES.

Enhanced high-resolution structural crack detection using hybrid interacting Particle-Kalman filter

Monitoring the health of large-scale infrastructure with the required precision necessitates high-dimensional support models and extensive instrumentation. However, in a model-based structural health monitoring (SHM) framework, the ability to localize damage is constrained by the discretization of the model. To enhance the resolution of discretization, dense instrumentation is essential to address the inherent challenges in solving the inverse problem. Yet, increasing dimensionality can introduce detection delays, a critical concern in SHM. Additionally, addressing uncertainties stemming from the model, measurements, or external factors is crucial for reliable real-world SHM. This study focuses on localized damages, such as cracks, where detection precision is paramount. To tackle these challenges, this study proposes an innovative hybrid interacting Particle-Kalman filter (h-IPKF)-based SHM approach that surpasses model discretization limitations for detection resolution. This approach employs two distinct indices for crack localization: global (GDI) and local (LDI) damage indices. GDI identifies the affected element using a coarsely discretized predictor model, while LDI precisely pinpoints the crack location within the element. This paper represents the crack as a massless rotational spring with deteriorated stiffness (γ) and parameterizes it using GDI, LDI, and γ. Subsequently, the h-IPKF framework is employed to estimate the crack parameters, capable of handling both continuous and discrete random variables, which is advantageous for addressing discrete variables like GDI. Extensive numerical and real validation tests on beam structures were conducted to assess the algorithm’s sensitivity to noise and damage severity, demonstrating its efficiency, promptness, and precision in detecting cracks within structures.

State of Charge Estimation for Lithium‑Ion Batteries Based on Extended Kalman Particle Filter and Orthogonal Optimized Battery Model

AbstractState of charge (SOC) is a key state variable in lithium‑ion battery management system. The battery model and estimation algorithm are important factors that affect the accuracy of SOC estimation. In this paper, the optimization battery model is created by optimizing the hybrid power pulse characteristic (HPPC) parameter combination through orthogonal analysis. The simulation results demonstrate that optimizing the HPPC parameter combinations can improve battery modeling accuracy. Then, an extended Kalman particle filter (EKPF) algorithm is proposed by using the extended Kalman filter (EKF) algorithm as the density function of the particle filter (PF) algorithm. The EKPF algorithm is verified under the dynamic stress test and Beijing bus dynamic stress test conditions, the root mean absolute errors and root mean square errors in all cases are less than 1.5%. The experimental results show that the EKPF algorithm can combine the advantages of EKF and PF to estimate lithium‐ion battery SOC accurately.

An Iterative Augmented Unscented Kalman Particle Filter for Simultaneous State-Parameter-Input Estimation for Structural Systems Subjected to Gamma-Distribution Noise

Simultaneous estimations of the states, parameters and unknown inputs of nonlinear structural systems subjected to non-Gaussian noise are essential, because the inputs are not always available and the system noise is not always Gaussian. However, filters developed for this task require the inter-story drift measurements to be “fused” with the acceleration measurements to avoid the “drift phenomenon”. Because inter-story drifts may be inconvenient to obtain in practice, it is more desirable to use acceleration measurements only. To this end, this study develops a novel iterative augmented unscented Kalman particle filter (IAUKPF) for the simultaneous state-parameter-input estimation for systems subjected to non-Gaussian noise. The iterative strategy proposed in this study effectively corrects the “drift phenomenon” when only acceleration measurements are incorporated, so that the accuracies of the estimated unknown inputs are promoted. The importance density of the particle filter at each time step is provided by the augmented unscented Kalman filter so that the filter takes the best known information into consideration. Numerical examples of nonlinear structural systems affected by non-Gaussian noise are adopted to examine the effectiveness of the proposed IAUKPF.

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.

Co-estimation of SOC and SOH for Li-ion battery based on MIEKPF-EKPF fusion algorithm

This paper uses the EKPF algorithm to directly measure the state of charge (SOC) and state of health (SOH) of Li-ion batteries and proposes a combination of multi-innovation-based extended Kalman particle filter (MIEKPF) and extended Kalman particle filter (EKPF) to estimate SOC. Firstly, the EKPF algorithm is applied to identify parameters and estimate SOH online, and the identification results of resistance and capacitance parameters are as input to compensate for the errors arising from considering the effects of battery aging in estimating SOC, thus improving the model accuracy. Secondly, the proposed fusion of multiple new interest discrimination theories and extended Kalman particle filtering algorithm, which takes into account the influence of past observations on the current value, enables the collaborative estimation of SOC and SOH over the whole Li-ion battery cycle. Finally, the MIEKPF-EKPF algorithm is compared with other existing algorithms to limit the average and maximum errors of SOC to 0.48% and 2%, respectively, during the New European Driving Cycle (NEDC) operating conditions. The simulation results verify the feasibility and accuracy of the proposed method.

Lithium-ion battery health estimation with real-world data for electric vehicles

Complex environments and variable working conditions lead to irreversible attenuation of battery pack capacity in electric vehicles (EVs). Online capacity estimation is of great significance for battery pack management and maintenance. This work proposes a state-of-health (SOH) attenuation model considering driving mileage and seasonal temperature for battery health estimation. Firstly, a variable forgetting factor recursive least square (VFFRLS) algorithm is proposed for battery model parameter identification. It adaptively adjusts the forgetting factor according to current fluctuations. Then, an extended Kalman-particle filter (EPF) algorithm is proposed for online capacity estimation. In addition, a battery pack SOH attenuation model is constructed considering seasonal temperature and driving mileage. Finally, the performance of the proposed model and algorithm is verified with nine months of actual vehicle data. The experimental results show that the proposed parameter identification and capacity estimation algorithm can accurately estimate the model parameters and capacity. The average capacity of the battery module decreases with the total mileage. The compensation of monthly driving mileage and ambient temperature factors effectively improves the accuracy of SOH model.

A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on a nonlinear and quadratic-type interaction function defined in terms of the sample covariance of the particles. Most of the literature in applied mathematics and computer science on these sophisticated interacting particle methods amounts to designing different classes of useable observer-type particle methods. These methods are based on a variety of inconsistent but judicious ensemble auxiliary transformations or include additional inflation/localisationtype algorithmic innovations, in order to avoid the inherent time-degeneracy of an insufficient particle ensemble size when solving a filtering problem with an unstable signal. To the best of our knowledge, the first and the only rigorous mathematical analysis of these sophisticated discrete generation particle filters is developed in the pioneering articles by Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the early 2010s. Nevertheless, besides the fact that these studies prove the asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly pessimistic meanerror estimates that grow exponentially fast with respect to the time horizon, even for linear Gaussian filtering problems with stable one dimensional signals. In the present article we develop a novel self-contained and complete stochastic perturbation analysis of the fluctuations, the stability, and the long-time performance of these discrete generation ensemble Kalman particle filters, including time-uniform and non-asymptotic mean-error estimates that apply to possibly unstable signals. To the best of our knowledge, these are the first results of this type in the literature on discrete generation particle filters, including the class of genetic-type particle filters and discrete generation ensemble Kalman filters. The stochastic Riccati difference equations considered in this work are also of interest in their own right, as a prototype of a new class of stochastic rational difference equation.

Remaining useful life prediction of lithium-ion battery based on chaotic particle swarm optimization and particle filter

The remaining useful life (RUL) prediction of lithium-ion batteries is crucial to ensure the safety and reliability of electric vehicles. Due to the complexity of the battery aging mechanism, the accurate prediction of RUL by traditional methods is difficult to guarantee. To improve the prediction performance of the particle filter (PF), an improved particle filter based on the chaotic particle swarm optimization algorithm (CPSO-PF) is presented. Then it is applied to predict the RUL of lithium-ion batteries. First, for a better posterior estimate in the PF, CPSO is used to drive the prior distribution of the particles toward a high likelihood probability to obtain a better-proposed distribution, which helps overcome the problem of degeneracy and impoverishment of particles. Then, Three models were employed to track the degradation trajectory of the batteries, including PF、the extended Kalman particle filter (EKPF), and CPSO-PF. Finally, the RUL of lithium-ion batteries was predicted with the three models. The experimental results demonstrate that CPSO-PF has higher prediction accuracy and strong robustness.

Timestamp-Free Synchronization Under Delays With Arbitrary Distribution in Wireless Sensor Networks

Clock synchronization is a key technology in wireless sensor networks (WSNs). It is significant and challenging to track clock parameters under arbitrary delay distributions. This letter proposes an Adaptive Gaussian mixture extended Kalman particle filter (AGMEKPF), which is robust to arbitrarily distributed delays in practical WSNs and can jointly track clock skew and offset. It is combined with the timestamp-free synchronization, which is a clock synchronization protocol that can effectively reduce energy consumption without exchanging timestamps. Simulation results show that the proposed method outperforms similar methods in terms of accuracy and complexity.

Direct tracking of noncircular sources for multiple arrays via improved unscented particle filter method

AbstractDirect tracking problem of moving noncircular sources for multiple arrays is investigated in this study. Here, we propose an improved unscented particle filter (I‐UPF) direct tracking method, which combines system proportional symmetry unscented particle filter and Markov Chain Monte Carlo (MCMC) algorithm. Noncircular sources can extend the dimension of sources matrix, and the direct tracking accuracy is improved. This method uses multiple arrays to receive sources. Firstly, set up a direct tracking model through consecutive time and Doppler information. Subsequently, based on the improved unscented particle filter algorithm, the proposed tracking model is to improve the direct tracking accuracy and reduce computational complexity. Simulation results show that the proposed improved unscented particle filter algorithm for noncircular sources has enhanced tracking accuracy than Markov Chain Monte Carlo unscented particle filter algorithm, Markov Chain Monte Carlo extended Kalman particle filter, and two‐step tracking method.

Feature Fusion-Based Inconsistency Evaluation for Battery Pack: Improved Gaussian Mixture Model

The large-scale grouping of the battery system leads to the inconsistency of the battery pack. Aiming at tacking this issue, an inconsistency evaluation method is deployed for the battery pack based on an improved Gaussian mixture model (GMM) and feature fusion approach. Specifically, the proposed adaptive forgetting factor recursive least squares (AFFRLS) algorithm allows the open-circuit voltage and other parameters to be jointly identified without the open circuit voltage-state of charge (OCV-SOC) test. An online capacity estimation approach with the extended Kalman particle filter (EPF) is put forward for capacity estimation. Further, an improved GMM is proposed to visualize battery pack inconsistency, using the K-means++ algorithm to initialize category centers. The standard deviation coefficient approach quantifies the inconsistency. Finally, the real-life vehicle data are performed to validate the effectiveness of the proposed method. The experimental results show that the proposed method can evaluate the battery parameters accurately. With the increase in service time, the inconsistency of the battery pack is gradually deteriorating.

Hyperelliptic Kalman filter-based aeroengine sensor fault FDIA system under multi-source uncertainty

Aeroengine faces multi-source uncertainty while operating. To reduce the conservativeness and improve the performance of the diagnosis system in complex environments, the multi-source uncertainty environment, which consists of aeroengine epistemic uncertainty and stochastic uncertainty of the control system, is considered in this paper. Based on polynomial chaos expansion (PCE), the uncertainty of the state response and output response is quantified. In addition, by proposing the hyperelliptic Kalman filter (HeKF), the optimal estimation of state correlation and output variance is realized, and the adaptive weighting matrix is provided on this basis. Combined with the thresholds calculated by design indicators of the diagnosis system, conservativeness-reduced fault detection is achieved. Ultimately, based on the fault matching idea, the hyperelliptic Kalman filter bank (HeKFB) is established and implemented for fault isolation and accommodation. Open-loop and closed-loop numerical simulations demonstrate that the proposed HeKF-based aeroengine sensor fault detection, isolation, and accommodation (FDIA) system is efficient under multi-source uncertainty conditions. Furthermore, compared to the extended Kalman filter (EKF) and the Kalman particle filter (KPF), the HeKF-based FDIA system is less conservative, more sensitive to minor faults, and superior in guaranteeing the security and reliability of aeroengine operation.

XGBoost-Based Remaining Useful Life Estimation Model with Extended Kalman Particle Filter for Lithium-Ion Batteries

The instability and variable lifetime are the benefits of high efficiency and low-cost issues in lithium-ion batteries.An accurate equipment's remaining useful life prediction is essential for successful requirement-based maintenance to improve dependability and lower total maintenance costs. However, it is challenging to assess a battery's working capacity, and specific prediction methods are unable to represent the uncertainty. A scientific evaluation and prediction of a lithium-ion battery's state of health (SOH), mainly its remaining useful life (RUL), is crucial to ensuring the battery's safety and dependability over its entire life cycle and preventing as many catastrophic accidents as feasible. Many strategies have been developed to determine the prediction of the RUL and SOH of lithium-ion batteries, including particle filters (PFs). This paper develops a novel PF-based technique for lithium-ion battery RUL estimation, combining a Kalman filter (KF) with a PF to analyze battery operating data. The PF method is used as the core, and extreme gradient boosting (XGBoost) is used as the observation RUL battery prediction. Due to the powerful nonlinear fitting capabilities, XGBoost is used to map the connection between the retrieved features and the RUL. The life cycle testing aims to gather precise and trustworthy data for RUL prediction. RUL prediction results demonstrate the improved accuracy of our suggested strategy compared to that of other methods. The experiment findings show that the suggested technique can increase the accuracy of RUL prediction when applied to a lithium-ion battery's cycle life data set. The results demonstrate the benefit of the presented method in achieving a more accurate remaining useful life prediction.

A Composite State of Charge Estimation for Electric Vehicle Lithium-Ion Batteries Using Back-Propagation Neural Network and Extended Kalman Particle Filter

Accurate estimation of battery state of charge (SOC) plays a crucial role for facilitating intelligent battery management system development. Due to the high nonlinear relationship between the battery open-circuit voltage (OCV) and SOC, and the shortcomings of traditional polynomial fitting approach, it is an even more challenging task for predicting battery SOC. To address these challenges, this paper presents a composite SOC estimation approach for lithium-ion batteries using back-propagation neural network (BPNN) and extended Kalman particle filter (EKPF). First, a second order resistance capacitance model is established to make parameters identification of a lithium-ion battery cell using recursive least squares algorithm with forgetting factors (FFRLS) approach. Then, BPNN is used to fit the desired OCV-SOC relationship with relatively high precision. Next, by incorporating the extended Kalman filter (EKF) into the particle filter (PF), an expected EKPF approach is presented to realize the SOC estimation. Last, the performances of SOC estimation using different methods, namely the PF, EKF and the EKPF are compared and analyzed under constant current discharge and urban dynamometer driving schedule working conditions. The experimental results show that the proposed method has higher accuracy and robustness compared to the other two SOC estimation methods.

A generalized extended Kalman particle filter with unknown input for nonlinear system‐input identification under non‐Gaussian measurement noises

It is necessary to investigate the identification of structural systems and unknown inputs under non-Gaussian measurement noises. In recent years, a few scholars have proposed methods of particle filter (PF) with unknown input for such task. However, these PF with unknown input require that unknown inputs appear in structural measurement equations. Such requirement may not always met, which restrict their practical application. To overcome this limitation, a generalized extended Kalman particle filter with unknown input (GEKPF-UI) is proposed for the simultaneous identification of structural systems and unknown inputs under non-Gaussian measurement noises. The proposed method is more general than the existing methods of PF with unknown input as it is applicable whether measurement equations contain or do not contain unknown inputs. It is proposed to establish the importance density function of PF by the generalized extended Kalman filter with unknown input (GEKF-UI) recently developed by the authors, in which GEKF-UI is utilized to generate particles and allow particles to carry the latest observational information. The effectiveness of the proposed method is verified through two numerical identification examples of a nonlinear hysteretic structure under two types of unknown inputs, including unknown external excitation and unknown seismic inputs, respectively.

Decision-directed Kalman particle filter with application to the MIMO phase noise channel

Demodulation of data transmitted over time-varying channels with a free running hidden Markov state, like the phase noise channel or the fading channel, requires that the receiver tracks the hidden channel state. The tracking technique adopted in the paper is based on non-data-aided sequential importance sampling, also known as particle filtering.The paper proposes a new particle filtering framework for data communication receivers based on an importance distribution such that each individual particle becomes a decision-directed Kalman filter relying upon its local symbol-by-symbol hard decisions. In this framework, different particles are left free to take different sequences of decisions. This leaves to the receiver the possibility of exploring different sequences of transmitted modulation symbols. The weight of the particle will be high for those particles that took in the past the correct sequence of decisions, while will be low for those particles that took wrong decisions. In the resampling procedure, particles with high weight will survive, while particles with low weight will be terminated, leaving space to the birth of new particles resampled from the surviving ones.The crucial point in importance sampling is the choice of the importance distribution and the main novelty of the paper is the proposal of an importance distribution such that the particles of the particle filter become decision-directed Kalman filters. One important benefit brought by our proposed method is that, being non-data-aided, it does not need pilot symbols, thus allowing to preserve the transmission rate. A significant application example, presented and developed in the paper, is constituted by MIMO systems affected by phase noise, where the channel state vector consists of many parameters.