Fading Factor Research Articles

A Novel Speed Estimation Algorithm for a Permanent Magnet Linear Synchronous Motor Using an Extended Kalman Filter With Multiple Fading Factors

A Novel Speed Estimation Algorithm for a Permanent Magnet Linear Synchronous Motor Using an Extended Kalman Filter With Multiple Fading Factors

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Improving the performance of a MEMS-IMU system based on a false state-space model by using a fading factor adaptive Kalman filter

In this study, we introduce a novel algorithm, the low error rate adaptive fading Kalman filter (LERAFKF), designed to predict system states in the presence of uncertainty in both the system matrix and the model. The purpose of developing the LERAFKF is to address challenges arising from measurement difficulties, system parameter uncertainties, and state–space model inaccuracies. Several studies have utilized the Kalman filter (KF) and extended Kalman filter (EKF) algorithms to handle uncertainties in system parameters, corrupted measurements with unknown covariances, and incorrectly defined system modeling. Our work distinguishes itself by proposing a new approach that achieves lower error and deviation rates by combining the current Kalman estimation algorithm and the fading factor adaptive filter. To achieve this goal, we transformed the KF into an adaptive KF by introducing a forgetting factor, and the algorithm was subsequently reconfigured to calculate an optimized forgetting factor. In this study, we conducted simulations and measurements using both linear and nonlinear systems. The linear system represents the motion of an object, and the simulation involved measurements from the inertial navigation system (INS) sensor, specifically the Pololu IMU01b three-axis inertial measurement unit (IMU) sensor. We employed the SDI33 system with 9 degrees of freedom (DoF) mounted on a three-axis rotary table for the nonlinear system. This system simulates a missile as a 4th-order nonlinear system. Our findings demonstrate that the proposed LERAFKF filter outperforms KF and EKF in estimating system states, particularly in measurement-related error scenarios. Mean square error analysis further confirmed that LERAFKF exhibited the lowest error values, showcasing superior performance over KF and EKF in linear and nonlinear systems.

A method of voltage sag detection based on strong tracking SVD-UKF

Abstract Addressing issues of the traditional strong tracking unscented Kalman filtering (STUKF) algorithm in the process of voltage sag detection, such as inadequate precision, large computational complexity, and unstable iterative procedures, a method of voltage sag detection based on strong tracking SVD-UKF is proposed. Only one unscented transformation (UT) is used per iteration by establishing the linear state equation based on the voltage signal model, which simplifies the calculation procedure. Substituting singular value decomposition (SVD) for Cholesky decomposition averts the challenge of non-positive-definite error covariance matrix, ensuring stable execution of the algorithm. The action position of the fading factor is improved to further enhance detection precision. Through simulation experiments, we validate that the proposed method could effectively detect voltage sag characteristics, including amplitude, phase, and duration time.

Statistical spatial information based power optimization algorithm for multi-user massive MIMO systems

Power optimization has a significant role in multi-user massive multiple-input and multiple-output (mMIMO) wireless communication systems, whereas the acquisition of instantaneous channel state information (I-CSI) is a serious challenge in practical scenarios. The statistical spatial information (SPI), which contains angle-of-departures (AoDs) and corresponding large-scale fading factors, is slowly varying. The power optimization based on SPI to improve system performance needs to be explored for multi-user mMIMO systems. In this paper, two novel algorithms for SPI-based power optimization are proposed to maximize the ergodic sum-rate (ESR) under total power constraint for the system. Specifically, the minorization-maximization-based power optimization (MM-PO) algorithm and the closed-form power optimization (CF-PO) algorithm are proposed utilizing the minorization-maximization (MM) method and the fractional programming (FP) method, respectively. Moreover, the ESR is expressed based on the extracted SPI. The approximate expression of the ESR is derived. The complexity of the algorithms depends on the number of users, and the algorithms are scalable in the system. The proposed algorithms can effectively achieve the advantages of SPI while being robust to the uncertainty of I-CSI. Simulation results verify the ESR of our two proposed algorithms is 1.47 and 1.4 times higher than that of the equal power allocation algorithm at a high SNR when the number of antenna and user are equal to 64 and 20, respectively.

Agent-based Emotional Persuasion in the Psychological Counselling System for University Students

Chinese college students have a high demand for psychological counselling, and a survey by the National Institute of Psychology shows that college students are resistant to face-to-face psychological counselling. This paper integrates the emotion model with the emotion fading factor and emotion evaluation factor based on Agent and builds the models to give Agent the complex emotional characteristics of humans. This paper applies the agent-based emotional persuasion to the psychological counselling system and uses the emotional persuasion model to give full play to the influence of the Agent s decision-making process in the psychological counselling system.

SOC Estimation of Li-Ion Power Battery Based on Strong Tracking UKF with Multiple Suboptimal Fading Factors

SOC Estimation of Li-Ion Power Battery Based on Strong Tracking UKF with Multiple Suboptimal Fading Factors

A Combined UWB/IMU Localization Method with Improved CKF.

Aiming at the problem that ultra-wide band (UWB) cannot be accurately localized in environments with large noise variations and unknown statistical properties, a combinatorial localization method based on improved cubature (CKF) is proposed. First, in order to overcome the problem of inaccurate local approximation or even the inability to converge due to the initial value not being set near the optimal solution in the process of solving the UWB position by the least-squares method, the Levenberg-Marquardt algorithm (L-M) is adopted to optimally solve the UWB position. Secondly, because UWB and IMU information are centrally fused, an adaptive factor is introduced to update the measurement noise covariance matrix in real time to update the observation noise, and the fading factor is added to suppress the filtering divergence to achieve an improvement for the traditional CKF algorithm. Finally, the performance of the proposed combined localization method is verified by field experiments in line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios, respectively. The results show that the proposed method can maintain high localization accuracy in both LOS and NLOS scenarios. Compared with the Extended Kalman filter (EKF), unbiased Kalman filter (UKF), and CKF algorithms, the localization accuracies of the proposed method in NLOS scenarios are improved by 25.2%, 18.3%, and 11.3%, respectively.

A Li-Ion Battery State of Charge Estimation Strategy Based on the Suboptimal Multiple Fading Factor Extended Kalman Filter Algorithm

The state of charge (SOC) is an important indicator for evaluating a battery management system (BMS), which is crucial for the reliability, performance, and life management of a battery. In this paper, the characteristics of a Li-ion battery are deeply studied to explore the charge/discharge curve under different environments. Meanwhile, a second-order RC equivalent circuit model is constructed. The function identification of the EMF and SOC is performed based on the least squares method. The model estimation error is verified by simulation to be less than 0.05 V. Based on the Suboptimal Multiple Fading Factor Extended Kalman Filter (SMFEKF) algorithm, the SOC under constant current and UDDS conditions are estimated. Matlab/simulink simulations illustrate that the estimated accuracy of the proposed algorithm is improved by 79.36% compared with the EKF algorithm. Finally, the validity of the algorithm is verified jointly with the BMS. The results show that the estimation error is within 4% in both constant current condition as well as UDDS conditions, and it can still be predicted quickly and accurately under the uncertainty in the initial value of the SOC.

Combined Cubature Kalman and Smooth Variable Structure Filtering Based on Multi-Kernel Maximum Correntropy Criterion for the Fully Submerged Hydrofoil Craft

This paper introduces a novel filter algorithm termed as an MKMC-CSVSF which combined square-root cubature Kalman (SR-CKF) and smooth variable structure filtering (SVSF) under multi-kernel maximum correntropy criterion (MKMC) for accurately estimating the state of the fully submerged hydrofoil craft (FSHC) under the influence of uncertainties and multivariate heavy-tailed non-Gaussian noises. By leveraging the precision of the SR-CKF and the robustness of the SVSF against system uncertainties, the MKMC-CSVSF integrates these two methods by introducing a time-varying smooth boundary layer along with multiple fading factors. Furthermore, the MKMC is introduced for the adjustment of kernel bandwidths across different channels to align with the specific noise characteristics of each channel. A fuzzy rule is devised to identify the appropriate kernel bandwidths to ensure filter accuracy without undue complexity. The precision and robustness of state estimation in the face of heavy-tailed non-Gaussian noises are improved by modifying the SR-CKF and the SVSF using a fixed-point approach based on the MKMC. The experimental results validate the efficacy of this algorithm.

A novel suppressing Kalman filter divergence method for the state of charge estimation of lithium-ion batteries under complex conditions

The estimation method for state of charge (SOC) of lithium-ion batteries based on the Extended Kalman Filter (EKF) is prone to losing the ability to track sudden changes under complex driving conditions. Thus, this method cannot guarantee estimation accuracy and robustness. To overcome this deficiency, fading factors are introduced into the error covariance to enhance the effect of newly generated measurement data on the current filtering estimation. A Suboptimal Multiple Fading EKF (SMFEKF) SOC estimation method is proposed herein. The fading factors are solved by forcing the new error sequence of the predicted and actual terminal voltage values to remain orthogonal. The new error sequence that remains orthogonal undergoes transitions from strong autocorrelation in the original stable state to weak autocorrelation. Through real-time adjustment of the Kalman gain matrix, the effective tracking ability of the system in the event of sudden changes gets enhanced. To verify the effectiveness of the proposed method, first, a battery dynamic condition test library covering multiple driving scenarios (such as cities, suburbs, and highways) is established through ADVISOR advanced vehicle simulator driving condition tests. Second, a second-order equivalent circuit model is established and the recursive least squares method is used for parameter identification. Finally, a detailed comparison is made between SMFEKF and EKF in terms of SOC estimation accuracy and robustness under driving conditions with different levels of complexity. It is found that four operating conditions are the main reasons for filtering divergence in EKF. The results show that the root mean square errors of SMFEKF are 63.72 %, 54.20 %, and 21.30 % those of EKF under the three complex conditions, respectively. The new method effectively reduces SOC estimation error and solves the problem of EKF filtering divergence under complex conditions.

An adaptive robust strategy based on hypothesis testing for satellite clock bias short-term forecasting

The study of short-term forecasting of satellite clock bias (SCB) is important to promote the development of real-time precise point positioning, and the Kalman filter model has certain advantages over other models in the single forecast model. However, the filtering performance will be degraded by the model bias, and a fading factor is constructed to control the effect brought by the model bias. Considering that the fading factor may cause the covariance matrix to be abnormally inflated or even invalid when the observed information is unreliable, the chi-square test is introduced as a test indicator. At the current epoch moment, the fading factor or robust estimation is conditionally applied based on the result of the hypothesis test. An improved IGGIII weight function is used by the robust estimation, which simplifies the solution of the parametric robust solution. BeiDou satellite navigation system-3 satellite clock bias data with different clock types were selected for the analysis of fitting accuracy and forecasting accuracy, and the experimental results showed that the proposed algorithm can well eliminate the anomalous perturbation phenomenon caused by model deviation and improve the fitting accuracy. The comparison of forecast accuracy between the proposed strategy and GM(1,1), quadratic polynomial, and autoregressive integrated moving average (ARIMA) models at 3, 6, and 12 h intervals reveals that the proposed strategy consistently demonstrates optimal forecast accuracy.

A novel robust interacting multiple model filter for manoeuvering target tracking

AbstractA robust interacting multiple model approach is proposed to address the problem of accuracy and non‐Gaussian measurement noise in manoeuvering target tracking. The proposed approach introduces multiple fading factors into the prediction covariance matrix and adjusts each channel of the gain matrix in real time to improve the accuracy caused by model mismatch and enhance state transition capability. Considering the non‐Gaussian noise, an improved IMM filter is constructed to further improve the robustness using the maximum correntropy criterion. The simulation results show that the proposed approach can effectively suppress the non‐Gaussian noise and improve the accuracy with adaptability and robustness.

Multi-innovation and strong tracking based H[formula omitted] filter for state of charge estimation of lithium-ion batteries

Accurate state of charge (SOC) is a crucial indicator of the battery management system, which ensures the safety performance of lithium-ion batteries (LiBs). However, traditional SOC estimation methods such as extended Kalman filter and H∞ filter (HIF) do not perform satisfactorily when dealing with sudden state changes, which pose a safety hazard to the normal operation of LiBs. This paper proposes two effective strategies to endow the HIF with the strong tracking capability to react to state mutations. Initially, the single innovation in the HIF is extended to the multi-innovation so that the estimation accuracy is ameliorated by incorporating the historical data. Additionally, a suboptimal fading factor is introduced into the HIF to adjust the gain matrix online by forcing the innovation sequence to keep orthogonal. The fading factor fully utilizes the rich information in the innovation sequence, enabling the filter to track changing states well. Finally, the discharge experiments and dynamic stress tests are conducted to verify that the proposed strategy can ameliorate the precision and robustness without bringing extra computational burden.

A novel adaptive maximum correntropy cubature Kalman filter based on multiple fading factors

In this paper, an adaptive maximum correntropy cubature Kalman filter based on multiple fading factors (MAMCKF) is proposed to address the problem of inaccurate process noise covariance and unknown measurement noise covariance together with outliers in target tracking. Although there are many adaptive filters and robust filters have been proposed to handle unknown measurement noise covariance or measurement outliers, most filters cannot deal with both unknown noise covariance and outliers simultaneously. In this article, we propose an adaptive and robust cubature Kalman filter. The modified measurement noise covariance matrix (MNCM) and innovation covariance matrix are used to construct multiple fading factors for correcting the prediction error covariance matrix (PECM), which can achieve adaptability. Then, the maximum correntropy criterion (MCC) is introduced to suppress outliers, which further enhances the robustness. Compared with the existing approaches, the proposed approach improves the performance by at least 5% in unknown time-varying noise, unknown time-varying heavy-tailed noise, and non-Gaussian heavy-tailed noise scenarios. The simulation results show that the proposed approach can effectively suppress inaccurate process noise covariance and unknown time-varying measurement noise together with outliers. Compared with the existing filtering approaches, the proposed approach exhibits both adaptability and robustness.

System Identification of a Structure Equipped with a Cable-Bracing Inerter System Using Adaptive Extended Kalman Filter

An innovative cable-bracing inerter system (CBIS) has been proposed and shown to be effective in mitigating the structural response under dynamic excitation. The CBIS comprises an inerter element, an eddy current damping element, and a pair of tension-only cables that can transfer the story drift to rotating flywheels. To further investigate the characteristics of the CBIS, a system identification approach based on an adaptive extended Kalman filter (AEKF) and a recursive least-squares (RLS) algorithm is proposed. Depending on the CBIS model’s availability, the proposed approach uses two strategies: the AEKF identifies the parameters of the structure and the CBIS when the model is specific; alternatively, when the model is unspecific, the KF combined with an RLS algorithm identifies the restoring force generated by the CBIS as an unknown fictitious input. In addition, the AEKF incorporates a time-variant fading factor to track the target adaptively. The proposed approach is validated through free vibration and shaking table tests, demonstrating the accuracy in identifying structural parameters and restoring force provided by the CBIS. The identification process involves two stages: initially, the AEKF identifies the parameters of the bare structure without the CBIS, followed by a dual strategy using either AEKF or KF-RLS for identifying the parameters of the CBIS or its restoring force, respectively. The findings also verify the feasibility and validity of the mechanical model and operating principle of the CBIS, thereby contributing to the advancement and application of the CBIS in future studies.

Target Tracking Algorithm Based on Adaptive Strong Tracking Extended Kalman Filter

Kalman filtering is a common filtering method for millimeter-wave traffic radars. The proposal is for an Adaptive Strong Tracking Extended Kalman Filter (EKF) algorithm that aims to address the issues of classic EKF’s low accuracy and lengthy convergence time. This method, which incorporates time-varying fading effects into the covariance matrix of the traditional EKF, is based on the ST algorithm. It allows the recalibration of the covariance matrix and precise filtering and state estimation of the target vehicle. By altering the fading and attenuating factors of the ST algorithm and using orthogonality principles, many fine-tuned fading factors produced from least-squares optimization are introduced together with regionally optimum attenuation factors. The results of Monte Carlo experiments indicate that the average velocity inaccuracy is reduced by at least 38% in comparison to existing counterparts. The results validate the efficacy of this methodology in observing vehicular movements in metropolitan regions, satisfying the prerequisites of millimeter-wave radar technology for traffic monitoring.

Adaptive STCPF for UCA pose estimation with improved GA-BPNN and multiple fading factors

In response to the challenge of pose estimation accuracy for unmanned carrier-based aircraft in complex maritime landing environments, we propose an adaptive strong tracking cubature particle filtering method based on an improved Genetic Algorithm-Based Backpropagation Neural Network (GA-BPNN) and multiple fading factors. Despite the effectiveness of strong tracking cubature Kalman filtering (STCKF) in adjusting the covariance of prediction estimation errors using fading factors, it still has limitations in terms of model correction and parameter estimation. Addressing this issue, our research delves deeper into the role of fading factors in adjusting process noise covariance and introduces two methods to maintain covariance matrix symmetry: direct matrix solving and trace matrix solving. This novel approach directly implements real-time dynamic feedback correction of system model parameters within the filtering framework, effectively resolving filtering divergence issues while maintaining a high level of conceptual clarity and interpretability. To further enhance the algorithm’s performance, we introduce an improved neural network algorithm to compensate for linear approximation errors in fading factor calculations, thereby improving filtering accuracy. Moreover, considering the limitations of cubature Kalman filtering when dealing with non-Gaussian systems, we integrate the adaptive STCKF based on the improved GA-BPNN into particle filtering as an importance function, aiming to enhance non-Gaussian processing performance and alleviate particle degeneracy issues. In conclusion, both simulation and real-world data tests confirm the superiority of our research approach.

Estimation of road adhesion coefficient and sideslip angle for electric vehicles with slip-aware constraints using strong tracking unscented Kalman filter

Accurate estimation of road adhesion coefficient and sideslip angle are crucial for safer driving and ride quality of electric vehicles (EVs). To that end, an estimation algorithm of road adhesion coefficient and sideslip angle for EVs with slip-aware constraints and strong tracking unscented Kalman filter (SSTUKF) algorithm is designed in this paper. First, a vehicle system model is established as the basis for deriving the desirable estimation algorithm. Then, a strong tracking unscented Kalman filter (STUKF) algorithm with fading factor is presented to strengthen the correction effect of error covariance matrix used in unscented Kalman filter (UKF) algorithm. Meanwhile, slip-aware constraints are considered to calculate the adaptive compensated steering angle, which is obtained by repeated iteration of the fitness function. Additionally, a data fusion estimator is established based on the extremum theory to solve the problem of inaccurate estimation of sideslip angle under complex driving conditions. Finally, the CarSim-MATLAB/Simulink simulation platform is used to simulate under different driving conditions, and the simulation results reveal that the presented SSTUKF algorithm can enhance the estimation performance.

Fault-Tolerant Cubature Kalman Filter for Engineering Estimation Control Systems.

The cubature Kalman filter (CKF) overcomes the limitations of the Kalman filter in strong nonlinear systems, which has been widely used in many fields. However, in practical engineering, the abnormal measurement information obtained by the sensor causes the measurement noise covariance to change, which may deteriorate the filtering performance and even cause the filter failure. The fault-tolerant filter can deal with the state estimation problem for the systems with abnormal measurements. The key of the fault-tolerant filter is to forcefully correct filter innovation by using a fading factor. The fault-tolerant filter technology has been extensively applied in many practical systems, but it is still lack of reasonable theoretical analysis. To this end, the measurement noise model is established and the magnitude of the noise deviation is analyzed. The filtering performance under abnormal measurement is analyzed by three mean squared errors (MSEs), which are the ideal MSE, the filter calculated MSE and the true MSE. In order to solve the influence of sampling approximation deviation of CKF on fault detection, an improved fault detection algorithm is proposed. The performance of fault-tolerant CKF is analyzed from two views. The first view is about comparing the filter calculated MSEs of CKF and of fault-tolerant CKF, the second view is about comparing the relative closeness of the filter calculated MSE to the true MSE for the two algorithms. Numerical examples further verify these conclusions.