Extended Kalman Filter Algorithm Research Articles

The Efficiency of the Kalman Filter in Nodal Redundancy

The growing integration of distributed energy resources underscores the critical importance of having precise insights into the dynamics of an electrical power system (EPS). Consequently, an estimator must align with the EPS dynamics to enhance the overall reliability, safety, and system stability. This alignment ensures that operators can make informed decisions during system operations. An initial step in gaining insight into the system’s state involves examining its state vector, which is represented by voltage phasors. These results are derived through the application of a distributed state-estimation process in large-scale systems. This study delved into the effectiveness of Bayesian filters, with a particular emphasis on the extended Kalman filter (EKF) algorithm in the context of distributed state estimation. To analyze the outcomes, the nodal partitioning process was incorporated within the distributed state-estimation framework. The synergy between the EKF algorithm and the partitioning method was evaluated using the IEEE118 test system.

Study on the estimation of the state of charge of lithium-ion battery

Lithium-ion battery (LIB) occupies a major position in rechargeable batteries. However, if the state of charge (SOC) estimation of LIB is not accurate, it will lead to the decline of battery life. SOC is often estimated by the extended Kalman filter (EKF) algorithm, but this method depends on the accuracy of model parameters. The sampling point interval time can affect the accuracy of SOC estimation. In this paper, the first-order RC model parameters are identified by two methods and the SOC is estimated by the EKF algorithm. Using this method, the battery parameters are received more accurate and the SOC estimation error is smaller. When the sampling interval is 0.03 s, the SOC estimation error is the smallest. And the second-order RC model can receive the same result. When the sampling interval is 0.03 s, the SOC estimation error of the 1RC-1 method is less than 1.4 %, the SOC estimation error of the 1RC-2 method is less than 0.017, and the root mean square error (RMSE) is 0.0087 and 0.01084. The conclusion is also used in the second-order RC model and contributes to the improvement of the SOC estimation accuracy. An effective method to estimate the battery SOC range is also proposed. This paper provides an effective method for obtaining more accurate SOC.

Adaptive nonlinear Kalman filters based on credibility theory with noise correlation

To solve the divergence problem and overcome the difficulty in guaranteeing filtering accuracy during estimation of the process noise covariance or the measurement noise covariance with traditional new information-based nonlinear filtering methods, we design a new method for estimating noise statistical characteristics of nonlinear systems based on the credibility Kalman Filter (KF) theory considering noise correlation. This method first extends credibility to the Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) based on the credibility theory. Further, an optimization model for nonlinear credibility under noise related conditions is established considering noise correlation. A combination of filtering smoothing and credibility iteration formula is used to improve the real-time performance of the nonlinear adaptive credibility KF algorithm, further expanding its application scenarios, and the derivation process of the formula theory is provided. Finally, the performance of the nonlinear credibility filtering algorithm is simulated and analyzed from multiple perspectives, and a comparative analysis conducted on specific experimental data. The simulation and experimental results show that the proposed credibility EKF and credibility UKF algorithms can estimate the noise covariance more accurately and effectively with lower average estimation time than traditional methods, indicating that the proposed algorithm has stable estimation performance and good real-time performance.

Research on Vision-Based Servoing and Trajectory Prediction Strategy for Capturing Illegal Drones

A proposed strategy for managing airspace and preventing illegal drones from compromising security involves the use of autonomous drones equipped with three key functionalities. Firstly, the implementation of YOLO-v5 technology allows for the identification of illegal drones and the establishment of a visual-servo system to determine their relative position to the autonomous drone. Secondly, an extended Kalman filter algorithm predicts the flight trajectory of illegal drones, enabling the autonomous drone to compensate in advance and significantly enhance the capture success rate. Lastly, to ensure system robustness and suppress interference from illegal drones, an adaptive fast nonsingular terminal sliding mode technique is employed. This technique achieves finite time convergence of the system state and utilizes delay estimation technology for the real-time compensation of unknown disturbances. The stability of the closed-loop system is confirmed through Lyapunov theory, and a model-based hardware-in-the-loop simulation strategy is adopted to streamline system development and improve efficiency. Experimental results demonstrate that the designed autonomous drone accurately predicts the trajectory of illegal drones, effectively captures them using a robotic arm, and maintains stable flight throughout the process.

Temperature homogenization control of parabolic trough solar collector field based on hydraulic calculation and extended Kalman filter

Parabolic Trough Collector fields serve as the heat-absorbing components in large-scale commercial solar trough power plants. However, they frequently encounter challenges related to uneven spatial distribution of solar irradiation and heat transfer fluid flow. These disparities often lead to temperature inhomogeneity across the field, thereby jeopardizing both the safety and economic efficiency of the collector field. To address these issues, this study first introduces a proportional-integral and feedforward based flow control strategy designed to stabilize the fluid outlet temperature in the collector field. Subsequently, a flow allocation scheme aimed at achieving temperature uniformity across individual collector loops is presented. This scheme relies on the effective irradiation estimates for each collector loop, calculated using the extended Kalman filter algorithm and a suggested hydraulic model. Simulation results demonstrate that these control strategies not only stabilize the outlet temperature of the collector field at the desired set value but also significantly diminish temperature variances among individual collector loops, with reduced computational overhead. The maximum temperature difference between loops can be reduced from 126.3 °C to 12.7 °C under uneven radiation intensity, ranging from 563 W/m2 to 885 W/m2, by the proposed temperature homogenization control strategy.

A novel multi-factor fuzzy membership function - adaptive extended Kalman filter algorithm for the state of charge and energy joint estimation of electric-vehicle lithium-ion batteries

In view of the unmeasurable state parameters of electric-vehicle lithium-ion batteries, this paper investigates a novel multi-factor fuzzy membership function - adaptive extended Kalman filter (MFMF-AEKF) algorithm for the online joint estimation of the state of charge and energy. Strong nonlinear characteristics of model parameters are characterized by considering multiple processing factors of electrochemical and diffusion effects for lithium-ion batteries and constructing an optimized multifactor coupling model. In the proposed MFMF-AEKF method, multi-space-scale factors are introduced to realize the numerical analysis of the multi-factor coupled model parameters and state estimation under dynamic working conditions of electric-vehicle lithium-ion batteries. The proposed MFMF-AEKF algorithm estimates the state of charge (SOC) with the overall best mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and maximum error (ME) values of 1.822 %, 4.322 %, 1.947 %, and 2.954 %, respectively, under challenging working conditions. And The MAE, MAPE, RMSE, and ME values for the state of energy (SOE) are 0.617 %, 1.711 %, 0.695 %, and 1.011 %, respectively. Both state estimation results are better than the traditional method. The proposed MFMF-AEKF algorithm has higher estimation accuracy which provides a feasible estimation algorithm for the joint SOC and SOE of lithium-ion batteries.

Real-Time Speed Estimation for an Induction Motor: An Automated Tuning of an Extended Kalman Filter Using Voltage-Current Sensors.

This paper aims at achieving real-time optimal speed estimation for an induction motor using the Extended Kalman filter (EKF). Speed estimation is essential for fault diagnosis in Motor Current Signature Analysis (MCSA). The estimation accuracy is obtained by exploring the noise covariance matrices estimation of the EKF algorithm. The noise covariance matrices are determined using a modified subspace model identification approach. In order to reach this goal, this method compares an estimated model of a deterministic system, derived from available input-output datasets (using voltage-current sensors), with the discrete-time state-space representation used in the Kalman filter equations. This comparison leads to the determination of model uncertainties, which are subsequently represented as noise covariance matrices. Based on the fifth-order nonlinear model of the induction motor, the rotor speed is estimated with the optimized EKF algorithm, and the algorithm is tested experimentally.

A novel method for electric vehicle insulation detection based on the extended Kalman filter algorithm

Addressing the critical need for enhanced safety in the burgeoning electric vehicle market, this study presents a novel insulation detection method based on the Extended Kalman Filter (EKF) algorithm. To resolve the conflict between the response speed and detection accuracy of the insulation detection system caused by Y-capacitors, the Levenberg–Marquardt (L-M) algorithm is employed to effectively estimate the parameters of the feedback voltage model developed for an unbalanced electrical bridge. The state equation of the insulation testing system has been constructed, and the EKF algorithm is applied innovatively to monitor insulation resistance and Y-capacitance, demonstrating superior anti-interference capabilities. Simulation experiments have underscored the significant contributions of the L-M algorithm in expanding the detection scope of the system. Bench tests confirmed the ability of the approach to monitor changes in insulation resistance and Y-capacitance rapidly and accurately. Under normal conditions, the maximum relative error for insulation resistance measurement is 1.56%, with a response time of 1.5 s.

Estimating the state of charge of lithium-ion batteries using different noise inputs

State of charge estimation (SOC) is the most significant functionality of a vehicle's battery management system (BMS). The methods for this estimation are conventionally oriented towards model-based methods. As part of this paper, we introduce a first order equivalent circuit estimation approach known as the Thevenin model, along with an extended Kalman filter (EKF) approach to accurately estimate the SOC. We then deploy and simulate it in MATLAB by using a reference load profile from the new European driving cycle (NEDC). Afterwards, the simulation results are reviewed based on various initial noise values, and the results are compared to those of other EKF algorithms. According to the results, SOC estimation accuracy has significantly increased as a result of the improvements made. Specifically, the root-mean-square error decreased from 0.0068 to 0.0020.

Network Analysis of Active and Passive Radar Based on the Extended Kalman Filter

In this current work, a sequential extended Kalman filter (EKF) algorithm is proposed to solve the quandary of regional accuracy disparity for time difference of arrival (TDOA) positioning in passive radar. The proposed approach entails merging the complete set of active radar observation data with the TDOA data of passive radar in a serial fashion, followed by the deployment of the EKF algorithm for the purpose of filtering. The simulation results show that the proposed data fusion method effectively solves the regional accuracy imbalance problem caused by the fuzzy area and no solution area of the TDOA positioning solution through the conflation of the precision merits of active and passive radar, and improves the overall target detection accuracy.

Performance enhancement of diffuse fluorescence tomography based on an extended Kalman filtering-long short term memory neural network correction model.

To alleviate the ill-posedness of diffuse fluorescence tomography (DFT) reconstruction and improve imaging quality and speed, a model-derived deep-learning method is proposed by combining extended Kalman filtering (EKF) with a long short term memory (LSTM) neural network, where the iterative process parameters acquired by implementing semi-iteration EKF (SEKF) served as inputs to the LSTM neural network correction model for predicting the optimal fluorescence distributions. To verify the effectiveness of the SEKF-LSTM algorithm, a series of numerical simulations, phantom and in vivo experiments are conducted, and the experimental results are quantitatively evaluated and compared with the traditional EKF algorithm. The simulation experimental results show that the proposed new algorithm can effectively improve the reconstructed image quality and reconstruction speed. Importantly, the LSTM correction model trained by the simulation data also obtains satisfactory results in the experimental data, suggesting that the SEKF-LSTM algorithm possesses strong generalization ability and great potential for practical applications.

A Planar Multi-Inertial Navigation Strategy for Autonomous Systems for Signal-Variable Environments.

The challenge of precise dynamic positioning for mobile robots is addressed through the development of a multi-inertial navigation system (M-INSs). The inherent cumulative sensor errors prevalent in traditional single inertial navigation systems (INSs) under dynamic conditions are mitigated by a novel algorithm, integrating multiple INS units in a predefined planar configuration, utilizing fixed distances between the units as invariant constraints. An extended Kalman filter (EKF) is employed to significantly enhance the positioning accuracy. Dynamic experimental validation of the proposed 3INS EKF algorithm reveals a marked improvement over individual INS units, with the positioning errors reduced and stability increased, resulting in an average accuracy enhancement rate exceeding 60%. This advancement is particularly critical for mobile robot applications that demand high precision, such as autonomous driving and disaster search and rescue. The findings from this study not only demonstrate the potential of M-INSs to improve dynamic positioning accuracy but also to provide a new research direction for future advancements in robotic navigation systems.

Reduce state of charge estimation errors with an extended Kalman filter algorithm

Li-ion batteries (LiBs) are accurately estimated under varying operating conditions and external influences using extended Kalman filtering (EKF). Estimating the state of charge (SOC) is essential for enhancing battery efficiency, though complexities and unpredictability present obstacles. To address this issue, the paper proposes a second-order resistance-capacitance (RC) battery model and derives the EKF algorithm from it. The EKF approach is chosen for its ability to handle complex battery behaviors. Through extensive evaluation using a Simulink MATLAB program, the proposed EKF algorithm demonstrates remarkable accuracy and robustness in SOC estimation. The root mean square error (RMSE) analysis shows that SOC estimation errors range from only 0.30% to 2.47%, indicating substantial improvement over conventional methods. These results demonstrate the effectiveness of an EKF-based approach in overcoming external influences and providing precise SOC estimations to optimize battery management. In addition to enhancing battery performance, the results of the study may lead to the development of more reliable energy storage systems in the future. This will contribute to the wider adoption of LiBs in various applications.

Enhanced Fault Detection and Localization Strategy for High-Speed Protection in Medium-Voltage DC Distribution Networks Using Extended Kalman Filtering Algorithm

Enhanced Fault Detection and Localization Strategy for High-Speed Protection in Medium-Voltage DC Distribution Networks Using Extended Kalman Filtering Algorithm

Analysis of a safe utilization algorithm for retired power batteries from new energy vehicles

The graded utilization of waste batteries has gained research significance due to recent reports of new energy vehicle lithium-ion batteries exploding whilst awaiting recycling or in end-of-life storage. In this study, we innovatively selected battery performance parameters such as the internal resistance, charge and discharge rate, and current maximum available capacity to evaluate the safety of retired power batteries from the perspective of inducing thermal runaway. A fractional calculus theory was then introduced, and the fractional second-order resistance as well as a capacitance model and an adaptive genetic algorithm were established for the identification of the parameters. An improved dual-scale filtering algorithm was generated, which combined the extended Kalman filter algorithm and the unscented Kalman filter algorithm to improve the accuracy of the parameter estimation. The final test outcomes indicated that the equivalent circuit model optimized by incorporating multiple filtering algorithms had error rates of 1.87 %, 1.65 %, and 1.27 % for the state of charge of the battery in three different operating condition testbeds, with average errors of 0.62 %, 0.69 %, and 0.59 %, respectively. When an initial experimental platform was constructed for the detection of the parameters, the voltage error quickly stabilized to within 0.03 V. It also displayed many advantages of data detection and calculation, such as faster convergence, faster tracking, and the highest result accuracy when compared with the battery model using other algorithms. This experiment highlighted that a fractional second-order resistive–capacitive circuit equivalent battery state detection model incorporating various filtering algorithms has practicality and feasibility.

Leveraging digital twins for fault diagnosis in autonomous ships

Autonomous ships are vulnerable to a spectrum of potential faults, including propeller damage, shaft-line failures, and electrical supply disruptions. Swift fault detection is critical to minimize the potentially catastrophic consequences of these issues. In this paper, we introduce an innovative digital twin-based method for diagnosing faults in autonomous ships. Our digital twin system collects data from the ship’s sensor array, conducts comprehensive analysis, computes fault parameters, and provides real-time visualizations of the findings. To achieve this, we utilize the ship’s dynamical model and employ a novel adaptive extended Kalman filter (AEKF) algorithm to estimate the severity of these faults. We evaluate the effectiveness of this approach through numerical simulations and practical implementation in an autonomous surface vehicle called the Otter, developed by Maritime Robotics. The experimental results, which consider both normal and faulty ship propulsion systems, underscore the significant potential of this novel approach to improve ship condition monitoring during operational activities.

An Extended Kalman Filter Design for State-of-Charge Estimation Based on Variational Approach

State of charge (SOC) is a very important variable for using batteries safely and reliably. To improve the accuracy of SOC estimation, a novel variational extended Kalman filter (EKF) technique based on least square error method is herein provided by establishing a second-order equivalent circuit model for the battery. It was found that when SOC decreased, resistance polarization occurred in the electrochemical model, and the parameters in the equivalent RC model varied. To decrease the modeling error in the equivalent circuit model, the system parameters were identified online depending on the SOC’s estimated result. Through the SOC-estimation process, the variation theorem was introduced, which enabled the system parameters to track the real situations based on the output measured. The experiment results reveal the comparison of the SOC-estimation results of the variational EKF algorithm, the traditional EKF algorithm, the recursive least square (RLS) EKF algorithm, and the forgotten factor recursive least square (FFRLS) EKF algorithm based on different indices, including the mean square error (MSE) and the mean absolute error (MAE). The variational EKF algorithm provided in this paper has higher estimation accuracy and robustness than the traditional EKF, which verifies the superiority and effectiveness of the proposed method.

State of charge estimation of lithium-titanate battery based on multi-model extended Kalman filter considering temperature and current rate

To tackle the issue of accurately estimating the state of charge (SOC) of lithium-titanate (Li-Ti) batteries in complex vehicle applications, a multi-model extended Kalman filter (MM-EKF) algorithm considering the effects of temperature and current rate is proposed. Based on the operational characteristics of Li-Ti batteries in the context of electric vehicle applications, second-order RC equivalent circuit models (ECMs) are established to account for the temperature and current rate influences. Model parameters are identified using an adaptive recursive least squares method with a forgetting factor based on experimental data. Subsequently, a SOC estimation method based on the MM-EKF algorithm for Li-Ti batteries is proposed and its effectiveness is validated under different ambient temperatures. Experimental results demonstrate that the MM-EKF algorithm, which considers the effects of temperature and current rate, can accurately estimate the SOC of Li-Ti batteries. The maximum estimation error is within 5 % at different ambient temperatures, and the algorithm can quickly eliminate initial SOC errors. Consequently, it fulfills the requirements for SOC estimation of hybrid tracked vehicles in intricate operating conditions.

Machine learning-based design of a linear self-resistant attitude control system for UAV string level

Abstract This paper mainly investigates the attitude control method of the quadrotor against unknown external interference and improves the control accuracy for the subsequent design of the control algorithm by establishing a more accurate mathematical model of the quadrotor. The extended Kalman filtering algorithm is used to obtain the real-time attitude state of the vehicle for attitude solving. The inertial guidance fusion uses the Kalman filter algorithm with delay correction to estimate the vehicle’s position and velocity information. Finally, the attitude control method of serial linear self-immunity control is proposed, which estimates and compensates for the external perturbation and internal uncertainty in real-time by linear expansion observer, while the position controller is designed by using PIV control. The simulation study analyzes that this paper’s method reduces the UAV attitude angle maximum error magnitude between about 1.04° and 4.07°compared with the traditional ADRC and serial PID. The maximum tracking error of pitch angle under white noise interference is only 0.37°using the control method of this paper, and the fluctuation amplitude is reduced by 0.81 on average, which shows a stronger anti-interference ability.

A Robust GPS Navigation Filter Based on Maximum Correntropy Criterion with Adaptive Kernel Bandwidth

Multiple forms of interference and noise that impact the receiver’s capacity to receive and interpret satellite signals, and consequently the preciseness of positioning and navigation, may be present during the processing of Global Positioning System (GPS) navigation. The non-Gaussian noise predominates in the signal owing to the fluctuating character of both natural and artificial electromagnetic interference, and the algorithm based on the minimum mean-square error (MMSE) criterion performs well when assuming Gaussian noise, but drops when assuming non-Gaussian noise. The maximum correntropy criteria (MCC) adaptive filtering technique efficiently reduces pulse noise and has adequate performance in heavy-tailed noise, which addresses the issue of filter performance caused by the presence of non-Gaussian or heavy-tailed unusual noise values in the localizing measurement noise. The adaptive kernel bandwidth (AKB) technique employed in this paper applies the calculated adaptive variables to generate the kernel function matrix, in which the adaptive factor can modify the size of the kernel width across a reasonably appropriate spectrum, substituting the fixed kernel width for the conventional MCC to enhance the performance. The conventional maximum correntropy criterion-based extended Kalman filter (MCCEKF) algorithm’s performance is significantly impacted by the value of the kernel width, and there are certain predetermined conditions in the selection based on experience. The MCCEKF with a fixed adaptive kernel bandwidth (MCCEKF-AKB) has several advantages due to its novel concept and computational simplicity, and gives a qualitative solution for the study of random structures for generalized noise. Additionally, it can effectively achieve the robust state estimation of outliers with anomalous values while guaranteeing the accuracy of the filtering.