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.

Estimating the Optimal State of Charge for Electric Car Batteries Using an Extended Kalman Filter

The efficient management of battery state of charge (SOC) is crucial for maximizing the performance, range, and longevity of electric vehicle (EV) batteries. This paper presents a novel approach for estimating the optimal state of charge of electric car batteries using an Extended Kalman Filter (EKF). The EKF is a recursive algorithm that combines measurements from various sensors with a dynamic battery model to estimate the current SOC and predict future SOC values with high accuracy. The paper provides a detailed explanation of the EKF algorithm and its application to battery SOC estimation, highlighting its ability to handle nonlinearities, uncertainties, and measurement noise inherent in battery systems. Furthermore, this research presents a simulation-based validation of the proposed EKF approach using real-world driving data from electric vehicles. The simulation results demonstrate the effectiveness of the EKF algorithm in accurately estimating the SOC of electric car batteries under various operating conditions, including different driving patterns, temperatures, and battery degradation scenarios.

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.

State-of-charge estimation of lithium-ion battery: Joint long short-term memory network and adaptive extended Kalman filter online estimation algorithm

With the widespread use of lithium-ion batteries, estimating the State of Charge (SOC) has been one of the most critical tasks in the battery management system (BMS). In this paper, a joint long short-term memory recurrent neural network (LSTM-RNN) and adaptive extended Kalman filter (AEKF) algorithm is proposed to achieve accurate SOC estimation. The proposed algorithm generates an initial SOC estimation value through a trained LSTM-RNN with a sliding time window signal sequence as input. The initial estimation value is then used as a feedback input to the AEKF. The results show that only a 30-s time series as the input of the LSTM-RNN can achieve satisfactory estimation results. Compared with traditional adaptive extended Kalman filter and unscented Kalman filter (UKF), the proposed algorithm has a better performance of estimation accuracy under various discharging conditions, especially when applied at low temperatures. Finally, the SOC estimation results under four operating conditions and various temperatures show that the maximum error is less than 2.5 %, in particular, the root mean square error (RMSE) and the mean absolute error (MAE) are below 1.01 % and 0.64 %. The proposed algorithm is an effective SOC estimation method with good robustness and high estimation accuracy.

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.

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.

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.

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.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

Innovative Applications of Intelligent Assistive Systems in Interior Design

Abstract With the development of smart homes, virtual reality, and other technologies, people’s demand for digital modeling and visualization of interior space is increasing. How to quickly and accurately estimate the layout of the interior space has become a matter of great concern. This paper develops a 3D virtual visual interior design platform structure based on this. By studying the indoor multi-sensor fusion localization system, the localization module in the navigation process was designed based on this fusion result. The visual localization algorithm, WiFi localization, PDR localization, and AMCL fusion localization algorithms are introduced, respectively. The extended Kalman filter algorithm is used to fuse the algorithm with the highest state value for localization, which is used for scene recognition according to the algorithm localization effect. To achieve the 3D virtual visual impact, a 3D virtual visual interior design platform is created based on 3D virtual vision. Experiments are conducted on the localization system in the platform, and the error of all the localization points of the localization method combining vision and AMCL is no more than 1.1m, with the maximum error of 1.071m and the average error of 0.481m, which is the lowest error among all the algorithms. The localization sensor constructed by the localization algorithm using vision and AMCL with extended Kalman filtering has an average error of 10.33cm, which allows for good scene recognition. The data analyzes designers’ satisfaction with the use of the platform, and the independent variable in the regression equation that contributes most significantly to total satisfaction is the platform’s time-saving, with a coefficient of 0.324. The platform’s focus should be on enhancing time efficiency.

Short-term wind power forecasting using interval A2-C1 type-2 TSK FLS method with extended Kalman filter algorithm

Short-term wind power forecasting using interval A2-C1 type-2 TSK FLS method with extended Kalman filter algorithm

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.