Unscented Kalman Filter Algorithm Research Articles

L-PCM: Localization and Point Cloud Registration-Based Method for Pose Calibration of Mobile Robots

The autonomous navigation of mobile robots contains three parts: map building, global localization, and path planning. Precise pose data directly affect the accuracy of global localization. However, the cumulative error problems of sensors and various estimation strategies cause the pose to have a large gap in data accuracy. To address these problems, this paper proposes a pose calibration method based on localization and point cloud registration, which is called L-PCM. Firstly, the method obtains the odometer and IMU (inertial measurement unit) data through the sensors mounted on the mobile robot and uses the UKF (unscented Kalman filter) algorithm to filter and fuse the odometer data and IMU data to obtain the estimated pose of the mobile robot. Secondly, the AMCL (adaptive Monte Carlo localization) is improved by combining the UKF fusion model of the IMU and odometer to obtain the modified global initial pose of the mobile robot. Finally, PL-ICP (point to line-iterative closest point) point cloud registration is used to calibrate the modified global initial pose to obtain the global pose of the mobile robot. Through simulation experiments, it is verified that the UKF fusion algorithm can reduce the influence of cumulative errors and the improved AMCL algorithm can optimize the pose trajectory. The average value of the position error is about 0.0447 m, and the average value of the angle error is stabilized at about 0.0049 degrees. Meanwhile, it has been verified that the L-PCM is significantly better than the existing AMCL algorithm, with a position error of about 0.01726 m and an average angle error of about 0.00302 degrees, effectively improving the accuracy of the pose.

A Method for State of Charge and State of Health Estimation of LithiumBatteries Based on an Adaptive Weighting Unscented Kalman Filter

This paper considers the estimation of SOC and SOH for lithium batteries using multi-innovation Levenberg–Marquardt and adaptive weighting unscented Kalman filter algorithms. For parameter identification, the second-order derivative of the objective function to optimize the traditional gradient descent algorithm is used. For SOC estimation, an adaptive weighting unscented Kalman filter algorithm is proposed to deal with the nonlinear update problem of the mean and covariance, which can substantially improve the estimation accuracy of the internal state of the lithium battery. Compared with fixed weights in the traditional unscented Kalman filtering algorithm, this algorithm adaptively adjusts the weights according to the state and measured values to improve the state estimation update accuracy. Finally, according to simulations, the errors of this algorithm are all lower than 1.63 %, which confirms the effectiveness of this algorithm.

Sideslip Angle Estimation for Distributed Drive Electric Vehicles Based on Robust Unscented Particle Filter

An accurate and reliable sideslip angle is crucial for active safety control systems and advanced driver-assistance systems (ADAS). The direct measurement method of the sideslip angle suffers from challenges of high costs and environmental sensitivity, so sideslip angle estimation has always been a significant research issue. To improve the precision and robustness of sideslip angle estimation for distributed drive electric vehicles (DDEV) in extreme maneuvering scenarios, this paper presents a novel robust unscented particle filter (RUPF) algorithm based on low-cost onboard sensors. Firstly, a nonlinear dynamics model of DDEV is constructed, providing a theoretical foundation for the design of the RUPF algorithm. Then, the RUPF algorithm, which incorporates the unscented Kalman filter (UKF) to update importance density and utilizes systematic random resampling to mitigate particle degradation, is designed for estimation. Eventually, the availability of the proposed RUPF algorithm is validated on the co-simulation platform with non-Gaussian noises. Simulation results demonstrate that RUPF algorithm attains a higher precision and stronger robustness compared with the traditional PF and UKF algorithms.

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.

Human-Following Strategy for Orchard Mobile Robot Based on the KCF-YOLO Algorithm

Autonomous mobile robots play a vital role in the mechanized production of orchards, where human-following is a crucial collaborative function. In unstructured orchard environments, obstacles often obscure the path, and personnel may overlap, leading to significant disruptions to human-following. This paper introduces the KCF-YOLO fusion visual tracking method to ensure stable tracking in interference environments. The YOLO algorithm provides the main framework, and the KCF algorithm intervenes in assistant tracking. A three-dimensional binocular-vision reconstruction method was used to acquire personnel positions, achieving stabilized visual tracking in disturbed environments. The robot was guided by fitting the personnel’s trajectory using an unscented Kalman filter algorithm. The experimental results show that, with 30 trials in multi-person scenarios, the average tracking success rate is 96.66%, with an average frame rate of 8 FPS. Additionally, the mobile robot is capable of maintaining a stable following speed with the target individuals. Across three human-following experiments, the horizontal offset Error Y does not exceed 1.03 m. The proposed KCF-YOLO tracking method significantly bolsters the stability and robustness of the mobile robot for human-following in intricate orchard scenarios, offering an effective solution for tracking tasks.

State estimation of buses: A hybrid algorithm of deep neural network and unscented Kalman filter considering mass identification

Accurately obtaining vehicle state parameters is a crucial prerequisite for active safety control. However, key stability parameters of buses, such as sideslip angle and roll angle, are difficult to measure directly. Moreover, changes in the bus mass during the driving route can impact the vehicle state. To tackle these challenges, we identify the bus mass before state estimation, and propose a hybrid state estimation algorithm based on deep neural network (DNN) and unscented Kalman filter (UKF). First, the mass is identified using the recursive least squares (RLS) method based on longitudinal dynamics at each start of bus, and the yaw and roll moment of inertia are adaptively adjusted based on the identified mass. Second, a composite DNN combining the convolutional neural network (CNN), gated recurrent unit (GRU), and attention mechanism is designed to estimate sideslip and roll angles. As for the training dataset, it is acquired from different maneuvers simulated by TruckSim. Third, a UKF estimator is established based on 4-degree of freedom (DOF) vehicle dynamics model and magic tire formula, and the estimated values of DNN are inserted into UKF estimator as virtual observations. Finally, the proposed hybrid algorithm is validated through simulation maneuvers and real driving maneuvers based on MATLAB/Simulink and TruckSim software. The comparative results demonstrate that the proposed algorithm outperforms individual DNN estimation and UKF estimation, enhancing both estimation accuracy and reliability.

Joint estimation of state-of-charge and state-of-power for hybrid supercapacitors using fractional-order adaptive unscented Kalman filter

As a new type of energy storage device, hybrid supercapacitors have the advantages of both lithium-ion batteries and supercapacitors. State of charge and state of power estimation are crucial for system operation and energy management. This work proposes a joint estimation method for the state-of-charge (SoC) and state-of-power (SoP) of hybrid supercapacitors based on a fractional-order model and unscented Kalman filter algorithm. Firstly, a parameter identification method for second-order fractional-order models is proposed using a competitive learning-based particle swarm optimization algorithm. On this basis, a SoC estimation method is designed based on the fractional-order adaptive unscented Kalman filter. Then, a SoP estimation method considering multiple constraint conditions is proposed. Finally, the proposed parameter identification and state estimation algorithms are validated under different operating dynamic conditions and environmental temperatures. The experimental results show that the error of model voltage is lower than 100 mV and the SoC estimation error is lower than 2% in the vast majority of cases, which proves the proposed algorithms have good accuracy and robustness in different environments.

Adaptive unscented Kalman filter methods for identifying time‐variant parameters via state covariance re‐updating

AbstractThe conventional parameter identification process generally assumes that parameters remain constant. However, under extreme loading conditions, structures may exhibit nonlinear behavior, and parameters could demonstrate time‐variant characteristics. The unscented Kalman filter (UKF), as an efficient online recursive estimator, is widely used for identifying parameters of nonlinear systems. Nevertheless, it exhibits limitations when attempting to identify time‐variant parameters. To address this issue, this paper proposes a covariance matching technique that produces an array of adaptive UKF algorithms. Firstly, the sensitivity parameter η is defined to identify the instant when the parameter change occurs, and its threshold is calculated based on the sensitivity parameter time history curve. Secondly, an adaptive forgetting factor is introduced to simultaneously update the innovation, cross, and state covariance matrices when the kth‐step sensitive parameter surpasses the threshold. Finally, a secondary correction forgetting factor (SCFF) is employed to further re‐update the state covariance values at the identified damage locations. This creative step enhances the adaptive capability and optimizes the identification accuracy of the proposed algorithms. Both the numerical simulations and shaking table test demonstrate that the proposed adaptive algorithms can efficiently identify the time‐variant stiffness‐type parameters, and accurately capture their time‐variant characteristics.

State Estimation of Drive-by-Wire Chassis Vehicle Based on Dual Unscented Particle Filter Algorithm

Accurate vehicle dynamic information plays an important role in vehicle driving safety. However, due to the characteristics of high mobility and multiple controllable degrees of freedom of drive-by-wire chassis vehicles, the current mature application of traditional vehicle state estimation algorithms can not meet the requirements of drive-by-wire chassis vehicle state estimation. This paper proposes a state estimation method for drive-by-wire chassis vehicle based on the dual unscented particle filter algorithm, which make full use of the known advantages of the four-wheel drive torque and steer angle parameters of the drive-by-wire chassis vehicle. In the dual unscented particle filter algorithm, two unscented particle filter transfer information to each other, observe the vehicle state information and the tire force parameter information of the four wheels respectively, which reduce the influence of parameter uncertainty and model parameter changes on the estimation accuracy during driving. The performance with the dual unscented particle filter algorithm, which is analyzed in terms of the time-average square error, is superior of the unscented Kalman filter algorithm. The effectiveness of the algorithm is further verified by driving simulator test. In this paper, a vehicle state estimator based on dual unscented particle filter algorithm was proposed for the first time to improve the estimation accuracy of vehicle parameters and states.

SOC estimation of lead–carbon battery based on GA-MIUKF algorithm

The paper proposes a SOC (State of Charge) estimation method for lead–carbon batteries based on the GA-MIUKF algorithm. The GA-MIUKF algorithm combines GA (Genetic Algorithm) for global search and optimization with the MI-UKF (Multi-innovation Unscented Kalman Filter) algorithm for estimating the SOC of lead–carbon batteries. By establishing an equivalent circuit model for the battery, the GA is employed to globally search and optimize the battery model parameters and the noise variance parameters in the MI-UKF algorithm. Comparative analyses with the UKF (Unscented Kalman Filter) algorithms and MI-UKF algorithms reveal that the SOC estimation method based on the GA-MIUKF algorithm yields more accurate results for lead–carbon battery SOC estimation, with an average estimation error of 2.0%. This highlights the efficacy of the proposed approach in enhancing SOC estimation precision.

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.

Online estimation of lithium battery SOC based on fractional order FOUKF‐FOMIUKF algorithm with multiple time scales

AbstractAiming at the matter of poor precision in predicting the charge of lithium battery by applying conventional integer‐order models and offline parameter identification, this paper proposes a joint fractional‐order multi‐innovations unscented Kalman filter (FOUKF‐FOMIUKF) algorithm for predicting the cells' state of charge (SOC) online and uses the theory of singular‐value decomposition to tackle the issue of failure of the traceless transformation. Initially, the circuitry model of fractional order is built. The parameters of the model are recognized online by fractional‐order unscented Kalman filtering (FOUKF), and the obtained parameters are then transmitted to the method known as the fractional order multi‐innovations unscented Kalman filter (FOMIUKF) to calculate the SOC of the cell. The algorithm was validated under four working conditions such as FUDS (US Federal Urban Driving Distance), BJDST (Beijing Dynamic Stress Test), DST (Dynamic Stress Test), and US06 (Highway Driving Distance Test), respectively, and compared with the FOMIUKF, MIUKF, and FOUKF algorithms for offline identification. The conclusions demonstrate that the SOC estimated by the FOUKF‐FOMIUKF method is controlled within 0.5% of the mean absolute error under the four conditions and the root‐mean‐square error is controlled within 0.8%. It is not difficult to find that the FOUKF‐FOMIUKF algorithm estimates SOC with higher accuracy and robustness.

Combing dynamic parameter identification and singular value decomposition adaptive unscented Kalman filter for predictive state of charge of lithium-ion batteries

The development of a secure battery management system (BMS) for electric vehicles depends heavily on the correct assessment of the online state-of-charge (SOC) of Li-ion batteries. The ternary lithium battery is used as the research object in this paper, and a second-order RC equivalent circuit model is developed to characterize the dynamic operating characteristics of the battery. In order to solve the problem that the adaptive unscented Kalman filter (AUKF) algorithm is easy to fail SOC estimation because the error covariance matrix is not positively definite due to the incomplete accuracy of the equivalent circuit model, a corresponding solution is proposed. Considering the poor real-time battery SOC estimate caused by the battery model’s fixed parameters, therefore we propose the Variable Forgetting Factor Recursive Least Squares (VFFRLS) algorithm for joint estimation of Li-battery SOC and the Singular Value Decomposition-AUKF (SVD-AUKF) algorithm. The SVD-AUKF algorithm can accurately estimate the SOC of the battery when the error covariance is negative. The algorithm can be adaptively adjusted in both the parameter identification and SOC estimation stages, which can effectively solve the problem of poor estimation accuracy caused by fixed parameters. According to experiments, under two separate dynamic operating situations, the joint estimation algorithm’s error is less than 2%, and its stability has also been greatly enhanced. At the same time, when the initial SOC value is set incorrectly, the convergence time of the algorithm proposed in this paper can reach within 2.1 seconds for BBDST and DST conditions, which can be well adapted to complex working conditions.

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.

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.

Open circuit voltage - state of charge curve calibration by redefining max–min bounds for lithium-ion batteries

The relationship between open circuit voltage (OCV) and state of charge (SoC) is essential for SoC estimation of lithium-ion batteries, which can be secured by either low-current OCV test or incremental OCV test, with incremental OCV test demonstrating better results. Nevertheless, low current always leads to a discharge capacity that is inconsistent with maximum available capacity, which is a key parameter in SoC estimation. Therefore, the resultant OCV-SoC curve fails to provide a consistent SoC range and thus affects SoC estimation. In this paper, OCV-SoC curves obtained from low-current OCV tests are calibrated by redefining max–min bounds to improve SoC estimation accuracy. Max–min bounds of SoC are redefined by measuring, calculating and resetting upper and lower cut-off voltages of the OCV-SoC curve. Based on second-order RC model, model parameters are identified online and adaptive square-root unscented Kalman filter (ASRUKF) algorithm is introduced to perform SoC estimation, which is proved to be precise and adaptive. The calibrated OCV-SoC curve achieves an overall better SoC estimation performance than that obtained from the low-current OCV test and incremental OCV test, which is validated by experiments of LiNiMnCoO2 (NMC) batteries at 0°C and 25°C.

Novel Unscented Kalman Filter-based method to assess the thermal behavior of carbon brake discs for high-performance motorcycles

In the past few decades, braking systems with carbon discs have become the dominant technology for many racing applications, such as in the MotoGP class. Indeed, they provide higher friction coefficients. Moreover, thanks to their lightweight materials (with respect to conventional steel brakes), the unsprung masses and the gyroscopic effects can be reduced. Therefore, the motorcycle dynamic performance can be significantly improved. The usage of carbon brakes requires a very accurate assessment of their thermal behavior. In fact, although their operating temperature in real racing conditions may cover a wide range, their optimal braking performance can be achieved only within a relatively narrow temperature range. This work focuses on the development of the Unscented Kalman Filter (UKF) algorithm as a suitable mathematical tool for assessing the temperature gradient of the carbon disc mounted on the motorcycles competing in the MotoGP™ world championship. A one-dimensional (1D) finite element (FE) model of the disc is developed to provide the a priori state estimate that the filter will combine with the information measured by the temperature sensor available on board to compute the optimal posterior temperature estimation. Besides estimating temperature, the UKF is also exploited to identify the convection heat transfer coefficient (h) of the disc, which is a fundamental parameter for a proper model calibration.

Vehicle state and parameter estimation based on adaptive anti-outlier unscented Kalman filter and GA-BPNN method

A multi-machine-learning improved adaptive Kalman filtering method is proposed to address the problem of handling abnormal data encountered in the vehicle state estimation. Firstly, the unscented Kalman filter (UKF) algorithm is improved by introducing a BP neural network improved by the genetic algorithm (GA-BPNN) to regulate and correct the global error of the UKF method. Then, the anti-outlier technique is applied to fully eliminate isolated and speckled outliers in the measurement, achieving further improvement on GA-BPNN-UKF and significantly improving the robustness of the filtering process. Finally, a simulation is applied to verify the effectiveness of the proposed new algorithm, and then its results are analyzed to obtain a firm substantiation of its effectiveness for further practical applications. The simulation results indicate that the estimation performance of the GA-BPNN algorithm is significantly better than that of Extended Kalman filter (EKF) method.

Underwater Doppler-bearing maneuvering target motion analysis based on joint estimated adaptive unscented Kalman filter

Noncooperative maneuvering target motion analysis is one of the challenging tasks in the field of underwater target localization and tracking for passive sonar. Underwater noncooperative targets often perform various maneuvers, and the targets are commonly modeled as a combination of constant-velocity models and coordinate-turn models with unknown turning rates. Traditional algorithms for Doppler-bearing target motion analysis are incapable of processing noncooperative maneuvering targets because the algorithms rely on a priori information of the turning rate and the center frequency. To address these shortcomings, this paper proposes the joint estimated adaptive unscented Kalman filter (JE-AUKF) algorithm. The JE-AUKF places the center frequency and turning rate into the state vector and constructs a time-varying state model that self-adapts to a maneuvering target. The JE-AUKF also introduces a time-varying fading factor into the process noise covariance matrix to improve the tracking performance. Simulations and sea trials are conducted to compare the performance of the JE-AUKF with the iterative unscented Kalman filter, the interacting multiple model-unscented Kalman filter, the interacting multiple model-iterative unscented Kalman filter, and the interacting multiple model-joint estimated unscented Kalman filter. The result shows that the JE-AUKF achieves better tracking performance for noncooperative maneuvering targets.

State-space modeling for electrochemical performance of Li-ion batteries with physics-informed deep operator networks

Online estimation of unobservable internal states is significant for safe operation of Li-ion batteries, and it constitutes one of the main functions of battery management system (BMS). The next-generation BMS expects model-based state estimation, especially with electrochemical models, which are accurate but often costly for solving. Therefore, it is required to build more easily executable state-space representation of electrochemical models for online state estimation. However, the traditional numerical methods for time discretization are relatively complicated, and the discretized system is not very flexible in modifying predictive time intervals. To address such issues, we introduce the concept of physics-informed operator learning for state-space modeling. Specifically, we propose an architecture, termed the physics-informed multiple-input operator network (PI-MIONet), to reformulate the state-space representation of the extended single particle (eSP) model. In this work, the PI-MIONet takes the Li-ion concentration of the whole electrode particle and current densities at the current time as the input functions, and predicts Li-ion concentration at any spatial-temporal location, which means that the forward predictions can be realized with user-defined step size. In addition, due to the capability of taking discretized functions as inputs, the PI-MIONet can be used for estimating states in the form of long vectors, and it can be conducted very efficiently, which makes it highly suitable for online applications in BMS. We verify the predictive performance of PI-MIONet through several synthetic experiments, and successfully apply it to the estimation of Li-ion concentration across the full particle with unscented Kalman filter algorithms.