Adaptive Unscented Kalman Filter Research Articles

A fractional order model of auxiliary power batteries suitable for hydrogen fuel cell hybrid systems heavy-duty trucks

Aiming at the problem that the existing battery fractional order model is not suitable for the auxiliary power battery of hydrogen fuel cell heavy-duty trucks, considering the characteristics of multiple influencing factors and nonlinearity in actual driving processes, a fractional order model of auxiliary power batteries is proposed based on the hydrogen fuel cell heavy-duty trucks model and the batteries' fractional order model. Then, to solve the charge state estimation error increases due to the high frequency and large rate charging and discharging, H∞ filter is introduced into the adaptive unscented Kalman filter to optimize the charge state estimation in the model. Additionally, the model's parameters are identified using the evolutionary algorithm and the recursive least squares technique based on the forgetting factor. Finally, the model is verified by dynamic conditions. The results show that compared with the auxiliary power batteries' fractional order model, the optimized model reduces the MAE by 0.08% and the RMSE by 0.22% when estimating voltage, and reduces the MAE by 0.25% and the RMSE by 2.66% when estimating SOC. Therefore, the optimized fractional order model of auxiliary power battery has higher accuracy and applicability.

State of Charge Estimation of Flooded Lead Acid Battery Using Adaptive Unscented Kalman Filter

Flooded Lead Acid (FLA) batteries remain a cost-effective choice in various industries. Accurate State of Charge (SOC) estimation is crucial for effective battery management systems. This paper thoroughly examines the behavior of Open-Circuit Voltage (OCV) during hysteresis in FLA batteries, proposing a novel hysteresis modeling approach based on this behavior to enhance the SOC estimation accuracy. Additionally, we introduce an Adaptive Unscented Kalman Filter (AUKF) to further refine the SOC estimation precision. Experimental validation confirms the effectiveness of the proposed hysteresis modeling. A comparative analysis against the traditional Unscented Kalman Filter (UKF) under random charge/discharge profiles underscores the superior performance of AUKF, showcasing an improved convergence to the correct SOC value and a significant reduction in the SOC estimation error to approximately 2%, in contrast to the 5% error observed with the traditional UKF.

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.

DFFRLS-FAUKF: accurate and reliable monorail longitudinal slope identification method

Monorail cranes have always played an important role in mine auxiliary transportation systems owing to their excellent transportation performance and are therefore a desirable area in which to apply driverless technologies. However, the low-accuracy recognition of monorail track slopes and the poor reliability of recognition results make it difficult and dangerous to implement fully driverless monorail cranes. Aiming to solve these problems, a method for the accurate identification of longitudinal monorail slopes based on the use of a dynamic forgetting factor for recursive least squares (DFFRLS) and a fuzzy adaptive unscented Kalman filter (FAUKF) is proposed. First, acquired acceleration and velocity data are pre-processed using a rolling window. Second, the real-time longitudinal track-curvature value is calculated using the DFFRLS algorithm with the processed data and an established track-curvature model. Finally, based on existing track-curvature values, dynamic recognition of the monorail track slope is realized using the FAUKF algorithm with a fuzzy control factor, improving the accuracy of track gradient recognition. Experiments show that the DFFRLS-FAUKF algorithm improves the accuracy of track-slope recognition by up to 21.26% and 33.93% on average compared with that of DFFRLS with an adaptive extended Kalman filter (DFFRLS-AEKF) or an adaptive unscented Kalman filter (DFFRLS-AUKF).

Optimal vehicle position estimation using adaptive unscented Kalman filter based on sensor fusion

Precise position recognition systems are actively used in various automotive technology fields such as autonomous vehicles, intelligent transportation systems, and vehicle driving safety systems. In line with this demand, this paper proposes a new vehicle position estimation algorithm based on sensor fusion between low-cost standalone global positioning system (GPS) and inertial measurement unit (IMU) sensors. In order to estimate accurate vehicle position information using two complementary sensor types, adaptive unscented Kalman filter (AUKF), an optimal state estimation algorithm, is applied to the vehicle kinematic model. Since this AUKF includes an adaptive covariance matrix whose value changes under GPS outage conditions, it has high estimation robustness even if the accuracy of the GPS measurement signal is low. Through comparison of estimation errors with both extended Kalman filter (EKF) and UKF, which are widely used state estimation algorithms, it can be confirmed how improved the estimation performance of the proposed AUKF algorithm in real-vehicle experiments is. The given test course includes roads of various shapes as well as GPS outage sections, so it is suitable for evaluating vehicle position estimation performance.

State of charge estimation for a parallel battery pack jointly by fuzzy-PI model regulator and adaptive unscented Kalman filter

Parallel battery pack (PBP) is an important unit for its application in electric vehicles and energy storage, and precise state of charge (SOC) is the basic parameter for battery efficient operation. However, the SOC is an internal hidden immeasurable variable, and the measurable battery parameters of the PBP are limited, which makes it difficult to precisely estimate SOC for the PBP. The main efforts are as follows: An improved equivalent circuit model of the PBP is first established on the basis of the fuzzy-proportional integral model regulator, which can accurately describe the influence of battery cell inconsistency on the PBP discharging characteristics. Under constant current and UDDS operating conditions, the battery model voltage can accurately capture the measured voltage during the discharging process, especially at the final stage of discharge with the maximum voltage absolute error below 0.12 V (about 3.2%). A model-based SOC prediction algorithm using an adaptive unscented Kalman filter (AUKF) with a sliding window noise estimator is developed for the PBP. It can adaptively achieve accurate process and measurement noise statistics of the PBP for the AUKF. The SOC of the PBP can be precisely estimated using the developed method with the absolute errors below 2% even if the noise statistics are randomly given respectively. Moreover, compared to the unimproved AUKF and the Sage-Husa method, the presented algorithm illustrates the highest SOC prediction precision with the lowest root mean square error of 1.12% and the minimum mean absolute error of 1.08%.

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.

An Adaptive Unscented Kalman Filter for the Estimation of the Vehicle Velocity Components, Slip Angles, and Slip Ratios in Extreme Driving Manoeuvres.

This paper presents a novel unscented Kalman filter (UKF) implementation with adaptive covariance matrices (ACMs), to accurately estimate the longitudinal and lateral components of vehicle velocity, and thus the sideslip angle, tire slip angles, and tire slip ratios, also in extreme driving conditions, including tyre-road friction variations. The adaptation strategies are implemented on both the process noise and measurement noise covariances. The resulting UKF ACM is compared against a well-tuned baseline UKF with fixed covariances. Experimental test results in high tyre-road friction conditions show the good performance of both filters, with only a very marginal benefit of the ACM version. However, the simulated extreme tests in variable and low-friction conditions highlight the superior performance and robustness provided by the adaptation mechanism.

Co-estimation of state-of-charge and state-of-temperature for large-format lithium-ion batteries based on a novel electrothermal model

The safe and efficient operation of the electric vehicle significantly depends on the accurate state-of-charge (SOC) and state-of-temperature (SOT) of Lithium-ion (Li-ion) batteries. Given the influence of cross-interference between the two states indicated above, this study establishs a co-estimation framework of battery SOC and SOT. This framwork is based on an innovative electrothermal model and adaptive estimation algorithms. The first-order RC electric model and an innovative thermal model are components of the electrothermal model. Specifically, the thermal model includes two lumped-mass thermal submodels for two tabs and a two-dimensional (2-D) thermal resistance network (TRN) submodel for the main battery body, capable of capturing the detailed thermodynamics of large-format Li-ion batteries. Moreover, the proposed thermal model strikes an acceptable compromise between the estimation fidelity and computational complexity by representing the heat transfer processes by the thermal resistances. Besides, the adaptive estimation algorithms are composed of an adaptive unscented Kalman filter (AUKF) and an adaptive Kalman filter (AKF), which adaptively update the state and noise covariances. Regarding the estimation results, the mean absolute errors (MAEs) of SOC and SOT estimation are controlled within 1% and 0.4 ​°C at two temperatures, indicating that the co-estimation method yields superior prediction performance in a wide temperature range of 5–35 ​°C.

Improvement of axial deformation prediction in high-rise buildings with field monitoring and adaptive unscented Kalman filter

The deformation of vertical reinforced concrete members in high-rise buildings during their construction is constantly changing due to the complexity of the deformation mechanism, as well as the uncertainties that arise during the construction process; in some cases, accurate estimation of the vertical displacement is crucial. Based on on-site strain monitoring data and an adaptive unscented Kalman filter, this paper establishes a state equation for the axial deformation process. The elastic, inelastic and temperature deformation of concrete during the entire construction process are reasonably considered. Deformation is predicted using both the traditional Kalman filter and unscented Kalman filter, both of which achieved satisfactory results. But the unscented Kalman filter can improve the prediction accuracy and robustness by utilizing unscented transformations. Anomaly detection is integrated into every inference step to detect abrupt changes in external conditions and dynamically adjust calculation parameters, thereby reducing the dependency of the prediction results on input parameters.

An Adaptive UKF for Vehicle State Estimation With Delayed Measurements and Packet Loss

An Adaptive UKF for Vehicle State Estimation With Delayed Measurements and Packet Loss

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

Attitude motion parameters estimation of the space non-cooperative tumbling target is the premise of the on-orbit target capture task. However, existing methods cannot balance the estimation accuracy and efficiency. In this paper, an adaptive hybrid Kalman filter is presented to estimate the attitude, angular velocity and inertia motion parameters of the space non-cooperative tumbling target. First, the dynamic model of the non-cooperative tumbling target is derived, and the nonlinear discrete state-space equation is obtained. Then, a hybrid Kalman filter is designed by combining the extended Kalman filter and the unscented Kalman filter. The adaptive technique is introduced to track time-varying uncertain measurement noise caused by complex space disturbances. After that, based on the first-order linearization technique, the sufficient condition for the local convergence of the proposed method is proved. Finally, the numerical simulation experiment was conducted to compare the proposed method with the adaptive extended Kalman filter and the adaptive unscented Kalman filter. The experimental results show that the estimation accuracy of the proposed method is much higher than that of the adaptive extended Kalman filter and slightly lower than that of the adaptive unscented Kalman filter, and the iteration-average Central-Processing-Unit time is 64.2% smaller than that of the adaptive unscented Kalman filter and slightly longer than that of the adaptive extended Kalman filter. The proposed method achieves a much higher accuracy with a slight loss of iteration-average Central-Processing-Unit time.

SOC estimation for lithium-ion battery based on AGA-optimized AUKF

The window size for covariance matching (CM) of the adaptive unscented Kalman filter (AUKF) affects the state of charge (SOC) estimation performance due to changes with time in the distribution of error innovation sequence (EIS). A new adaptive genetic algorithm (AGA) to address this problem is proposed in this paper. The proposed AUKF (AGA-AUKF1) obtains its best window size determined by the AGA. A novel AUKF (AGA-AUKF2) is proposed to prevent the uncertainty caused by time-varying EIS with the combination of AGA and CM methods. Firstly, the influence of different temperatures on the prediction performance of the algorithm is investigated by FUDS data. The influence of various parameters on the algorithm is further analyzed by FUDS. For different temperatures, initial SOC values, and initial measurement noise covariance, the SOC estimation results show that the accuracy of AGA-AUKFs is better than AUKF. The population size and termination algebra simulation results indicate that the proposed AGA performs well in parameter optimization. Subsequently, the SOC estimation capability of two proposed methods in different working conditions is analyzed by BJDST and US06. The results show that AGA-AUKF2 has better accuracy and robustness than AGA-AUKF1.

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-of-charge estimation of Lithium-ion batteries using an adaptive dual unscented Kalman filter based on a reduced-order model

It is critical to accurately estimate the state of charge (SOC) of Lithium-ion batteries for the efficient, reliable, and safe operation of Electric Vehicles (EVs). Therefore, it is crucial to improve the methods for SOC determination by finding a beneficial trade-off between higher accuracy and increasing complexity within the Battery Management System (BMS). Physics-based models outperform the Equivalent Circuit Model (ECM) in terms of inherent electrochemical representation. This paper develops a new model based on the derivation of the reduced-order battery model in a control-oriented state space model to incorporate with the adaptive unscented Kalman filter (ADUKF). This allows the BMS to use a physics-based model with a low number of battery parameters resulting in a complexity deduction and much less effort in electrochemical parameter identification for online co-estimation of SOC and the battery model parameters. Moreover, an adaptive dual spherical UKF is implemented with the forgetting factor to reduce the computational capacity required for the traditional UKF and also to improve the covariance matching of measurement and system process noises. The proposed method is validated against driving cycle profiles, considering various conditions such as erroneous initial SOC, inaccurate battery capacity, and current sensor inaccuracy. Further, the robustness of the proposed method is verified against the impact of different temperatures. Lastly, the result is compared to ADUKF based on ECMs in terms of accuracy and computational cost.

A dual adaptive robust control for nonlinear systems with parameter and state estimation

Stabilization and learning are imperative to the high-performance feedback control of nonlinear systems. A dual adaptive robust control (DARC) scheme is proposed for nonlinear systems with model uncertainties to achieve a desired level of performance. Only the output of the nonlinear system is accessible in this work, all the states and parameters are learned online. Firstly, the DARC uses the prior physical bounds of systems to design a discontinuous projection with update rate limits which confines the bounds of parameter and state estimation. Then robustness of the nonlinear system can be guaranteed by the deterministic robust control (DRC) method. Secondly, a dual adaptive estimation mechanism (DAEM) is developed to learn the unknown parameters and states of systems. One part of the DAEM is the bounded gain forgetting (BGF) estimator, which is developed to handle inaccurate parameters and parametric variations. The other is the adaptive unscented Kalman filter (AUKF) synthesized for state estimation. The AUKF contains a statistic estimator based on the maximum a posterior (MAP) rule to estimate the unknown covariance matrix. Finally, simulation results illustrate the effectiveness of the suggested method.

A deep reinforcement learning approach for state of charge and state of health estimation in lithium-ion batteries

Accurate estimation of state variables such as State of Charge (SOC) and State of Health (SOH) is pivotal in the management of lithium-ion batteries. Existing methods, including the unscented Kalman filter (UKF), often require manual tuning of parameters and may not adapt well to the non-linear and non-stationary characteristics of batteries. This paper introduces a novel approach to optimize the parameters of an adaptive unscented Kalman filter (AUKF) using deep reinforcement learning (DRL). The DRL agent learns to adjust the parameters of the AUKF to maximize the estimation accuracy through interaction with the battery environment. This approach is capable of adapting to different battery types and operating conditions, eliminating the need for manual parameter tuning. Our results indicate that the DRL-optimized AUKF outperforms traditional UKF methods in terms of SOC and SOH estimation accuracy, demonstrating the potential of this approach for improving battery management systems.

A Novel Adaptive Square Root UKF with Forgetting Factor for the Time-Variant Parameter Identification

The unscented Kalman filter (UKF) serves as an efficient estimator widely utilized for the recursive identification of parameters. However, the UKF is not well suited for tracking time-variant parameters. Moreover, the unscented transformation (UT) used in the UKF typically relies on Cholesky decomposition to perform the square root operation of the covariance matrix. This method necessitates the matrix to maintain symmetry and positive definiteness. Due to the adverse influence of rounding error and noise, it becomes challenging to guarantee the positive definiteness of the matrix in each recursive step for practical engineering. The square root UKF (SRUKF) eliminates the need for the square root operation in the UT by directly updating the square root of the covariance matrix during each recursion. However, the SRUKF still relies on the rank 1 update to the Cholesky factorization to perform the recursive process, which also necessitates the matrix to be positive definite. Furthermore, the SRUKF is ineffective in the identification of time-variant parameters. Therefore, this paper proposes a modification to the SRUKF that ensures unconditional numerical stability by utilizing QR decomposition. Subsequently, the modified square root UKF (MSRUKF) method is enhanced by incorporating an adaptive forgetting factor that can be adjusted based on the residual information from each recursive step. This adaptation leads to the development of the adaptive SRUKF with forgetting factor (ASRUKF-FF) method, which significantly improves the tracking capability for time-variant parameters. To validate the effectiveness of the proposed method, this paper demonstrates its application in identifying the time-variant stiffness and damping parameters of a three-story frame structure. In addition, the method is employed to estimate the time-variant stiffness of the bridge excited by vehicles. The simulation results show that the proposed method has the superiority of high accuracy, strong robustness, and widespread applicability, even with incomplete measurements and inappropriate parameter settings.

Joint state–parameter estimation for structures with seismic isolation and damping systems: Theoretical observability and experimental verification

The objective of this study is to examine the feasibility of estimating the parameters of various devices in seismic control systems and evaluating the maximum responses of the quantities of interest. The observability condition was applied to determine the sensor layout and modeling assumptions of the structure for the joint estimation problem and to eliminate unsuitable layouts. To estimate the parameters of multiple members at the isolation layer, including laminated rubber bearings, oil dampers, and elastic sliding bearings, and to evaluate the maximum response, an adaptive unscented Kalman filter was utilized. Moreover, the study investigated the influence of partially unmeasured inputs on the observability of the established system through a case study involving the base layer of the building model colliding with the retaining walls. Experimental data from a full-scale shaking table test on a seismic isolation building was used as an example for validation purposes. The results demonstrated that even under varying initial estimates, varying sensor layouts, and the occurrence of unmeasured impact forces, the parameters and maximum responses of interest can be estimated with acceptable accuracy when the observability condition is met.