Unscented Kalman Filter Research Articles

An Iterative Augmented Unscented Kalman Particle Filter for Simultaneous State-Parameter-Input Estimation for Structural Systems Subjected to Gamma-Distribution Noise

Simultaneous estimations of the states, parameters and unknown inputs of nonlinear structural systems subjected to non-Gaussian noise are essential, because the inputs are not always available and the system noise is not always Gaussian. However, filters developed for this task require the inter-story drift measurements to be “fused” with the acceleration measurements to avoid the “drift phenomenon”. Because inter-story drifts may be inconvenient to obtain in practice, it is more desirable to use acceleration measurements only. To this end, this study develops a novel iterative augmented unscented Kalman particle filter (IAUKPF) for the simultaneous state-parameter-input estimation for systems subjected to non-Gaussian noise. The iterative strategy proposed in this study effectively corrects the “drift phenomenon” when only acceleration measurements are incorporated, so that the accuracies of the estimated unknown inputs are promoted. The importance density of the particle filter at each time step is provided by the augmented unscented Kalman filter so that the filter takes the best known information into consideration. Numerical examples of nonlinear structural systems affected by non-Gaussian noise are adopted to examine the effectiveness of the proposed IAUKPF.

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%.

Neural Sliding Mode Control of a Buck-Boost Converter Applied to a Regenerative Braking System for Electric Vehicles

This paper presents the design and simulation of a neural sliding mode controller (NSMC) for a regenerative braking system in an electric vehicle (EV). The NSMC regulates the required current and voltage of the bidirectional DC-DC buck–boost converter, an element of the auxiliary energy system (AES), to improve the state of charge (SOC) of the battery of the EV. The controller is based on a recurrent high-order neural network (RHONN) trained using the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) as the tools to train the neural networks to obtain a higher SOC in the battery. The performance of the controller with the two training algorithms is compared with a proportional integral (PI) controller illustrating the differences and improvements obtained with the EKF and the UKF. Furthermore, robustness tests considering Gaussian noise and varying of parameters have demonstrated the outcome of the NSMC over a PI controller. The proposed controller is a new strategy with better results than the PI controller applied to the same buck–boost converter circuit, which can be used for the main energy system (MES) efficiency in an EV architecture.

Nonlinear Filtering and Reinforcement Learning Based Consensus Achievement of Uncertain Multi-Agent Systems

Abstract This paper introduces a novel approach for designing estimators to achieve consensus in uncertain multi-agent systems (MAS), even when various fault conditions are present and communication is assumed to be undirected and connected. The method includes an adaptive fault detection technique to detect faults and a unique adaptation in the unscented Kalman filter (UKF) to adjust noise covariance matrices and reconstruct uncertain states in the multi-agent system is proposed in the framework of Q-learning. Additionally, it involves training neural network internal parameters using previous measurements. A Chebyshev neural network (CNN) is employed to model the uncertain plant, and a hyperbolic tangent-based robust control term is used to mitigate neural network approximation errors. This novel approach is known as reinforced UKF (RUKF). The paper also discusses the asymptotic stability of the proposed method and presents numerical simulations to demonstrate its effectiveness with reduced computational load.

A dynamic state estimation method for integrated energy system based on radial basis kernel function

For state estimation (SE) of dynamic electro-thermal gas coupled systems, measurements usually assume that the measurement noise obeys a Gaussian distribution. The extended Kalman filter and the unscented Kalman filter (UKF) are some of the widely used estimation methods in SE. However, the measurement noise does not always follow Gaussian distribution in practice. When the measurement noise is non-Gaussian, the performance of these methods may not be satisfactory. In this paper, we propose an unscented Kalman filtering method based on minimizing radial basis kernel function criterion (MRBFC-UKF), which explores the optimal values of the shape parameters of the kernel function instead of using the widely used Gaussian and exponential kernel functions. Simulations are run dynamically in an integrated energy system which comprises an IEEE 14-bus, a 20-node natural gas network and a 32-node local thermal network. The results show that the proposed MRBFC-UKF method has good robustness and accuracy, and can effectively cope with the presence of unexpected bad data inputs.

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.

Remaining useful life prediction of proton exchange membrane fuel cell based on Wiener process and Bayesian GRU network considering multi-source uncertainties

ABSTRACT Proton exchange membrane fuel cell (PEMFC) is considered as one of the most promising green energy devices. Although fruitful results can be available for the remaining useful life (RUL) prediction of PEMFC, stochastic uncertainties have never been considered. To tackle this problem, a hybrid method is proposed in this paper. Wiener process with temporal uncertainty and individual uncertainty is adopted to model the degradation of the state of health (SOH), which is then estimated from monitoring voltage with measurement noise using the unscented Kalman filter (UKF), where unknown filtering and model parameters are jointly identified by expectation-maximization (EM) algorithm and Rauch-Tung-Striebel (RTS) smoother. Finally, gated recurrent unit (GRU) network is employed to realize the RUL prediction with the prediction uncertainty quantified by the Bayesian variational inference technology. The proposed method is verified on the experimental data. Results indicate that smaller mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) values can be obtained compared with other methods. When 60% data are used for prediction, the proposed method can achieve a RUL prediction accuracy with 1.63% and 2.17% relative errors under static and dynamic conditions, respectively, which illustrates the feasibility and superiority of the proposed method.

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.

Nonlinear Control Structure of Grid Connected Modular Multilevel Converters

This paper implements nonlinear control structure based on Adaptive Fuzzy Sliding Mode (AFSM) Current Control and Unscented Kalman Filter (UKF) to estimate the capacitor voltages from the measurement of arm currents of Modular Multilevel Converter (MMC). UKF use nonlinear unscented transforms in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab/Simulink environment to verify the performance of the overall proposed control structure during different case studies.

Effective capacity early estimation of lithium thionyl chloride batteries for autonomous underwater vehicles

Effective capacity early estimation is one of the critical tasks for electric autonomous underwater vehicles (AUV) to guide energy allocation and ensure equipment reliability. An effective capacity estimation method for Li/SOCl2 is proposed here. Firstly, we generate a comprehensive dataset consisting of 138 Li/SOCl2 cells, where the test-matrix is designed based on the AUV's working modes. Then, an effective capacity estimation architecture is established. In this architecture, a calendar aging model (CAM) based on the storage mode is obtained; a polynomial regression model (PRM), trained by features exacted from the early discharge data, is coupled to CAM based on the unscented Kalman filter (UKF), where one-step fusion is adopted to ensure lightweight. The verification results show that the architecture significantly improves prediction accuracy compared to traditional methods only considering the single working mode and performs well with generalization ability in the new database. Moreover, the early prediction and lightweight characteristics make it the most promising candidate for AUV power estimation in engineering.

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.

Vision-aided intelligent and adaptive vehicle pose estimation during GNSS outages

In this paper, a novel multi-information fusion methodology is proposed for vehicle pose estimation. The purpose is to improve the pose estimation accuracy during global navigation satellite system (GNSS) outages, mainly from two aspects: (1) extra observations of accurate velocities and angular rates without cumulative errors; (2) adaptive and intelligent fusion. Firstly, a multidimensional motion perception network (MMPN) is designed in order to estimate the velocities and angular rates. At the same time, the motion state is also output. The inputs of the network are two consecutive images. Thus, the estimated velocities and angular rates are not affected by cumulative errors. Besides, because the corresponding velocities and angular rates measured by high-quality inertial measurement unit (IMU) with low noise and drift are used as the training samples, the accuracy of the estimated velocities and angular rates are guaranteed. Further, an unscented Kalman filter with federal structure (UKF-F) with different motion models is designed for pose estimation. The local filters of UKF-F use the current probabilities of belonging to the motion patterns output by the MMPN as the information-sharing factors. Thus, the fusion is adaptive to the actual vehicle motion state. In addition, a gate recurrent unit (GRU)-based error compensation module is introduced to further reduce the position errors during GNSS outages. The GRU-based module is trained offline with the input of MMPN and IMU observations. Due to the advantages of time series forecasting, the GRU-based module can accurately predict the position error of IMU/MMPN integration online. The KITTI dataset with different driving scenarios is used to confirm the feasibility of the proposed methodology. The results of the experiments verify that the proposed methodology can achieve precise vehicle pose estimation during GNSS outages.

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.

Robust Cubature Kalman Filter for Moving-Target Tracking with Missing Measurements.

Handling the challenge of missing measurements in nonlinear systems is a difficult problem in various scientific and engineering fields. Missing measurements, which can arise from technical faults during observation, diffusion channel shrinking, or the loss of specific metrics, can bring many challenges when estimating the state of nonlinear systems. To tackle this issue, this paper proposes a technique that utilizes a robust cubature Kalman filter (RCKF) by integrating Huber's M-estimation theory with the standard conventional cubature Kalman filter (CKF). Although a CKF is often used for solving nonlinear filtering problems, its effectiveness might be limited due to a lack of knowledge regarding the nonlinear model of the state and noise-related statistical information. In contrast, the RCKF demonstrates an ability to mitigate performance degradation and discretization issues related to track curves by leveraging covariance matrix predictions for state estimation and output control amidst dynamic disruption errors-even when noise statistics deviate from prior assumptions. The performance of extended Kalman filters (EKFs), unscented Kalman filters (UKFs), CKFs, and RCKFs was compared and evaluated using two numerical examples involving the Univariate Non-stationary Growth Model (UNGM) and bearing-only tracking (BOT). The numerical experiments demonstrated that the RCKF outperformed the EKF, EnKF, and CKF in effectively handling anomaly errors. Specifically, in the UNGM example, the RCKF achieved a significantly lower ARMSE (4.83) and ANCI (3.27)-similar outcomes were observed in the BOT example.

Speed Tracking and Anti-Slip Control for Heavy Freight Trains Considering the Conicity of the Wheel

To ensure the safe and punctual transportation of freight trains, it is crucial for the train to travel at the targeted speed on the track. This paper proposes a scheme for speed tracking and anti-slip control for freight trains. The speed tracking is implemented through predictive auto disturbance rejection control (PADRC), which includes a flexible Smith estimation module capable of accurately predicting the output of large time delay systems, such as freight trains. The key to anti-slip control relies on the precise observation of the radial velocity and slip rate. Therefore, an unscented Kalman filter observer is designed in this article, incorporating an adaptive parameter adjustment mechanism to enhance observation accuracy. The anti-slip parameters obtained from this observer can then be used to determine the anti-slip control scheme. The effectiveness of this scheme is demonstrated through simulations of the HXD1 electric traction locomotive’s driving process, using line data from the Geku line section in China. Compared to conventional active disturbance rejection control, PADRC reduces speed fluctuation by 55%, and freight trains under anti-slip control decrease the slip speed by 90%.

Design and experiment of the simulated electronic corn ear based on UWB/IMU technology

In order to explore kinematic and dynamic parameters of corn ear in the process of threshing, and reveal threshing principle and grain impact damage mechanism, a simulation electronic corn ear was designed based on ultra wide band (UWB) and inertial measurement unit (IMU) technology. The spatial positioning algorithm and impact force analysis algorithm of electronic corn ear were studied, and a simulated threshing test bench was built. Then free fall impact force detection test and comprehensive performance test of the electronic corn ear were carried out. The experimental results showed that the average detection error of free fall impact force was about 0.69 N, with an accuracy more than 95 %, and the average detection error of impact force in the process of simulation threshing was about −0.27 N, with an accuracy more than 97 %. The spatial positioning accuracy of electronic corn ear was related to the number, layout and positioning algorithm of UWB positioning base station. Unscented kalman filter (UKF) tight combination positioning algorithm had the highest positioning accuracy (about 100 % probability of positioning error within ± 0.15 m) under the condition of non-line of sight (NLOS) (5 base stations, 3.2 m height difference). Extended kalman filter (EKF) tight combination positioning algorithm had the second highest positioning accuracy (about 100 % probability of positioning error within ± 0.2 m), followed by kalman filter (KF) loose combination, UWB single positioning and IMU single positioning algorithm. The results are helpful for obtaining kinematic and dynamic parameters in the process of ear threshing and separation, understanding the mechanism of efficient and low-damage threshing, and provide a basis for the segmented optimization design of subsequent devices.

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.

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.

Improved State-of-Charge Estimation of Lithium-Ion Battery for Electric Vehicles Using Parameter Estimation and Multi-Innovation Adaptive Robust Unscented Kalman Filter

In this study, an improved adaptive robust unscented Kalman Filter (ARUKF) is proposed for an accurate state-of-charge (SOC) estimation of battery management system (BMS) in electric vehicles (EV). The extended Kalman Filter (EKF) algorithm is first used to achieve online identification of the model parameters. Subsequently, the identified parameters obtained from the EKF are processed to obtain the SOC of the batteries using a multi-innovation adaptive robust unscented Kalman filter (MIARUKF), developed by the ARUKF based on the principle of multi-innovation. Co-estimation of parameters and SOC is ultimately achieved. The co-estimation algorithm EKF-MIARUKF uses a multi-timescale framework with model parameters estimated on a slow timescale and the SOC estimated on a fast timescale. The EKF-MIARUKF integrates the advantages of multiple Kalman filters and eliminates the disadvantages of a single Kalman filter. The proposed algorithm outperforms other algorithms in terms of accuracy because the average root mean square error (RMSE) and the mean absolute error (MAE) of the SOC estimation were the smallest under three dynamic conditions.

Application of model updating to a large‐scale hybrid simulation

AbstractModel updating can enhance hybrid simulation by utilizing the experimental data from the physically tested substructure to update the parameters of like‐components in the numerical substructure throughout the test, improving the overall accuracy and reducing the extent of the experimental setup. Identifying and updating parameters can be challenging, especially when coupling between degrees of freedom (DOF) must be considered or the specimen experiences loading scenarios which result in newly observed behavior. To explore the performance of model updating under these challenging conditions, a large‐scale hybrid simulation was conducted using a model of a major toll bridge with seismic isolation lead rubber bearings (LRB). One LRB is physically tested considering axial, shear, and rotational loading, while the remainder of the bearings are simulated and updated with a phenomenological model within the numerical substructure. A weighted adaptive constrained unscented Kalman filter is applied as the online model updating algorithm. The study explored the effect of learning over different loading patterns, the selection of initial model parameters, and the selection of the physically tested substructure. The improvement of numerical model hysteresis performance accuracy of the force prediction demonstrates the benefits of model updating in large‐scale hybrid simulation.