Smooth Variable Structure Filter Research Articles

Model-based impending lithium battery terminal voltage collapse detection via data-driven and machine learning approaches

Lithium battery is an important power source of an electrical vehicle (EV). Practically, when a battery is about to fail, it needs to be removed from the load because keeping it connected can lead to permanent damage. Hence, it is important to detect battery failure to sustain the lifespan of the battery and avoid safety issues which will contribute to the sustainability of the EV. However, determining the effective disconnecting or discharging moment of the battery remains a challenging issue in EV applications. In order to solve the abovementioned problem, a control framework and maximum likelihood estimation are proposed to estimate the parameters of a battery model. In addition, both the sparse representation and dynamic mode decomposition (DMD) approaches are applied to protect the physical battery unit from a failure scenario. For comparison purposes, the proposed framework is compared to a Lyapunov-based detection approach along with neural network (NN) and linear discriminant analysis (LDA). Moreover, several state estimation algorithms are applied to estimate battery state of charge (SOC) at each time step: extended Kalman filter, extended Kalman smooth variable structure filter, and cubature Kalman filter. Finally, the experimental results showed that the proposed DMD approach outperforms the sparse representation, NN, LDA, and Lyapunov-based approaches in terms of detection accuracy. Moreover, the proposed DMD strategy is more robust towards the inaccuracy of the estimated SOC. Besides that, the proposed battery model parameter estimation approach exhibited fast processing time; therefore, it is a reliable choice for recomputing the model parameters from time to time to compensate aging effect. An autonomous unmanned aerial vehicle (UAV) was simulated as a proof-of-concept in a MATLAB environment to verify the detection performance of the proposed methods. Both actual and UAV results showed that the DMD demonstrated more robust detection performance than other methods in terms of processing time and detection accuracy.

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter.

Online estimation of state-of-charge inconsistency for lithium-ion battery based on SVSF-VBL

It is of great significance to estimate cell inconsistency for improving the service life and safety performance of the power battery pack. To accurately estimate the state-of-charge (SOC) inconsistency of cells with different performance parameters and working states, a method combining adaptive robust unscented Kalman filter and smooth variable structure filter with time-varying smoothing boundary layer (SVSF-VBL) is proposed. The cell mean-difference model is used to simulate the behavior characteristics of the battery module, including the cell mean model expressed by the dual polarization (DP) model and the cell difference model characterized by the hypothetical Rint model. Firstly, the improved forgetting factor recursive least square is applied to identify parameters of the DP model, and the unscented Kalman filter incorporating robust estimation and adaptive filter tuning is employed to estimate the SOC of the battery module. Then, SVSF-VBL is used to estimate the SOC difference between each cell and module based on the Rint model for improving the estimation accuracy and robustness. In addition, the comprehensive inconsistency of the cells can be captured by the secondary performance indicator inherent in SVSF-VBL, which contributes to the in-depth study of cell inconsistency. Finally, a series of tests are carried out to verify the performance of the proposed method, and the results show that the method can improve the estimation accuracy and convergence performance while effectively suppressing the system disturbance.

State of Charge Estimation of Lithium-ion Battery in Electric Vehicles Using the Smooth Variable Structure Filter: Robustness Evaluation against Noise and Parameters Uncertainties

State of Charge (SoC) of Lithium-ion battery is a key parameter in battery management systems for electric vehicles. This paper uses the fundamental theory of the smooth variable structure filter (SVSF) and proposes a SoC estimation algorithm for a Manganese Cobalt (NMC) cell with a nominal capacity of 20 Ah. Several tests are conducted considering different types of noise and parameters variation. A nonrandom Gaussian noise is first added to the battery voltage. The maximum root mean square error (RMSE) of the estimated SoC is about for a standard deviation of the noise set to P.U. The same noise is applied to the battery current and the maximum RMSE of the SoC is obtained as 1.36%. Moreover, an EMI noise is added to the battery voltage and the obtained RMSE of the SoC is about 1.73% for a peak amplitude of the noise set to 0.07 P.U. The convergence of the algorithm is also confirmed under battery parameters variation due to the temperature change. However, its accuracy degrades considerably. Finally, a comparative study is carried out with the extended Kalman filter and shows the superiority of SVSF in terms of accuracy and robustness against measurement noise.

A Novel Calibration Algorithm of SINS/USBL Navigation System Based on Smooth Variable Structure

Aiming at the problem that the USBL installation error is difficult to accurately calibrate in the complex underwater environment. In this paper, based on smooth variable structure and unscented Kalman filter, a novel USBL installation error calibration algorithm is proposed. Firstly, the nonlinear system model of USBL installation error based on the filter estimation principle is analyzed. On this basis, the USBL installation error calibration algorithm based on the principle of unscented Kalman filter is given. Secondly, in view of the shortcomings of the UKF calibration algorithm, smooth variable structure is introduced, and a novel algorithm combining smooth variable structure and UKF is proposed. Finally, the effectiveness of the algorithm proposed in this paper is verified by simulation and river test. The results show that the algorithm proposed in this paper can accurately and stably estimate the USBL installation error parameters when the underwater acoustic signal is disturbed.

Multispectral Target Tracking with Robust Correlation and Optimal Position Prediction

Object tracking using only visible-light sensor is usually problematic when facing some challenging scenes related to a complex environment like darkness, strong light, rain, fog, etc. In this paper, we have taken images, both thermal and visible light spectrum, from RGBT234 dataset as inputs for our proposed tracker which works as follows: First, the single shot multibox detector (SSD) is proposed to produce automatically the initial position of the target for visible and infrared modes. Second, a switching fuzzy logic controller (FLC) has been proposed to ensure automatic selection and switching between tracking modes (visible-light or thermal infrared spectrum) when a new environment is detected using confidence measures on some relevant features of the frames for each mode. Finally, to improve the kernelized correlation filter as a base tracker and overcome the limitation of the multimodal visual tracking, especially during tracking mode switching when visual information is not available, robust optimal smooth variable structure filter (SVSF) is proposed. Experiments on the recently public benchmark RGB-T234 demonstrate the effectiveness of our proposed method when compared to other state-of-the-art trackers.

Adaptive SVSF-KF estimation strategies based on the normalized innovation square metric and IMM strategy

The smooth variable structure filter (SVSF) is highly robust to modeling uncertainty and unknown disturbances. Recent developments to the SVSF have allowed for the creation of an adaptive estimation scheme termed the SVSF-KF, which balances the optimality of the Kalman filter (KF) with the robustness of the SVSF. The approach utilizes the KF estimate during normal operation, and utilizes the robust SVSF gain to estimate the states during the presence of a fault. However, the gain adaptation involved in detecting a fault and switching between the KF and SVSF estimates suffers from several limitations, including unwanted chattering. In this work, we review the original SVSF-KF approach and present two novel SVSF-KF strategies based on the normalized innovation square metric and the interacting multiple model strategy to address these limitations. Experimental simulations involving a simple harmonic oscillator subject to a fault condition are conducted, which verify the effectiveness of our proposed approaches.

Enhanced EKF and SVSF for state of charge estimation of Li‐ion battery in electric vehicle using a fuzzy parameters model

The precision of equivalent circuit model (ECM)-based state of charge (SoC) estimation methods is vulnerable to the variation of the battery parameters, due to several internal and external factors. In this regard, this study proposes a fuzzy logic method for the approximate estimation of the ECM parameters at different temperatures and SoC levels. The fuzzy inference system is designed to handle the non-linear deviation of the battery parameters from their reference values. On this basis, the extended Kalman filter and smooth variable structure filter are used to estimate the SoC. The two algorithms with fuzzy parameters (FP), namely FP-EKF and FP-SVSF, are tested on a 20 Ah Nickel Manganese Cobalt cell with maximum voltage of 4.2 V. The results show that the maximum root mean square error (RMSE) of the estimated SoC is kept within 1.51% with the FP-EKF and 0.68% with the FP-SVSF. Moreover, the reduction of the maximum absolute error may reach 0.34% with the FP-EKF, and 0.82% with the FP-SVSF, compared to the same algorithms without the proposed FP method. The executable codes are implemented on a low-cost controller, and the average computational time is obtained as 215 μs, which confirms the real-time practicality of the proposed method.

An efficient field programmable gate arrays based real‐time implementation of smooth variable structure filter to estimate the state of charge of Li‐ion battery in electric vehicle application

The computational efficiency is a challenging task in the real-time implementation of battery State of Charge (SoC) estimation algorithms in Electric Vehicle (EV) application. This study proposes for the first time a pure hardware architecture of a Smooth Variable Structure Filter (SVSF) to estimate the SoC of a lithium-ion battery in an EV. The proposed embedded architecture is implemented on a Xilinx Zynq-7000 field programmable gate arrays board without using any soft-core, and validated with real-time tests carried out on a 20 Ah NMC battery with nominal voltage about 3.65 V. The whole embedded architecture of the SVSF needs a reduced execution time in the range of 921 ns, and it consumes only 466 mW. The average estimation errors of the SoC and battery voltage at different temperatures are kept within 4.95% and 2.35% respectively. The successful convergence of the algorithm and the accurate results obtained in different circumstances, prove the practicability and computational efficiency of the proposed hardware architecture.

Hardware Implementation of Attitude Estimation Methods Using Multiple GPS Receivers

This paper deals with the attitude estimation issue for navigation of Unmanned Aerial Vehicles (UAVs). We propose a new multi-GPS sensor fusion, based on Extended Kalman Filter (EKF) and Smooth Variable Structure Filter (SVSF), using an Inertial Measurement Unit (IMU) and three GPS receivers. Two methods; the Direct Computing Method (DCM) and the Least Square Method (LSM) are used to estimate the full attitude of the UAV. Performance and robustness are tested with numerical simulation. Experimental validation is carried out on fixed-wing aircraft to evaluate the capabilities of the proposed approaches in attitude estimation. Through this framework, it is proven that subdegrees order of estimation error can be guaranteed when real dynamic situations are applied to the aircraft.

A Hybrid SVSF Algorithm for Automotive Radar Tracking

This paper concerns the robust state estimation of automotive radar targets in presence of model uncertainty. Smooth variable structure filter (SVSF) achieves error-bounded estimation for target state, even with an inaccurate description of target kinematic model. However, it suffers the undesired chattering phenomenon especially in case of a high model uncertainty level, and its performance is sensitive to a preset smoothing boundary layer parameter. In this paper, we propose a novel hybrid SVSF algorithm to handle these two problems simultaneously. First, we derive a nonlinear generalized variable smoothing boundary layer (NGVBL) parameter based on the conventional Tanh-SVSF method by minimizing the pseudo posterior estimation error covariance. Then this NGVBL is employed to realize an adaptive two-module switching strategy with respect to the uncertainty level to calculate the correction gain. If the uncertainty level is high, the undesired chattering is effectively suppressed by the standard Tanh-SVSF gain. In case of a low uncertainty level, the NGVBL is utilized to replace the preset smoothing boundary layer parameter and reformulate the correction gain. Furthermore, it is demonstrated that the NGVBL-based gain is quasi-optimal in the mean square error (MSE) sense. Accordingly, this novel NGVBL-based hybrid SVSF (NGVBL-SVSF) algorithm improves the estimation performance by avoiding parameter sensitivity in a low uncertainty level case, and maintains effective chattering suppression and robustness to increasing uncertainties. Simulation and real-world automotive radar data experiment results show that, the proposed NGVBL-SVSF outperforms existing SVSFs and the classical Kalman filter in terms of tracking accuracy and track continuity.

Robust attitude estimation for an unmanned aerial vehicle using multiple GPS receivers

Estimation of the system state is an important task in the field of control, localization, and navigation. Many sensors are used to extract the attitude information. GPS (Global Positioning System) is widely used to provide position and velocity for ground and aerial vehicles. However, only a few research works have addressed the problem of attitude estimation using multiple GPS receivers. The main contribution of this paper consists on proposing a robust algorithm for attitude estimation of an unmanned aerial vehicle using INS/3GPS integration. First, we propose two alternative methods for attitude determination with three GPS receivers: Direct Computing Method (DCM) and Least Square Method (LSM) based on Singular Value Decomposition (SVD). Second, the attitude given by GPS receivers is fused with the measurement of a three-axis gyroscope using a robust Smooth Variable Structure Filter (SVSF). The optimal geometric configuration of GPS antennas is determined based on a deep performance analysis of the proposed system. Then, robustness analysis is assessed against measurement noise and parameters uncertainties. Simulation results are presented to demonstrate the robustness of the proposed approach. A more realistic evaluation of the proposed solution is obtained using an aerial vehicle type “Helicopter” from the Virtual Robot Experimentation Platform (VREP simulator). The proposed filter is compared with an Extended Kalman Filter (EKF). The obtained results have confirmed how much the SVSF is robust for attitude estimation in presence of the considered disturbances.

A Novel Smooth Variable Structure Filter for Target Tracking Under Model Uncertainty

Model uncertainty is a serious challenge for robustness of tracking algorithms in radar systems. The smooth variable structure filter (SVSF) achieves error-bounded estimations for target state by scaling the magnitude of kinematic modeling error and accordingly performing a flexible switching strategy for the correction gain. However, the SVSF, without any smoothing functions, suffers from undesired chattering phenomenon since the measurement noise causes random disturbance to the identification of actual level of uncertainties, leading to obvious deterioration of tracking accuracy. In this paper, we present a new switching function for SVSF, i.e. the hyperbolic tangent function, for effective chattering suppression. Then we propose a new algorithm named as the Tanh-SVSF, which reformulates the correction gain with the new switching function, to improve the estimation accuracy for target state. A mathematical definition of SVSF chattering is proposed to quantify the chattering amplitude. It is demonstrated that the new switching function exerts a nonlinear compressing effect on the likelihood of measurement innovation and substantially reduces the disturbance of measurement noise, leading to elimination of the chattering problem. The stability of the Tanh-SVSF is analyzed, based on a proposed stability theorem and the numerical exhaustion strategy. Finally, the proposed method is tested on a simulated vehicle tracking scenario and real-world radar data from the Oxford Radar RobotCar Dataset, and shows superior performance over existing SVSF formulations and the Kalman filter, in view of tracking accuracy, track continuity and the proposed chattering indicator.

Performance evaluation of a novel adaptive variable structure state estimator

An improved nonlinear adaptive state estimator called Adaptive Smooth Variable Structure Filter ASVSF has been proposed and its algorithm described. ASVSF extends the functionality and performance of a previously reported robust smooth variable structure filter (SVSF) with optimal boundary layer (SVSF-OBL). Improvement in performance includes the provision for accommodating unknown and time varying process noise covariance, which generally characterizes modelling uncertainty. The novelty of this proposed ASVSF estimator, which inherits the features of the SVSF, is that it adaptively provides an estimate of the unknown time varying process noise covariance (and hence called adaptive SVSF or ASVSF) which is required for determining the optimal boundary layer width of SVSF-OBL thus obviating the need of the prior knowledge of the process noise covariance. This makes the proposed estimator performance to be insensitive to (and therefore robust with respect to) unknown time varying process noise covariance while retaining the optimality of SVSF-OBL. The performance of the proposed ASVSF estimator is evaluated using Monte Carlo simulation and is compared with previously reported state estimators using a case of maneuvering civilian aircraft where a simplified and grossly approximate process model is used in the estimator/filter for tracking and thereby generating a time varying and unknown process noise covariance situation. Three different measures of Root Mean Square (RMS) error over the trajectory have been used for comparison which demonstrates the strengths of the proposed ASVSF estimator.

Homography‐based uncalibrated visual servoing with neural‐network‐assisted robust filtering scheme and adaptive servo gain

AbstractIn this paper, a homography‐based uncalibrated visual servo system with neural‐network‐assisted robust filtering scheme and adaptive servo gain is presented. This system employs a homography‐based task function which is robust to image defects. A neural‐network‐assisted robust filtering method which combines the new form of smooth variable structure filter (SVSF) with a radial basis function (RBF) neural network is proposed to estimate the total Jacobian between task function and robot joints. The RBF neural network in this filtering method plays the role as a corrector to further improve the accuracy and compensate the interference caused by the measurement errors of image features. The controller that directly controls the robot joints based on the estimated total Jacobian is designed for achieving the robustness to robot parameters errors. By adopting this filtering scheme, the visual servo system shows better accuracy and convincing anti‐interference ability. In addition, a novel Q‐learning strategy is introduced for this homography‐based system to make adaptive adjustment for the servo gain. This adaptive gain enables the system to achieve a faster convergence speed while ensuring the accuracy. Several simulations and experiments have been carried out to verify the performance of the proposed system.

An Augmented Multiple Imputation Particle Filter for River State Estimation With Missing Observation

In this article, a new form of data assimilation (DA) method namely multiple imputation particle filter with smooth variable structure filter (MIPF–SVSF) is proposed for river state estimation. This method is introduced to perform estimation during missing observation by presenting new sets of data. The contribution of this work is to overcome the missing observation, and at the same time improve the estimation performance. The convergence analysis of the MIPF–SVF is discussed and shows that the method depends on the number of particles and imputations. However, the number of particles and imputations is influenced by the error difference in the likelihood function. By bounding the error, the ability of the method can be improved and the number of particles and computational time are reduced. The comparison between the proposed method with EKF during complete data and multiple imputation particle filter shows the effectiveness of the MIPF–SVSF. The percentage improvement of the proposed method compared to MIPF in terms of root mean square error is between 12 and 13.5%, standard deviation is between 14 and 15%, mean absolute error is between 2 and 7%, and the computational error is reduced between 73 and 90% of the length of time required to perform the estimation process.

Online power and efficiency estimation of a fuel cell system for adaptive energy management designs

The temporal changes of power and efficiency in a fuel cell (FC) stack can cause malperformance in the energy management strategy (EMS) of a FC hybrid electric vehicle. Therefore, the online estimation of these physical attributes is becoming an integral part of any EMS. This paper aims to utilize a two-step method to extract the maximum power and efficiency points of a FC system online. In this respect, an online parameter estimation technique, composed of smooth variable structure filter (SVSF) and Kalman filter (KF), is utilized in the first step to estimate the parameters of a FC semi-empirical voltage model. KF generates statistically optimal estimates for a linear, well-designed system model in the existence of Gaussian noise. However, these assumptions do not always hold in real applications and can lead to unstable estimation. A practical solution to deal with these instabilities is to enforce boundaries on the state estimates through SVSF which is based on sliding mode estimation concept. Hence, unlike the other similar studies, this paper synthesizes the robustness of SVSF with the precision of KF to enhance the characteristics estimation process of a FC stack. In the second step, the updated voltage model is utilized to extract the efficiency and power curves of the real FC system. To corroborate the potential of the proposed approach, a thorough comparison with KF, as an attested estimation method, is performed. The experimental tests on a 500-W FC stack indicate the superior performance of the SVSF-KF compared to that of KF.

A new strategy of smooth variable structure filter to estimate unmeasured states in target tracking

In the field of target tracking, the Kalman filter is one of the most popular filters, but its robustness will decrease when target maneuvers. The novel smooth variable structure filter (SVSF) has attracted much attention for its robustness against disturbances and uncertainties. In linear systems, the existing methods of SVSF can estimate unmeasured states, which refer to the states that cannot be measured by sensors, but the estimation is with low accuracy. And there is little research on the estimation for unmeasured states by SVSF in nonlinear systems. Therefore, this paper has put forward a novel strategy to improve the estimation accuracy of unmeasured states in both linear and nonlinear systems. The proposed strategy uses the correlation of error covariance among state elements to calculate the value of unmeasured states. On the basis of the strategy deduced from linear system, one algorithm in linear system and two new extended algorithms in nonlinear systems are proposed. In simulations, different filter models are used by all filters to process Gaussian and non-Gaussian noise in linear and nonlinear systems. The comprehensive results prove that, the proposed linear algorithm has better performance than the existing methods of SVSF in linear systems. Two nonlinear algorithms also show good performance in the estimation for unmeasured states in nonlinear and non-Gaussian systems.

Adaptive Smooth Variable Structure Filter Strategy for State Estimation of Electric Vehicle Batteries

Battery Management Systems (BMSs) are used to manage the utilization of batteries and their operation in Electric and Hybrid Vehicles. It is imperative for efficient and safe operation of batteries to be able to accurately estimate the State of Charge (SoC), State of Health (SoH) and State of Power (SoP). The SoC and SoH estimation must remain robust and accurate despite aging and in presence of noise, uncertainties and sensor biases. This paper introduces a robust adaptive filter referred to as the Adaptive Smooth Variable Structure Filter with a time-varying Boundary Layer (ASVSF-VBL) for the estimation of the SoC and SoH in electrified vehicles. The internal model of the filter is a third-order equivalent circuit model (ECM) and its state vector is augmented to enable estimation of the internal resistance and current bias. It is shown that system and measurement noise covariance adaptation for the SVSF-VBL approach improves the performance in state estimation of a battery. The estimated internal resistance is then utilized to improve determination of the battery’s SoH. The effectiveness of the proposed method is validated using experimental data from tests on Lithium Polymer automotive batteries. The results indicate that the SoC estimation error can remain within less than 2% over the full operating range of SoC along with an accurate estimation of SoH.

Multispectral Visual Odometry Using SVSF for Mobile Robot Localization

In this paper, we propose a novel method for mobile robot localization and navigation based on multispectral visual odometry (MVO). The proposed approach consists in combining visible and infrared images to localize the mobile robot under different conditions (day, night, indoor and outdoor). The depth image acquired by the Kinect sensor is very sensitive for IR luminosity, which makes it not very useful for outdoor localization. So, we propose an efficient solution for the aforementioned Kinect limitation based on three navigation modes: indoor localization based on RGB/depth images, night localization based on depth/IR images and outdoor localization using multispectral stereovision RGB/IR. For automatic selection of the appropriate navigation modes, we proposed a fuzzy logic controller based on images’ energies. To overcome the limitation of the multimodal visual navigation (MMVN) especially during navigation mode switching, a smooth variable structure filter (SVSF) is implemented to fuse the MVO pose with the wheel odometry (WO) pose based on the variable structure theory. The proposed approaches are validated with success experimentally for trajectory tracking using the mobile robot (Pioneer P3-AT).