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In order to improve the accuracy of internal temperature estimation in batteries, a 10-parameter time-varying multi-surface heat transfer model including internal heat production, heat transfer and external heat transfer is established based on the structure of a lithium iron phosphate pouch battery and its three directional anisotropic heat conduction characteristics. The entropy heat coefficient, internal equivalent heat capacity and internal equivalent thermal resistance related to the SOC and temperature state of the battery were identified using experimental tests and the least square fitting method, and were then used for online calculation of internal heat production and heat transfer in the battery. According to the time-varying and nonlinear characteristics of the heat transfer between the surface and the environment of the battery, an internal temperature estimation algorithm based on the square root cubature Kalman filter was designed and developed. By iteratively calculating the estimated surface temperature and the measured value, dynamic tracking and online correction of the internal temperature of the battery can be achieved. The verification results using FUDS and US06 dynamic working condition data show that the proposed method can quickly eliminate the influence of initial temperature deviations and accumulated process errors and has the characteristics of a high estimation accuracy and good robustness. Compared with the estimation results of the adaptive Kalman filter, the proposed method improves the estimation accuracy of FUDS and US06 working conditions by 67% and 54%, respectively, with a similar computational efficiency. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of internal temperature estimation in batteries, a 10-parameter time-varying multi-surface heat transfer model including internal heat production, heat transfer and external heat transfer is established based on the structure of a lithium iron phosphate pouch battery and its three directional anisotropic heat conduction characteristics. The entropy heat coefficient, internal equivalent heat capacity and internal equivalent thermal resistance related to the SOC and temperature state of the battery were identified using experimental tests and the least square fitting method, and were then used for online calculation of internal heat production and heat transfer in the battery. According to the time-varying and nonlinear characteristics of the heat transfer between the surface and the environment of the battery, an internal temperature estimation algorithm based on the square root cubature Kalman filter was designed and developed. By iteratively calculating the estimated surface temperature and the measured value, dynamic tracking and online correction of the internal temperature of the battery can be achieved. The verification results using FUDS and US06 dynamic working condition data show that the proposed method can quickly eliminate the influence of initial temperature deviations and accumulated process errors and has the characteristics of a high estimation accuracy and good robustness. Compared with the estimation results of the adaptive Kalman filter, the proposed method improves the estimation accuracy of FUDS and US06 working conditions by 67% and 54%, respectively, with a similar computational efficiency.

In this paper, a square root cubature Kalman filter based multi-innovation least square (SRCKF-MILS) algorithm is proposed for state of charge (SOC) estimation. First, a second-order resistor-capacitor (RC) equivalent circuit model is constructed to approximate the dynamic performance of the battery. Then, the multi-innovation least square and the square root cubature Kalman filter are used to interactively estimate the battery model parameters and SOC. Since the state vector contains outliers, the strong tracking filtering (STF) theory is introduced to adaptively adjust the gain matrix. The STF theory combined with SRCKF-MILS algorithm can improve the robustness of the algorithm. Simulation examples show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Background and Objectives:The target tracking problem is an essential component of many engineering applications.The extended Kalman filter (EKF) is one of the most well-known suboptimal filter to solve target tracking. However, since EKF uses the first-order terms of the Taylor series nonlinear extension functions, it often makes large errors in the estimates of state. As a result, target tracking based on EKF may diverge. Methods: In this manuscript, an adaptive square root cubature Kalman filter (ASRCKF) is poposed to solve the maneuvering target tracking problem. In the proposed method, the covariance of process and measurement noises is estimated adaptively. Thus, the performance of proposed method does not depend on the noise statistics and its performance is robust with unknown prior knowledge of the noise statistics. Morover, it has a consistently improved numerical stability why the matrices of covariance are guaranteed to remain semi- positive. The performance of the proposed method is compared with EKF, and the unscented Kalman filter (UKF) for target tracking problem. Results:To evaluate the proposed method, many experiments is performed. The proposed method is evaluated on the non-maneuvering and maneuvering target tracking. Conclusion: The results show that the proposed method has lower estimation errors with faster convergence rate than other methods. The proposed method can track the tates of moving target effectively and improve the accuracy of the system.

Background and Objectives:The target tracking problem is an essential component of many engineering applications. The extended Kalman filter (EKF) is one of the most well-known suboptimal filter to solve target tracking. However, since EKF uses the first-order terms of the Taylor series nonlinear extension functions, it often makes large errors in the estimates of state. As a result, target tracking based on EKF may diverge. Methods: In this manuscript, an adaptive square root cubature Kalman filter (ASRCKF) is poposed to solve the maneuvering target tracking problem. In the proposed method, the covariance of process and measurement noises is estimated adaptively. Thus, the performance of proposed method does not depend on the noise statistics and its performance is robust with unknown prior knowledge of the noise statistics. Morover, it has a consistently improved numerical stability why the matrices of covariance are guaranteed to remain semi- positive. The performance of the proposed method is compared with EKF, and the unscented Kalman filter (UKF) for target tracking problem. Results:To evaluate the proposed method, many experiments is performed. The proposed method is evaluated on the non-maneuvering and maneuvering target tracking. Conclusion: The results show that the proposed method has lower estimation errors with faster convergence rate than other methods. The proposed method can track the tates of moving target effectively and improve the accuracy of the system. [ABSTRACT FROM AUTHOR]

This paper investigated the problem of multi-target tracking (MTT) over a vehicle sensor network. A novel adaptive square root cubature joint probabilistic data association (ASRCJPDA) was proposed. Motivated by enhancing the stability of joint probabilistic data association (JPDA) in practical application, the proposed methodology implemented a numerically stabled cubature Kalman filter for JPDA state estimate process. It improved numerical stability and acquired more accurate estimated results. Additionally, enlightened by enhancing the real time efficiency of JPDA, an adaptive tracking gate designed for the JPDA measurement associate process was proposed. It combined with the kinematics of vehicle to reduce the computational complexity of data association, which improved the robustness of MTT in complex scenarios. The virtual vehicle target tracking scenarios were built in PreScan software in order to better simulate the real traffic condition. Simulations of target tracking examples are presented to show great effectiveness and superiority of the proposed method.

The distributed drive arrangement form has better potential for cooperative control of dynamics, but this drive arrangement form increases the parameter acquisition workload of the control system and increases the difficulty of vehicle control accordingly. In order to observe the vehicle motion state accurately and in real-time, while reducing the effect of uncertainty in noise statistical information, the vehicle state observer is designed based on interacting multiple model theory with square root cubature Kalman filter (IMM-SCKF). The IMM-SCKF algorithm sub-model considers different state noise and measurement noise, and the introduction of the square root filter reduces the complexity of the algorithm while ensuring accuracy and real-time performance. To estimate the vehicle longitudinal, lateral, and yaw motion states, the algorithm uses a three degree of freedom (3-DOF) vehicle dynamics model and a nonlinear brush tire model, which is then validated in a Carsim-Simulink co-simulation platform for multiple operating conditions. The results show that the IMM-SCKF algorithm's fusion output results can effectively follow the sub-model with smaller output errors, and that the IMM-SCKF algorithm's results are superior to the traditional SCKF algorithm's results. [ABSTRACT FROM AUTHOR]

This study addresses the tracking–learning–detection (TLD) algorithm for long‐term single‐target tracking of moving vehicle from video streams. The problems leading to tracking failures in existing TLD methods are discovered, and an improved TLD (ITLD) tracking algorithm is proposed which is more robust to object occlusion and illumination variation. A square root cubature Kalman filter (SRCKF) is employed in the tracker of TLD to predict the position of the object when occlusion occurs. Besides, this study introduces fast retina keypoint (FREAK) feature into the tracker to alleviate the instability caused by illumination variation or scale variation. The overlap comparison and the normalised cross‐correlation coefficient (NCC) are introduced to the integrator of the TLD to obtain reliable bounding boxes with improved tracking precision. Experiments are conducted to compare the performance of the state‐of‐the‐art trackers and the proposed method, using the object tracking benchmark that includes 50 video sequences (OTB‐50) and TLD datasets. The experimental results show that the proposed ITLD outperforms on both tracking accuracy and robustness. The proposed method can track a moving vehicle even when it is temporally totally occluded.

The distributed drive arrangement form has better potential for cooperative control of dynamics, but this drive arrangement form increases the parameter acquisition workload of the control system and increases the difficulty of vehicle control accordingly. In order to observe the vehicle motion state accurately and in real-time, while reducing the effect of uncertainty in noise statistical information, the vehicle state observer is designed based on interacting multiple model theory with square root cubature Kalman filter (IMM-SCKF). The IMM-SCKF algorithm sub-model considers different state noise and measurement noise, and the introduction of the square root filter reduces the complexity of the algorithm while ensuring accuracy and real-time performance. To estimate the vehicle longitudinal, lateral, and yaw motion states, the algorithm uses a three degree of freedom (3-DOF) vehicle dynamics model and a nonlinear brush tire model, which is then validated in a Carsim-Simulink co-simulation platform for multiple operating conditions. The results show that the IMM-SCKF algorithm’s fusion output results can effectively follow the sub-model with smaller output errors, and that the IMM-SCKF algorithm’s results are superior to the traditional SCKF algorithm’s results.

Background: Robotic puncture system (RPS) consists of an optical tracking system (OTS) and a robotic arm gripping the puncture needle. Typically, the RPS requires hand-eye calibration before the surgery in order to obtain the relative position between the OTS and the robotic arm. However, if there is any displacement or angular deviation in either the robotic arm or the OTS, the calibration results become invalid, necessitating recalibration., Methods: We propose an uncalibrated robotic puncture method that does not rely on the hand-eye relationship of the RPS. By constructing angle and position graph jacobian matrices respectively, and employing Square Root Cubature Kalman Filter for online estimation. This enables obtaining control variables for the robot to perform puncture operations., Results: In simulation experiments, our method achieves an average error of 1.3495 mm and an average time consumption of 39.331 s., Conclusions: Experimental results indicate that our method possesses high accuracy, low time consumption, and strong robustness., (© 2023 John Wiley & Sons Ltd.)

Summary: The development of a novel method to estimate the state of charge (SOC) with low read‐only memory (ROM) occupancy, high stability, and high anti‐interference capability is very important for the battery management system (BMS) in actual electric vehicles. This paper proposes the square root cubature Kalman filter (SRCKF) with a temperature correction rule, based on the BMS of a common on‐board embedded micro control unit (MCU), to achieve smooth estimation of SOC. The temperature correction rule is able to reduce the testing effort and ROM space used for data table storage (189.3 kilobytes is much smaller than the storage of the MPC5604B, with 1000 kilobytes), while the SRCKF is adopted to achieve highly robust real‐time SOC estimation with high resistance to interference and moderate computing cost (68.3% of the load rate of the MPC5604B). The results of multiple experiments show that the proposed method with less computational complexity converges rapidly (in approximately 2.5 s) and estimates the SOC of the battery accurately under dynamic temperature condition. Moreover, the SRCKF algorithm is not sensitive to the high measuring interference and highly nonlinear working conditions (even with 1% current and voltage measurement disturbances, the root mean square error of the proposed method can be as high as 0.679%). [ABSTRACT FROM AUTHOR]

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.

In this paper, a co-estimation scheme of the state of charge (SOC) and available capacity is proposed for lithium−ion batteries based on the adaptive model-based algorithm. A three-dimensional response surface (TDRS) in terms of the open circuit voltage, the SOC and the available capacity in the scope of whole lifespan, is constructed to describe the capacity attenuation, and the battery available capacity is identified by a genetic algorithm (GA), together with the parameters related to SOC. The square root cubature Kalman filter (SRCKF) is employed to estimate the SOC with the consideration of capacity degradation. The experimental results demonstrate the effectiveness and feasibility of the co-estimation scheme.

With the increasing number of feature points of a map, the dimension of systematic observation is added gradually, which leads to the deviation of the volume points from the desired trajectory and significant errors on the state estimation. An Iterative Squared-Root Cubature Kalman Filter (ISR-CKF) algorithm proposed is aimed at improving the SR-CKF algorithm on the simultaneous localization and mapping (SLAM). By introducing the method of iterative updating, the sample points are re-determined by the estimated value and the square root factor, which keeps the distortion small in the highly nonlinear environment and improves the precision further. A robust tracking Square Root Cubature Kalman Filter algorithm (STF-SRCKF-SLAM) is proposed to solve the problem of reduced accuracy in the condition of state change on the SLAM. The algorithm is predicted according to the kinematic model and observation model of the mobile robot at first, and then the algorithm updates itself by spreading the square root of the error covariance matrix directly, which greatly reduces the computational complexity. At the same time, the time-varying fading factor is introduced in the process of forecasting and updating, and the corresponding weight of the data is adjusted in real time to improve the accuracy of multi-robot localization. The results of simulation shows that the algorithm can improve the accuracy of multi-robot pose effectively. [ABSTRACT FROM AUTHOR]

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This paper proposes two novel methods for fault detection in non-linear processes. These methods apply a Gaussian process (GP) to model the underlying process, and then the extended Kalman filter (EKF) and square root cubature Kalman filter (SCKF) are used to detect faults. Accordingly, two approaches called the Gaussian process–extended Kalman filter (GP-EKF) and Gaussian process–square root cubature Kalman filter (GP-SCKF) are proposed. The most important characteristic of these proposed methods is that there is no need for an accurate model of the system. Therefore, these methods are considered non-parametric approaches of fault detection in non-linear systems. To illustrate the performance of these algorithms in fault detection, they have been used in a continuous stirred-tank reactor system (CSTR). Both proposed methods are able to detect sensor faults at an early stage. [ABSTRACT FROM AUTHOR]

In this study, two fault detection methods are proposed for non‐linear systems. In these methods, Gaussian process (GP) is integrated into extended Kalman filter (EKF) and square root cubature Kalman filter (SCKF), which are called GP‐EKF and GP‐SCKF, respectively. The most important advantage of the proposed methods is that there is no need to know the accurate model of the system. Therefore, these methods are considered as non‐parametric approaches of fault detection in non‐linear systems. Moreover, by applying these methods, it is possible to detect the fault with high accuracy at early stage. First, GP‐EKF and GP‐SCKF are proposed for non‐linear state estimation, and then GP‐SCKF is compared with the GP‐EKF and the results of this comparison prove the superiority of GP‐SCKF regarding the complexity of computations and accuracy. In addition, simulation results show a good performance of GP‐EKF and GP‐SCKF in non‐linear system's fault detection. To illustrate performance of these algorithms in state estimation and fault detection, they are used in aircraft tracking system. Both of the proposed methods are able to detect the sensors faults at early stage. [ABSTRACT FROM AUTHOR]

A new filtering algorithm, adaptive square root cubature Kalman filter-Kalman filter (SRCKF-KF) is proposed to reduce the problems of amount of calculation, complex formula-transform, low accuracy, poor convergence or even divergence. The method uses cubature Kalman filter (CKF) to estimate the nonlinear states of model while its linear states are estimated by the Kalman filter (KF). The simulation and practical experiment results show that, compared to the extended Kalman filter (EKF) and unscented Kalman filter (UKF). The modified filter not only enhances the numerical stability, guarantees positive definiteness of the state covariance, but also increases accuracy, which has high practicability. [ABSTRACT FROM AUTHOR]

In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost. [ABSTRACT FROM AUTHOR]

In this paper, a co-estimation scheme of the state of charge (SOC) and available capacity is proposed for lithium–ion batteries based on the adaptive model-based algorithm. A three-dimensional response surface (TDRS) in terms of the open circuit voltage, the SOC and the available capacity in the scope of whole lifespan, is constructed to describe the capacity attenuation, and the battery available capacity is identified by a genetic algorithm (GA), together with the parameters related to SOC. The square root cubature Kalman filter (SRCKF) is employed to estimate the SOC with the consideration of capacity degradation. The experimental results demonstrate the effectiveness and feasibility of the co-estimation scheme. [ABSTRACT FROM AUTHOR]