This paper elaborates the Accurate Continuous-Discrete Extended Kalman Filter grounded in an ODE solver with global error control and its comparison to the Continuous-Discrete Cubature and Unscented ...Kalman Filters. All these state estimators are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn. The latter is considered to be a challenging one for testing nonlinear filtering algorithms. Our numerical results show that all the methods can be used for practical target tracking, but the Accurate Continuous-Discrete Extended Kalman Filter is more flexible and robust. It treats successfully (and without any manual tuning) the air traffic control scenario for various initial data and for a range of sampling times.
Accurate information about dynamic states is important for efficient control and operation of a power system. This paper compares the performance of four Bayesian-based filtering approaches in ...estimating dynamic states of a synchronous machine using phasor measurement unit data. The four methods are extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and particle filter. The statistical performance of each algorithm is compared using Monte Carlo methods and a two-area-four-machine test system. Under the statistical framework, robustness against measurement noise and process noise, sensitivity to sampling interval, and computation time are evaluated and compared for each approach. Based on the comparison, this paper makes some recommendations for the proper use of the methods.
This paper presents a visual-inertial odometry framework that tightly fuses inertial measurements with visual data from one or more cameras, by means of an iterated extended Kalman filter. By ...employing image patches as landmark descriptors, a photometric error is derived, which is directly integrated as an innovation term in the filter update step. Consequently, the data association is an inherent part of the estimation process and no additional feature extraction or matching processes are required. Furthermore, it enables the tracking of noncorner-shaped features, such as lines, and thereby increases the set of possible landmarks. The filter state is formulated in a fully robocentric fashion, which reduces errors related to nonlinearities. This also includes partitioning of a landmark’s location estimate into a bearing vector and distance and thereby allows an undelayed initialization of landmarks. Overall, this results in a compact approach, which exhibits a high level of robustness with respect to low scene texture and motion blur. Furthermore, there is no time-consuming initialization procedure and pose estimates are available starting at the second image frame. We test the filter on different real datasets and compare it with other state-of-the-art visual-inertial frameworks. Experimental results show that robust localization with high accuracy can be achieved with this filter-based framework.
•The surface heat flux and liquid-phase interface can be retrieved in real time.•A non-intrusive measurement technique is applied in the present study.•Comparing with EKF and UKF, the KF can only be ...used to solve linear problems.•Compared to UKF, the EKF can only be applied to solve weak nonlinear problem.
The non-intrusive inverse heat transfer technique based on the Kalman filtering (KF) method is proposed for on-line retrieving the time-dependent boundary heat flux, internal temperature distribution, and liquid-phase interface of the participating medium simultaneously. To obtain the measured temperature signals, the nonlinear conduction-radiation heat transfer with phase change in the participating medium is solved by the enthalpy method combined with discrete ordinate method. Three different types of retrieval algorithms have been employed: the original Kalman filter (KF), the extended KF (EKF), and the unscented KF (UKF). The ideal participating media, which is assumed to be anisotropic scattering, and opaque and diffuse gray boundary, is employed to verify the reliability and validity of the proposed algorithm. Comparing with the EKF and UKF, the original KF cannot be applied to solve the nonlinear problems. Comparing with the UKF, the EKF can only be employed to solve the weak nonlinear problem. For the inverse coupled conduction-radiation problem with phase change, the UKF is proved to be more robust to estimate the time-dependent heat flux, internal temperature distribution, and liquid-phase interface simultaneously in real time.
In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite ...estimation error covariance (UKF-GPS) is proposed and compared with five existing approaches, including UKF-schol, UKF-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\kappa } </tex-math></inline-formula>, UKF-modified, UKF-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\Delta Q} </tex-math></inline-formula>, and the square-root UKF (SR-UKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is found that UKF-schol, UKF-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\kappa } </tex-math></inline-formula>, and UKF-<inline-formula> <tex-math notation="LaTeX">\boldsymbol {\Delta Q} </tex-math></inline-formula> do not work well in some estimations while UKF-GPS works well in most cases. UKF-modified and SR-UKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.
Summary
The growing usage of electric vehicles (EVs) has led to significant advancements in batteries' technology. State of charge (SOC) estimation is an essential function of the battery management ...system—the heart of EVs and Kalman filtering is a standard SOC estimation method. Because of the non‐uniformities in tuning and testing scenarios, it is challenging to quantify SOC estimation algorithms' performance. A SOC estimation algorithm is developed in this work, extended Kalman filter (EKF), and tested for variable scenarios like adding sensor noise and bias to terminal voltage and current and varying state and parameter initializations. Also, a dual EKF is implemented to estimate the sensor voltage and current bias and compared it against the state EKF to estimate SOC. Finally, a comparative study has been introduced to decide which algorithm represents the most accurate estimation for the battery parameters, and it was found that the dual EKF gave the best results.
Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and ...lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system’s trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based extended Kalman filter (EKF) through both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system.
This paper presents a novel 7-in capacitive touch panel (CTP) system with a smooth tracking algorithm that accurately estimates the position where the panel is touched and tracks the trajectory of ...touch. The proposed CTP system consists of a microcontroller unit, a sensor IC, and an interface board. When a user draws at different speeds, the measurement noise caused by the sensor IC induces an error in the touched position and zigzag trajectory, especially when the motion is slow. The fuzzy-logic-based adaptive strong tracking Kalman filter method is implemented in a CTP system to mitigate the effect of measurement noise and provide a smooth tracking trajectory at different speeds. Moreover, the approach effectively measures and quantifies the "smoothness" of the touched trajectory. Experimental results indicate that the proposed method reduces the measurement noise and decreases the mean tracking error by 85.4% over that achieved using the moving average filter.
Summary
Lithium‐ion batteries (LIBs) are widely used in electric vehicles due to its high energy density and low pollution. As the key monitoring parameters of battery management system (BMS), ...accurate estimation of the state of charge (SOC) and state of health (SOH) can promote the utilization rate of battery, which is of great significance to ensure the safe use of LIBs. In this paper, a novel dual Kalman filter method is proposed to achieve simultaneous SOC and SOH estimation. This paper improves the estimation accuracy of SOC and SOH from the following four aspects. Firstly, the widely used equivalent circuit model is established as the battery model in this paper, and the forgetting factor recursive least squares (FFRLS) method is applied to identify the model parameters. Secondly, two kinds of single‐variable battery states are established to analyze the influence of OCV‐SOC curve and battery capacity on SOC estimation. Based on this, an error model is proposed combined with Kalman filter to achieve better estimation results of SOC and SOH. Besides, to promote the accuracy of SOC estimation, based on the error innovation sequence (EIS) and residual innovation sequence (RIS), the improved dual adaptive extended Kalman filter (IDAEKF) algorithm based on dynamic window is proposed. Finally, the superiority of the proposed model is verified under different cycles. Experimental results show that the estimation error of SOC and SOH is controlled within 1%.
Accurate battery state of charge (SOC) estimation can contribute to safe and reliable utilization of the battery. However, commonly used battery model-based SOC estimation methods suffer from the ...lack of a universal battery model for cells in a battery pack since the model parameters of each cell are inevitably different from each other and variable with battery aging, leading to difficulties in promoting the model-based methods for real applications. To solve this problem, a differential voltage (DV) analysis based universal battery model and two associated SOC estimation algorithms using extended Kalman filter (EKF) and particle filter (PF), respectively, are proposed in this paper. By means of a natural cubic interpolation approach, a battery SOC-DV model is firstly derived from the SOC based DV curves of various cells at different aging levels. A novel battery model-based scheme is then proposed to incorporate the SOC-DV model for the estimation. The robustness of the proposed approaches against different cell aging levels is evaluated, and the promising SOC estimates with the maximum absolute error of 1.75% and the root mean square error of less than 1.10% can be achieved.
•The DVA technique is developed for on-board battery SOC estimation.•A universal SOC-DV model is derived from battery test data at various aging cycles.•A novel model-based SOC estimation scheme with an EKF/PF and DV values is proposed.•The feasibilities of the universal model and proposed algorithms are validated.
PDF
