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To keep the global navigation satellite system functional during extreme conditions, it is a trend to employ autonomous navigation technology with inter-satellite link. As in the newly built BeiDou system (BDS-3) equipped with Ka-band inter-satellite links, every individual satellite has the ability of communicating and measuring distances among each other. The system also has less dependence on the ground stations and improved navigation performance. Because of the huge amount of measurement data, the centralized data processing algorithm for orbit determination is suggested to be replaced by a distributed one in which each satellite in the constellation is required to finish a partial computation task. In the present paper, the balanced extended Kalman filter algorithm for distributed orbit determination is proposed and compared with the whole-constellation centralized extended Kalman filter, the iterative cascade extended Kalman filter, and the increasing measurement covariance extended Kalman filter. The proposed method demands a lower computation power; however, it yields results with a relatively good accuracy.

Electric vehicles (EVs) have emerged as a promising solution for sustainable transportation. The high energy density, long cycle life, and low self-discharge rate of lithium-ion batteries make them an ideal choice for EVs. Recently, these batteries have been prone to faster decay in life span, leading to sudden failure of the battery. To avoid uncertainty among EV users with sudden battery failures, a robust health monitoring and prediction scheme is required for the EV battery management system. In this regard, the Unscented Kalman Filter (UKF)-based technique has been developed for accurate and reliable prediction of battery health status. The UKF approximates nonlinearity using a set of sigma points and propagates them via the nonlinear function to enhance battery health estimation accuracy. Furthermore, the UKF-based health estimation scheme considers the state of charge (SOC) and internal resistance of the battery. Here, the UKF-based health prediction technique is compared with the Extended Kalman filter (EKF) scheme. The robustness of the UKF and EKF-based health prognostic techniques were studied under varying initial SOC values. Under these abrupt changing conditions, the proposed UKF technique performed effectively in terms of state of health (SOH) prediction. Accurate SOH determination can help EV users to decide when the battery needs to be replaced or if adjustments need to be made to extend its life. Ultimately, accurate and reliable battery health estimation is essential in vehicular applications and plays a pivotal role in ensuring lithium-ion battery sustainability and minimizing environmental impacts.

This paper presents a learning-assisted approach for state estimation of quadruped robots using observations of proprioceptive sensors, including multiple inertial measurement units (IMUs). Specifically, one body IMU and four additional IMUs attached to each calf link of the robot are used for sensing the dynamics of the body and legs, in addition to joint encoders. The extended Kalman filter (KF) is employed to fuse sensor data to estimate the robot’s states in the world frame and enhance the convergence of the extended KF (EKF). To circumvent the requirements for the measurements from the motion capture (mocap) system or other vision systems, the right-invariant EKF (RI-EKF) is extended to employ the foot IMU measurements for enhanced state estimation, and a learning-based approach is presented to estimate the vision system measurements for the EKF. One-dimensional convolutional neural networks (CNN) are leveraged to estimate required measurements using only the available proprioception data. Experiments on real data from a quadruped robot demonstrate that proprioception can be sufficient for state estimation. The proposed learning-assisted approach, which does not rely on data from vision systems, achieves competitive accuracy compared to EKF using mocap measurements and lower estimation errors than RI-EKF using multi-IMU measurements.

A fusion navigation algorithm for the distributed satellites system（DSS） utilizing relative range measurements is proposed in this paper. Based on the quasi-consistent extended Kalman filter（QCEKF）, an on-line evaluation of the navigation precision can be provided by the fusion navigation algorithm. In addition,the upper bound for the estimation error obtained from the fusion navigation algorithm is lower than those with any groups of measurements, which indicates that the fusion navigation algorithm can automatically choose the suitable redundant measurements to improve the navigation precision. The simulations show the feasibility and effectiveness of the proposed fusion navigation algorithm.

This paper examines the critical role of indoor positioning for robots, with a particular focus on small and confined spaces such as homes, warehouses, and similar environments. We develop an algorithm by integrating deep neural networks (DNNs) with the extended Kalman filter (EKF) method, which is known as DNN-EKF, to obtain an accurate indoor localization for ensuring precise and reliable robot movements within the use of Ultra-Wideband (UWB) technology. The study introduces a novel methodology that combines advanced technology, including DNN, filtering techniques, specifically the EKF and UWB technology, with the objective of enhancing the accuracy of indoor localization systems. The objective of integrating these technologies is to develop a more robust and dependable solution for robot navigation in challenging indoor environments. The proposed approach combines a DNN with the EKF to significantly improve indoor localization accuracy for mobile robots. The results clearly show that the proposed model outperforms existing methods, including NN-EKF, LPF-EKF, and other traditional approaches. In particular, the DNN-EKF method achieves optimal performance with the least distance loss compared to NN-EKF and LPF-EKF. These results highlight the superior effectiveness of the DNN-EKF method in providing precise localization in indoor environments, especially when utilizing UWB technology. This makes the model highly suitable for real-time robotic applications, particularly in dynamic and noisy environments.

A new control scheme employing the Iterated Extended Kalman Filtering (IEKF) algorithm for synchronization of a PV system with a three‐phase grid is proposed. IEKF accurately estimates the fundamental sinusoidal component of the distorted voltage signals at the Point of Common Coupling (PCC) and the current signal of the load. The Kalman gain is updated through the minimization of the estimation error covariance yielding accurate estimation of the fundamental component of the aforementioned voltage and current signals. IEKF uses an iterative loop to reduce the mean square error and also increases the convergence speed. The proposed IEKF‐PI control scheme is implemented using MATLAB/Simulink first and then it is realised on a prototype of a single stage grid connected PV system developed in the laboratory. From the results obtained from both the simulation and experimental studies, it is concluded that after compensation, the grid current reaches the steady state faster using IEKF‐PI than using EKF‐PI and STF‐PI. The Total Harmonic Distortion (THD) of the grid current is compensated to a lowest value of 3.5% using the proposed IEKF‐PI control scheme than that obtained using both EKF‐PI and STF‐PI, despite distortion of PCC voltage and PCC voltage sag and swell condition.

This paper presents a new stochastic-based method for modelling and analysis of COVID-19 spread. A new deterministic Susceptible, Exposed, Infectious, Recovered (Re-infected) and Deceased-based Social Distancing model, named SEIR(R)D-SD, is proposed by introducing the re-infection rate and social distancing factor into the traditional SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model to account for the effects of re-infection and social distancing on COVID-19 spread. The deterministic SEIRD(R)D-SD model is further converted into the stochastic form to account for uncertainties involved in COVID-19 spread. Based on this, an extended Kalman filter (EKF) is developed based on the stochastic SEIR(R)D-SD model to simultaneously estimate both model parameters and transmission state of COVID-19 spread. Simulation results and comparison analyses demonstrate that the proposed method can effectively account for the re-infection and social distancing as well as uncertain effects on COVID-19 spread, leading to improved accuracy for prediction of COVID-19 spread. •It is difficult to track and predict the COVID-19 propagation based on a deterministic model due to the uncertain effects.•A stochastic framework based on classical SEIRD model is developed to investigate the transition between compartments.•A corresponded extended Kalman filter algorithm for stochastic model is also applied for evaluating the model performance.•The improved understanding of the mechanism of spread can contribute to improve the effectiveness of public health measures.

The vehicle dynamic state is essential for stability control and decision-making of intelligent vehicles. However, these states cannot usually be measured directly and need to be obtained indirectly using additional estimation algorithms. Unfortunately, most of the existing estimation methods ignore the effect of data loss on estimation accuracy. Furthermore, high-order filters have been proven that can significantly improve estimation performance. Therefore, a second-order fault-tolerant extended Kalman filter (SOFTEKF) is designed to predict the vehicle state in the case of data loss. The loss of sensor data is described by a random discrete distribution. Then, an estimator of minimum estimation error covariance is derived based on the extended Kalman filter (EKF) framework. Finally, experimental tests demonstrate that the SOFTEKF can reduce the effect of data loss and improve estimation accuracy by at least 10.6% compared to the traditional EKF and fault-tolerant EKF.

This paper proposes an improved initial alignment method for a strap-down inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system with large misalignment angles. Its methodology is based on the three-dimensional special Euclidean group and extended Kalman filter (SE2(3)/EKF) and aims to overcome the challenges of achieving fast alignment under large misalignment angles using traditional methods. To accurately characterize the state errors of attitude, velocity, and position, these elements are constructed as elements of a Lie group. The nonlinear error on the Lie group can then be well quantified. Additionally, a group vector mixed error model is developed, taking into account the zero bias errors of gyroscopes and accelerometers. Using this new error definition, a GNSS-assisted SINS dynamic initial alignment algorithm is derived, which is based on the invariance of velocity and position measurements. Simulation experiments demonstrate that the alignment method based on SE2(3)/EKF can achieve a higher accuracy in various scenarios with large misalignment angles, while the attitude error can be rapidly reduced to a lower level.

Accurate estimation of the state of charge (SOC) is essential for the optimal operation of batteries. However, to achieve such accuracy remains challenging for tri‐electrode rechargeable zinc–air flow batteries (TRZAFBs) due to their flat voltage profiles. This study presents an innovative SOC identification technique based on the optimization of battery model parameters derived from pulse response data. Model parameters are extracted from pulse steps within the experimental data, establishing correlations between these parameters and SOC. Such correlations are then utilized as constraints in the optimization process. Results indicate that the slope of total resistance effectively identifies SOC with acceptable accuracy. The proposed method is further enhanced by integrating it with an extended Kalman filter (EKF) to enable real‐time SOC estimation. Various initial SOC guess conditions and optimization frequencies are tested, demonstrating that EKF combined with the proposed optimization technique accurately tracks the true SOC in real‐time and effectively corrects the incorrect initial SOC guesses. Additionally, the results show that the proposed technique can compete with other alternative methods in terms of multiple‐cycle stability and surpass them in terms of convergence of true SOC for zinc–air batteries (ZABs).