Equivariant filtering framework for inertial-integrated navigation

This paper proposes an Equivariant Filtering (EqF) framework for the inertial-integrated state estimation. As the kinematic system of the inertial-integrated navigation can be naturally modeled on the matrix Lie group SE2(3), the symmetry of the Lie group can be exploited to design an equivariant filter which extends the invariant extended Kalman filtering on the group-affine system and overcomes the inconsitency issue of the traditional extend Kalman filter. We firstly formulate the inertial-integrated dynamics as the group-affine systems. Then, we prove the left equivariant properties of the inertial-integrated dynamics. Finally, we design an equivariant filtering framework on the earth-centered earth-fixed frame and the local geodetic navigation frame. The experiments show the superiority of the proposed filters when confronting large misalignment angles in Global Navigation Satellite Navigation (GNSS)/Inertial Navigation System (INS) loosely integrated navigation experiments.

Vertical Tire Forces Estimation of Multi-Axle Trucks Based on an Adaptive Treble Extend Kalman Filter

Vertical tire forces are essential for vehicle modelling and dynamic control. However, an evaluation of the vertical tire forces on a multi-axle truck is difficult to accomplish. The current methods require a large amount of experimental data and many sensors owing to the wide variation of the parameters and the over-constraint. To simplify the design process and reduce the demand of the sensors, this paper presents a practical approach to estimating the vertical tire forces of a multi-axle truck for dynamic control. The estimation system is based on a novel vertical force model and a proposed adaptive treble extend Kalman filter (ATEKF). To adapt to the widely varying parameters, a sliding mode update is designed to make the ATEKF adaptive, and together with the use of an initial setting update and a vertical tire force adjustment, the overall system becomes more robust. In particular, the model aims to eliminate the effects of the over-constraint and the uneven weight distribution. The results show that the ATEKF method achieves an excellent performance in a vertical force evaluation, and its performance is better than that of the treble extend Kalman filter.

Reliable and Robust Observer for Simultaneously Estimating State-of-Charge and State-of-Health of LiFePO4 Batteries

Batteries are everywhere, in all forms of transportation, electronics, and constitute a method to store clean energy. Among the diverse types available, the lithium-iron-phosphate (LiFePO4) battery stands out for its common usage in many applications. For the battery’s safe operation, the state of charge (SOC) and state of health (SOH) estimations are essential. Therefore, a reliable and robust observer is proposed in this paper which could estimate the SOC and SOH of LiFePO4 batteries simultaneously with high accuracy rates. For this purpose, a battery model was developed by establishing an equivalent-circuit model with the ambient temperature and the current as inputs, while the measured output was adopted to be the voltage where current and terminal voltage sensors are utilized. Another vital contribution is formulating a comprehensive model that combines three parts: a thermal model, an electrical model, and an aging model. To ensure high accuracy rates of the proposed observer, we adopt the use of the dual extend Kalman filter (DEKF) for the SOC and SOH estimation of LiFePO4 batteries. To test the effectiveness of the proposed observer, various simulations and test cases were performed where the construction of the battery system and the simulation were done using MATLAB. The findings confirm that the best observer was a voltage-temperature (VT) observer, which could observe SOC accurately with great robustness, while an open-loop observer was used to observe the SOH. Furthermore, the robustness of the designed observer was proved by simulating ill-conditions that involve wrong initial estimates and wrong model parameters. The results demonstrate the reliability and robustness of the proposed observer for simultaneously estimating the SOC and SOH of LiFePO4 batteries.

Paddle Stroke Analysis for Kayakers Using Wearable Technologies

Proper stroke posture and rhythm are crucial for kayakers to achieve perfect performance and avoid the occurrence of sport injuries. The traditional video-based analysis method has numerous limitations (e.g., site and occlusion). In this study, we propose a systematic approach for evaluating the training performance of kayakers based on the multiple sensors fusion technology. Kayakers’ motion information is collected by miniature inertial sensor nodes attached on the body. The extend Kalman filter (EKF) method is used for data fusion and updating human posture. After sensor calibration, the kayakers’ actions are reconstructed by rigid-body model. The quantitative kinematic analysis is carried out based on joint angles. Machine learning algorithms are used for differentiating the stroke cycle into different phases, including entry, pull, exit and recovery. The experiment shows that our method can provide comprehensive motion evaluation information under real on-water scenario, and the phase identification of kayaker’s motions is up to 98% validated by videography method. The proposed approach can provide quantitative information for coaches and athletes, which can be used to improve the training effects.

A Robust Indoor Mobile Localization Algorithm for Wireless Sensor Network in Mixed LOS/NLOS Environments

Wireless sensor network (WSN) is a self-organizing network which is composed of a large number of cheap microsensor nodes deployed in the monitoring area and formed by wireless communication. Since it has the characteristics of rapid deployment and strong resistance to destruction, the WSN positioning technology has a wide application prospect. In WSN positioning, the nonline of sight (NLOS) is a very common phenomenon affecting accuracy. In this paper, we propose a NLOS correction method algorithm base on the time of arrival (TOA) to solve the NLOS problem. We firstly propose a tendency amendment algorithm in order to correct the NLOS error in geometry. Secondly, this paper propose a particle selection strategy to select the standard deviation of the particle swarm as the basis of evolution and combine the genetic evolution algorithm, the particle filter algorithm, and the unscented Kalman filter (UKF) algorithm. At the same time, we apply orthogon theory to the UKF to make it have the ability to deal with the target trajectory mutation. Finally we use maximum likelihood localization (ML) to determine the position of the mobile node (MN). The simulation and experimental results show that the proposed algorithm can perform better than the extend Kalman filter (EKF), Kalman filter (KF), and robust interactive multiple model (RIMM).

SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System

The environment for practical applications of an energy storage system (ESS) in a microgrid system is very harsh, and therefore actual operating conditions become complex and changeable. In addition, the signal of the ESS sampling process contains a great deal of system and measurement noise, the sampled current fluctuates significantly, and also has high frequency. In this case, under such conditions, it is difficult to accurately estimate the state of charge (SOC) of the batteries in the ESS by common estimation methods. Therefore, this study proposes a compound SOC estimation method based on wavelet transform. This algorithm is very suitable for microgrid systems with large current, frequent fluctuating conditions, and high noise interference. The experimental results and engineering data show that the relative error of the method is 0.5%, which is much lower than the extend Kalman filter (EKF) based on wavelet transform.

Identification of Structural Parameters and Unknown Inputs Based on Revised Observation Equation: Approach and Validation

The identification of parameters of linear or nonlinear systems under unknown inputs and limited outputs is an important but still challenging topic in the context of structural health monitoring. Time-domain analysis methodologies, such as extend Kalman filter (EKF), have been actively studied and shown to be powerful for parameter identification. However, the conventional EKF is not applicable when the input is unknown or unmeasured. In this paper, by introducing a projection matrix in the observation equation, a time-domain EKF-based approach is proposed for the simultaneous identification of structural parameters and the unknown excitations with limited outputs. A revised version of observation equation is presented. The unknown inputs are identified using the least squares estimation based on the limited observations and the estimated structural parameters at the current time step. Particularly, an analytical recursive solution is derived. The accuracy and effectiveness of the proposed approach is first demonstrated via several numerical examples. Then it was validated by the shaking table tests on a five-story building model for the robustness in application to real structures. The results show that the proposed approach can satisfactorily identify the parameters of linear or nonlinear structures under unknown inputs.