Low-cost ultrawideband (UWB)/inertial measurement unit (IMU) integrated positioning faces performance degradation in complex non-Gaussian (NG) environments. Currently, the maximum correntropy (MC) filter has shown certain superiority in NG environments. In view of the problems of time-consuming, low adaptability, and numerical instability which are common in the current MC filtering, this article proposes a novel MC-based low-cost tightly-coupled (TC) UWB/IMU positioning method with the robust unscented Kalman filter (UKF), namely, MC-RUKF. Specifically, we propose an adaptive calculation method for MC Gaussian variable kernel bandwidth (VKB) based on UWB innovation (MC-VBK). Subsequently, the UWB measurement noise matrix can be adaptively calculated, referred to as the MC-VKB-R model, which can dynamically adjust the weight of UWB observations, aiming to adapt to more complex observation environments. Experimental results from three trajectory sets show that the MC-RUKF algorithm achieves optimal positioning accuracy in both Gaussian and NG environments. Moreover, the proposed MC-VKB method effectively reduces the impact of UWB abnormalities in UWB/IMU positioning and addresses the numerical instability issues associated with the traditional MC fixed kernel bandwidth (MC-FKB).

A Novel Low-Cost UWB/IMU Positioning Method with the Robust Unscented Kalman Filter Based on Maximum Correntropy

To obtain precise positional information, in this study, we propose an adaptive expectation–maximization (EM)-based Kalman filter (KF)/finite impulse response (FIR) integrated filter for inertial navigation system (INS)-based posture capture of human upper limbs. Initially, a data fusion model for wrist and elbow position is developed. Subsequently, the Mahalanobis distance is utilized to evaluate the performance of the filter. The integrated filter employs the EM-based KF to enhance noise estimation accuracy when the performance of KF declines. Conversely, upon deterioration in the performance of the EM-based KF, which is evaluated using the Mahalanobis distance, the FIR filter is employed to maintain the effectiveness of the data fusion filter. This research utilizes the proposed EM-based KF/FIR integrated filter to ascertain wrist and elbow positions. The empirical results demonstrate the proficiency of the proposed approach in estimating these positions, thereby overcoming the challenge and highlighting its inherent effectiveness.

Adaptive Expectation–Maximization-Based Kalman Filter/Finite Impulse Response Filter for MEMS-INS-Based Posture Capture of Human Upper Limbs

Accurate 1‐day global total electron content (TEC) forecasting is essential for ionospheric monitoring and satellite communications. However, it faces challenges due to limited data and difficulty in modeling long‐term dependencies. This study develops a highly accurate model for 1‐day global TEC forecasting. We utilized generative TEC data augmentation based on the International Global Navigation Satellite Service (IGS) data set from 1998 to 2017 to enhance the model's prediction ability. Our model takes the TEC sequence of the previous 2 days as input and predicts the global TEC value for each hourly step of the next day. We compared the performance of our model with 1‐day predicted ionospheric products provided by both the Center for Orbit Determination in Europe (C1PG) and Beihang University (B1PG). We proposed a two‐step framework: (a) a time series generative model to produce realistic synthetic TEC data for training, and (b) an auto‐correlation‐based transformer model designed to capture long‐range dependencies in the TEC sequence. Experiments demonstrate that our model significantly improves 1‐day forecast accuracy over prior approaches. On the 2018 benchmark data set, the global root mean squared error (RMSE) of our model is reduced to 1.17 TEC units (TECU), while the RMSE of the C1PG model is 2.07 TECU. Reliability is higher in middle and high latitudes but lower in low latitudes (RMSE < 2.5 TECU), indicating room for improvement. This study highlights the potential of using data augmentation and auto‐correlation‐based transformer models trained on synthetic data to achieve high‐quality 1‐day global TEC forecasting.

Synthesis‐Style Auto‐Correlation‐Based Transformer: A Learner on Ionospheric TEC Series Forecasting

The integration of micro-electro-mechanical system–inertial navigation systems (MEMS-INSs) with other autonomous navigation sensors, such as polarization compasses (PCs) and geomagnetic compasses, has been widely used to improve the navigation accuracy and reliability of vehicles in Internet of Things (IoT) applications. However, a MEMS-INS/PC integrated navigation system suffers from cumulative errors and time-varying measurement noise covariance in unknown, complex occlusion, and dynamic environments. To overcome these problems and improve the integrated navigation system’s performance, a dual data- and model-driven MEMS-INS/PC seamless navigation method is proposed. This system uses a nonlinear autoregressive neural network (NARX) based on the Gauss–Newton Bayesian regularization training algorithm to model the relationship between the MEMS-INS outputs composed of the specific force and angular velocity data and the PC heading’s angular increment, and to fit the integrated navigation system’s dynamic characteristics, thus realizing data-driven operation. In the model-driven part, a nonlinear MEMS-INS/PC loosely coupled navigation model is established, the variational Bayesian method is used to estimate the time-varying measurement noise covariance, and the cubature Kalman filter method is then used to solve the nonlinear problem in the model. The robustness and effectiveness of the proposed method are verified experimentally. The experimental results show that the proposed method can provide high-precision heading information stably in complex, occluded, and dynamic environments.

Seamless Micro-Electro-Mechanical System-Inertial Navigation System/Polarization Compass Navigation Method with Data and Model Dual-Driven Approach

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.

An Improved Initial Alignment Method Based on SE2(3)/EKF for SINS/GNSS Integrated Navigation System with Large Misalignment Angles

It is known that in seamless inertial navigation system (INS)-based integrated drone localization, once data outage occurs in auxiliary measurement technologies, such as global navigation satellite system and ultrawideband (UWB), traditional integrated navigation data fusion filters may give large errors. To overcome this issue, we develop a dual free-size least squares support vector machines (fLS-SVM) assisted maximum correntropy Kalman filter (KF) (mcKF) for fusing INS and UWB data. In the fLS-SVM structure, the interactive multiple models method is used to improve the adaptability of the training set of LS-SVM. Then, the fLS-SVM method is adopted to estimate position error from INS when the UWB data is outage and then used again to provide the estimation error of the previous LS-SVM algorithm. The mcKF is derived on the basis of the maximum correntropy criterion. One mcKF is to realize data fusion from INS and UWB, and another one is for estimating the INS's position error for the fLS-SVM's output. Experimental testing is done in INS/UWB-based indoor mobile drone localization environments. It is shown that the dual fLS-SVM assisted mcKF algorithm outperforms the KF, general KF with colored measurement noise, mcKF, KF+LS-SVM, and dual KF+LS-SVM it reduces the position errors by an average of about 93.64%, 93.63%, 93.63%, 39.99%, and 94.10%, respectively, in two tests.

Dual Free-Size LS-SVM Assisted Maximum Correntropy Kalman Filtering for Seamless INS-Based Integrated Drone Localization

Prediction of ionospheric total electron content (TEC) enables accurate ionospheric delay correction for global navigation satellite system (GNSS) services. Thus, it is crucial to extract the characteristics of the temporal periodicity and spatial correlation for TEC modeling and prediction. The self-attention mechanism of the transformer structure is utilized to capture the long-term characteristics of the TEC in China. The gated recurrent unit (GRU) network and long short-term memory (LSTM) were chosen for comparison because of their capability for nonlinear time series modeling. The results indicate that the proposed model outperforms LSTM by 23% from 2016 to 2018 and GRU by more than 4% from 2016 to 2017. In terms of small, moderate, and intense geomagnetic storms, the relative error at all involved latitude levels was reduced by 40%, 39%, and 5%, respectively, compared with GRU, as well as 44%, 47%, and 12%, respectively, compared with LSTM. Furthermore, the ensemble model (Ense-Trans) based on two proposed spatially embedded transformer models (Trans), compared with the original Trans model, reduced the relative error by 11.38%, 8.78%, and 11.78% in the summer, autumn, and winter of 2018, respectively. It is concluded that Trans has much better performance than GRU and LSTM, and Ense-Trans is better than Trans itself in terms of TEC prediction. This study will be of great significance for ionospheric real-time research and other space weather applications in the future.

Optimal Transformer Modeling by Space Embedding for Ionospheric Total Electron Content Prediction

Local Collision Avoidance for Unmanned Surface Vehicles Based on an End-to-End Planner With a LiDAR Beam Map

Real-Time Wing Deformation Monitoring via Distributed Fiber Bragg Grating and Adaptive Federated Filtering

In-Motion Alignment with MEMS-IMU Using Multilocal Linearization Detection

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