The integration of the BeiDou Navigation Satellite System(BDS) and the Inertial Navigation System(INS) can provide a more reliable and accurate navigation service than either system alone. The deeply coupled architecture for BDS and INS integration has more superior performance than the loosely coupled or the tightly coupled. Owing to the complicated dynamic scenario and the nonlinear system’s noise uncertainty, the adaptive Kalman filter(AKF) algorithm is often adopted in the deep integration(DI) system. The adaptive Sage window methods including innovation-based adaptive estimation(IAE) and residualbased adaptive estimation(RAE) are widely applied in AKF algorithms, but they have several limitations.We propose an improved adaptive unscented Kalman filter(AUKF) based on forgetting-factor-weight smoothing and multi-factor adaptation to overcome these limitations. Compared with the Sage window methods, the improved AUKF algorithm is immune to the quantity change of the satellites concerning integration and more sensitive to present dynamic. Furthermore, it can reduce the computation and storage burden in implementation. A simulation test based on a software platform and the deeply integrated BDS/INS navigation system is carried out to evaluate the performance of the improved AUKF. Simulation results show that the improved AUKF algorithm outperforms the extended Kalman filter(EKF) and has a similar performance with the RAE-AUKF.

Ionospheric delay is a critical error source in Global Navigation Satellite Systems (GNSSs) and a principal aspect of Satellite Based Augmentation System (SBAS) corrections. Grid Ionospheric Vertical Delays (GIVDs) are derived from the delays on Ionosphere Pierce Points (IPPs), which are observed by SBAS reference stations. SBAS master stations calculate ionospheric delay corrections by several methods, such as planar fit or Kriging. However, when there are not enough IPPs around an Ionosphere Grid Point (IGP) or the IPPs are unevenly distributed, the fitting accuracy of planar fit or Kriging is unsatisfactory. Moreover, the integrity bounds of Grid Ionospheric Vertical Errors (GIVEs) are overly conservative. Since Artificial Neural Networks (ANNs) are widely used in ionospheric research due to their self-adaptation, parallelism, non-linearity, robustness, and learnability, the ANN method for GIVD and GIVE derivation is proposed in this article. Networks are separately trained for IGPs, and five years of historical data are applied on network training. Principal Component Analysis (PCA) is applied for dimensionality reduction of geomagnetic and solar indices, which is employed as a network input feature. Furthermore, the GIVE algorithm of the ANN method is derived based on the distribution of the residual random variable. Finally, experiments are conducted on 12 IGPs over the East China region. Under normal ionospheric conditions, compared with the planar fit and Kriging methods, the residual reduction of the ANN method is approximately 15%. The ANN method fits the ionospheric delay residual error better. The percentage of GIVE availability under 2.7 m increases at least 25 points in comparison to Kriging. Under disturbed conditions, due to a lack of training samples, the ANN method is incompetent compared with planar fit or Kriging.

The navigation technology has developed rapidly and immensely over the past few decades. Among the multiple navigation technologies, the representative and promising techniques are Real-time Kinematic (RTK) technique and Simultaneous Localization and Mapping (SLAM). RTK can provide real-time positioning results with high accuracy, while SLAM can not only locate the user but also construct a map of the new ambient. The first smartphone, the Xiaomi MI 8, equipped with the dual-frequency Global Navigation Satellite System (GNSS), hit the market in May 2018, providing valid carrier-phase measurements for RTK owe to the developer option of "Force full GNSS measurements." Nevertheless, RTK underperforms in urban areas as the buildings and trees can block the satellite signals. RTK cannot even provide positioning results when the GNSS outage happens. However, SLAM can effectively make up the drawbacks of RTK as it utilizes no more information than the images. SLAM can also be combined with the Inertial Measurement Unit (IMU) called Visual-Inertial SLAM (VI-SLAM,) with the improvement of accuracy and robustness. Therefore, our study mainly aims to confirm the feasibility of continuous positioning based on RTK and VI-SLAM with the Xiaomi MI 8. An application is developed to execute the functions, including logging images, measurements of IMU, and GPS measurements in Receiver INdependent EXchange (RINEX) format with the Xiaomi MI 8. The performances of RTK with and without the assistance of VI-SLAM are assessed respectively in the urban area. The experimental results demonstrate that the combination of RTK and VI-SLAM based on smartphones can effectively provide continuous positioning results. We believe our application will facilitate research and development in relation to positioning algorithms. Readers have access to this application at https://github.com/Nronaldo/CIGRLogger.

Carrier phase measurements play a more critical role in achieving precise positioning for lower noise and insensitivity to multipath error over code (pseudorange) measurements. Real-time kinematic (RTK) is the most used precise positioning technique. However, the application costs are increased due to the demands for differential base stations. The undifferenced precise point positioning (PPP) does not require differential station assistance but is typically for static use. This paper proposes a dynamic continuous constrained phase (DCCP) method based on factor graph optimization for kinematic positioning without differential stations, even in the presence of cycle slips. The precise velocity estimated via integral doppler and the time correlation of phase ambiguity are regarded as the probability constraints in the factor graph. A real-world experiment was carried out to verify the feasibility of the DCCP method. Experimental results show that the proposed method had a better performance than the kinematic PPP method and window carrier phase (WCP) optimization method with 0.034m standard deviation and 1.338m mean error. It is our hope that this approach provides new insight into the study of other time-correlated state estimation problems.

The Inertial Navigation System (INS) is often fused with the Global Navigation Satellite System (GNSS) to provide more robust and superior navigation service, especially in degraded signal environments. Compared with loosely and tightly coupled architectures, the Deep Integration (DI) architecture has better tracking and positioning performance. Information is shared among channels, and the assistant information from INS helps to reduce the dynamic stress of tracking loops. However, this vector tracking architecture may result in easy propagation of errors among tracking channels. To solve this problem, a Fault Detection and Exclusion (FDE) method for the deeply integrated BeiDou Navigation Satellite System (BDS)/INS navigation system is proposed in this paper. This method utilizes pre-filters’ outputs and integration filter’s estimations to form test statistics. These statistics can help to detect and exclude both step errors and Slowly Growing Errors (SGEs) correctly. The monitoring capability of the method was verified by a simulation which was based on a software receiver. The simulation results show that the proposed FDE method works effectively. Additionally, the method is convenient to be implemented in real-time applications because of its simplicity.

This paper presents SWIFT (Swarm-Wise Inference for Fast Trajectory Planning), a distributed one-stage planner designed for efficient multi-quadrotor trajectory optimization in cluttered environments. SWIFT unifies depth-based perception, interaction-aware modeling, and trajectory prediction into a single lightweight network, enabling decentralized real-time planning without reliance on global maps. Each quadrotor processes its local depth observation and asynchronously received neighbor intentions to predict multiple candidate trajectories, leveraging a confidence-guided cross-attention mechanism to selectively model critical inter-agent interactions. The proposed framework achieves sub-millisecond planning latency while ensuring collision avoidance, dynamic feasibility, and cooperative behavior under limited communication. Furthermore, a visual-inertial odometry drift correction strategy based on inter-agent visual detections enhances positioning accuracy during real-world flights. Extensive simulations and forest experiments validate that SWIFT outperforms existing baselines in trajectory smoothness, success rate, scalability, and robustness across diverse scenarios.