Ning Liu

High-spinning aerial platforms operating under high-speed rotation and strong electromagnetic interference experience severe GNSS signal degradation, causing periodic outages and measurement gaps. Such conditions force the navigation system into pure inertial mode, resulting in rapidly accumulating position errors. To address sensor measurement gaps, this paper devel-ops a physics-informed mapping between IMU observa-tions and flight-phase states derived from 7-DOF dynam-ics equations. A Transformer-CNN-based virtual sensor is developed for real-time flight-phase identification and synthetic position-increment measurements, dynamically adapting the Kalman filter's measurement covariance matrix and measurement model. This dual-constraint sensor fusion framework improves GNSS/INS integration robustness during signal degradation. Hardware-in-the-loop (HIL) sensor simulations demonstrate that under sporadic electromagnetic interference (short-term GNSS outages), position and velocity RMSEs decrease by 63% and 16%, respectively; under sustained interference in electromag-netically contested environments (prolonged outages), reductions reach 42% and 11%. The approach mitigates pure inertial navigation error accumulation, substantially enhancing multi-sensor fusion accuracy in GNSS-challenged ex-treme environments. Comparative validation across multiple neural network architectures confirms the Transform-er-CNN's superiority in adaptive flight-phase recognition. This work provides a deployable virtual sensor-enhanced framework for multi-sensor fusion systems operating under severe electromagnetic interference, offering both theo-retical rigor and engineering viability for practical implementation.

Metal resonant gyroscopes are widely adopted in high-performance navigation and inertial measurement systems due to their structural stability and long-term reliability. However, their performance is often degraded by frequency splitting induced by structural asymmetry and fabrication errors. This effect compromises frequency consistency, induces modal coupling, and reduces sensing accuracy. To address this problem, this paper proposes an electrostatic stiffness-tuning strategy that actively suppresses frequency splitting without requiring structural modifications. By regulating the equivalent stiffness distribution of the resonant structure, this method enables adaptive frequency alignment and post-packaging implementation. A multi-degree-of-freedom dynamic model is first established to analyze the influence of stiffness perturbations and modal coupling. Based on this model, an electrostatic stiffness-tuning scheme is developed, employing voltage-controlled negative stiffness to attenuate sub-modal responses. Simulation results show that multiple tuning-electrode combinations can significantly suppress the secondary peak in the frequency domain, with suppression ratios exceeding 98%. Under the optimal tuning condition, the experimentally measured minimum relative power ratio of the secondary mode decreases to approximately 0.02 in air and 0.016 in vacuum, indicating effective suppression of the residual secondary-mode energy. These results confirm that electrostatic stiffness tuning is a practical and effective approach for modal frequency equalization in metallic resonant gyroscopes.

Multisource sensor fusion has become a research focus in navigation and positioning. However, the Kalman filter algorithm faces issues with real-time performance and positioning accuracy when handling asynchronous data fusion. The development of factor graph algorithms has significantly improved these issues. Meanwhile, research on vehicle-based manifold factor graph optimization algorithms in urban environments is relatively scarce. Therefore, this paper proposes a GNSS/IMU integrated navigation testing platform based on manifold factor graph optimization. The platform is designed to analyze the real-time performance and accuracy of the optimization algorithm under different path ranges. It optimizes IMU pre-integration using Lie group algorithms and constructs a manifold pre-integration factor model with keyframes. The testing algorithm integrates IMU pre-integration factors, GNSS factors, and state prior factors to achieve synchronous multisource fusion. By optimizing a sliding window, it performs nonlinear optimization of variables within the window and outputs the final navigation state. Simulation results show the proposed testing algorithm improves positioning accuracy by 96.67%, 95.36%, and 89.55% compared to three other algorithms. It maintains execution times below 10 seconds, demonstrating high real-time performance and efficiency.

The metal resonant gyro is characterized by small size, low cost, and strong overload resistance, and shows broad application prospects in the field of inertial navigation. Currently, structural optimization methods of resonators are based on single-objective parameter optimization and fail to consider the comprehensive impact of multiple structural parameters on overall performance indices. In this paper, a metal resonator with a tooth structure is designed based on thin shell theory and the energy loss principle. Using a finite element simulation method combined with multivariate linear regression equations, the linear influence of each structural parameter on overall performance is investigated. A multi-objective optimization model using three key indices as objective functions is constructed and optimized with the NSGA-II algorithm, providing a set of optimization parameters for subsequent research. It establishes equivalent mathematical models for different forms of electrostatic forces and verify their validity using finite element simulations. Finally, the resonator’s response under different excitation forms is experimentally validated. Results show that the resonator exhibits optimal resonance under single-octave sinusoidal excitation: the four-wave belly oscillation pattern remains intact in driving mode with no frequency crosstalk. The resonant amplitude limit is 0.34 nm, significantly greater than under other excitation forms. The proposed method achieves comprehensive performance optimization of the metal resonator and provides a theoretical basis for selecting excitation forms in resonant gyros.

To address the current problem that the speed of high-speed spinning bodies varies widely and it is difficult to achieve effective speed measurements throughout the entire flight, this paper proposes a real-time online rotational speed measurement method based on geomagnetic time domain scalar normalization data. First, the geomagnetic motion characteristics of the body flying under high-speed spinning conditions are investigated. The initial normalized value is determined based on the data received in the initial time window, and then, the initial rotational speed is calculated. Subsequently, the rotational speed derived from the previous moment is used to calculate the length of the next time window, and the received data are dynamically normalized within the time window. Finally, the zero moment in the geomagnetic normalized data curve is obtained, the rotational speed is calculated based on the obtained zero point, and the next time window length is determined. The received geomagnetic information is continuously solved by continuously updating the range of the time window and calculating the calculation mode of the rotational speed within the time window. The simulation results indicate that the difference between the calculated rotational speed and simulated true value is up to 4.57%, suggesting that effective measurement of the rotational speed of high-speed spinning bodies throughout the flight can be achieved.