Errors in microelectromechanical systems (MEMS) inertial measurement units (IMUs) are large, complex, nonlinear, and time varying. The traditional noise reduction and compensation methods based on traditional models are not applicable. This paper proposes a noise reduction method based on multi-layer combined deep learning for the MEMS gyroscope in the static base state. In this method, the combined model of MEMS gyroscope is constructed by Convolutional Denoising Auto-Encoder (Conv-DAE) and Multi-layer Temporal Convolutional Neural with the Attention Mechanism (MultiTCN-Attention) model. Based on the robust data processing capability of deep learning, the noise features are obtained from the past gyroscope data, and the parameter optimization of the Kalman filter (KF) by the Particle Swarm Optimization algorithm (PSO) significantly improves the filtering and noise reduction accuracy. The experimental results show that, compared with the original data, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 77.81% and 76.44% on the x and y axes, respectively; compared with the existing MEMS gyroscope noise compensation method based on the Autoregressive Moving Average with Kalman filter (ARMA-KF) model, the noise standard deviation of the filtering effect of the combined model proposed in this paper decreases by 44.00% and 46.66% on the x and y axes, respectively, reducing the noise impact by nearly three times.

With the increasing number of cislunar space missions, real-time and reliable navigation and communication services have become critical. It is necessary to develop the navigation constellations dedicated to cislunar space services. However, there are plenty of orbits in cislunar space providing alternative orbits, which makes constellation design a challenging task. To address this, this paper proposes a method for a cislunar navigation constellations configuration design via orbits with resonant periods. First, a periodic orbit catalog for the Earth–Moon system is constructed. Baseline orbits are selected from different orbital families, and all resonant orbits with periods proportional to the baseline orbits are compiled into a resonant orbit set. Second, a Dilution of Precision (DOP) model for navigation performance and a spatial zoning model are established. Then, resonant orbital combinations are screened based on orbital type composition, followed by resonance constellation generation according to predetermined constellation scales. All constellation configurations are categorized by orbital type to obtain a full resonant constellation set. Finally, the proposed method is applied to design optimal configurations providing navigation services for near-Earth and lunar regions. The simulation results shows that constellations combining L2 southern/northern Near-Rectilinear Halo Orbits (NRHOs) with vertical orbits at L4/L5 points deliver the optimal navigation performance in cislunar regions. The relationships between orbital radius and DOP values in target areas, as well as the DOP evolution patterns over constellation periods, are analyzed. The mean DOP values of the optimal constellation in both the near-Earth region and the lunar region increase as the spatial radius expands.

In high-orbit space missions, the significant attenuation of Global Navigation Satellite System (GNSS) signals due to long transmission distances and complex environmental interferences has led to a drastic degradation in the accuracy of traditional positioning models, which has attracted great attention in recent years. Although multi-system GNSS fusion positioning can alleviate the problem of insufficient satellite visibility, the existing methods are difficult to effectively cope with the challenges of multi-source noise coupling and inter-system error differences unique to high orbit. In this paper, we propose an adaptive GNSS positioning optimization framework for a high-orbit environment, which improves the orbiting reliability under complex signal conditions through dynamic weight allocation and a multi-system cooperative strategy. Different from the traditional weighting model, this method innovatively constructs a two-layer optimization mechanism: (1) Based on BP neural network, it evaluates the noise characteristics of pseudo-range observations in real time and realizes the adaptive suppression of receiver thermal noise, ionospheric delay, etc.; (2) it introduces Helmert variance component estimation to optimize the weighting ratio of GPS, GLONASS, BeiDou, and Galileo and reduces the impact of signal heterogeneity on the positioning solution of the multi-system. Simulation results show that the new method reduces the root-mean-square error of positioning by 32.8% compared with the traditional algorithm to 97.72 m in typical high-orbit scenarios and significantly improves the accuracy loss caused by the defective satellite geometrical configurations under multi-system synergy.

In Fourier Transform Spectrometers, phase errors in spectral measurement induce distortion in reconstructed spectra. Existing phase correction algorithms demonstrate insufficient precision in addressing both linear phase and instrumental phase components, resulting in limited applications for the restored spectra in the field of precision measurement. This paper proposes an algorithm called the Cross-Teager–Kaiser ${\psi }_B$ Energy Operator–Nonlinear Calibration Model (CTKB-NCM) for phase error correction. The algorithm first uses the cross-Teager–Kaiser ${\psi }_B$ energy operator (CTKB) method to correct linear phase errors, then applies the Nonlinear Calibration Model (NCM) to solve for the instrument phase correction parameters at each wavenumber, and finally uses the instrument phase correction parameters to correct the residual phase after the linear phase error has been corrected. The Rao algorithm is used to determine the optimal instrument phase correction parameters. Simulation experiments demonstrate that the CTKB-NCM method achieves an order-of-magnitude improvement in normalized reconstructed spectral accuracy for SO₂ gas compared to the conventional Mertz method.