The lunar reference frame provides a fundamental infrastructure for high-precision lunar navigation, mapping, and scientific exploration. This paper presents a systematic review of its definition, realization, maintenance, and future development. Firstly, the fundamental concepts of the lunar reference frame are introduced, with a clear distinction between the lunar reference system and the lunar reference frame. Particular emphasis is placed on the two principal realizations currently adopted for lunar geodetic applications, namely the principal axes (PA) frame and the mean Earth/rotation axis (ME) frame, including their defining principles and transformation relationships. Secondly, the techniques used for the maintenance and refinement of the lunar reference frame are reviewed, including lunar laser ranging (LLR), very long baseline interferometry (VLBI), and photogrammetry. Finally, the contribution of the Earth-Moon navigation system to the establishment of the lunar reference frame is discussed. As a key infrastructure for cislunar space activities, such a navigation system provides essential technical support for the realization and long-term maintenance of the lunar reference frame. Future development is expected to focus on enhancing high-precision observation capabilities, improving multi-source data fusion, accelerating standardization, and strengthening international collaboration, thereby advancing the international lunar reference frame as a unified spatiotemporal reference for future lunar exploration. 

This paper introduces the development of the lunar standard time and its definition based on general relativity and the simultaneity principle in four-dimensional spacetime. A three-step progressive approach is proposed to realize a coordinated lunar time. The primary step, with standard time on the earth ground adopted for traceability, applies to those without clocks deployed on lunar ground or in orbit thus unable to represent time unit on the moon. The intermediate step, with proper time of local clocks converted into coordinated time and an independent lunar standard time provided for time service, applies to those with at least 1 clock on the lunar ground representing SI second and are authorized as lunar local time reference by metrological administration. The advanced step, with time standard traced to an agreed convention by decentralized time keeping and broadcasting, time reference is not directly authorized anymore but replaced with different time keeping apparatus ID. This step applies to those with at least 4 time keeping devices deployed in lunar space or on the lunar ground. Users could obtain local time and position information from broadcast timestamps, and this mechanism is basically consistent with the existing Global Navigation Satellite System (GNSS) theories. Lunar standard time operates independently of Earth standard time. To meet the demand of users on both celestial bodies, timekeeping devices shall continuously monitor and release coordinate time comparison tables as well as terrestrial and lunar calendars. Those timekeeping methods in the three steps mentioned above provide theoretical reference for metrological specifications concerning the “Definition of Lunar Standard Time”.

In order to reduce the effect of systematic bias on the performance of stellar aberration navigation system, a systematic bias estimation and compensation method based on a parametric model and an extended Kalman filter (EKF) is proposed. The systematic bias is described uniformly as relative installation errors of sensors. A stellar aberration navigation system model is established where spacecraft motion state, measurement noise and systematic bias are taken into consideration. Then a navigation filter is designed based on the model to estimate the systematic bias parameters together with the position and velocity of the spacecraft. The feasibility of the systematic bias self-calibration method is analyzed through the calculation of the Cramer-Rao lower bound (CRLB). The numerical simulation is implemented for an Earth satellite. It shows that the unfavorable effect of the system is suppressed evidently by using the proposed method. With an inter-star angle measurement accuracy of 0.1″, after the systematic bias self-calibration, the positioning accuracy of the stellar aberration navigation system is improved from about 50km to less than 3km. In comparison with the existing approach where the systematic bias is modeled as the inter-star angle measurement bias, the main advantage of the proposed method is that the dimension of the state vector to be estimated is independent of the number of the measurement, which facilitates the design of the onboard navigation algorithms.

Autonomous terrain relative navigation (TRN) is expected to play a crucial role of upcoming planetary missions. Conventional TRN methods typically rely on landmark detection and image registration, which achieve relative pose estimation of the spacecraft by establishing data association between navigation images and onboard maps. The association problem between measurements and maps is a complex and computationally intensive task, and requires high accuracy in the prior knowledge onboard. Feature matching is a critical task in computer vision, aiming to achieve stable and accurate image registration under real-world varying conditions through robust visual models. This paper addresses the challenge of autonomous optical navigation for future deep space missions and for the first time, RoMa-TRN, an autonomous TRN method based on RoMa feature matching without maps is proposed. For sequential images captured by a monocular camera, the method employs the pre-trained visual model for front-end feature matching and constructs visual odometry. By solving a least-squares problem, it estimates the inter-frame direction of motion of the spacecraft. This measurement can be incorporated into an onboard navigation filter to update the state of spacecraft. Experimental results demonstrate that, compared with other feature matching methods, the proposed approach achieves accurate and robust image registration under varying illumination and viewpoint conditions. Under extreme scenarios with solar elevation angles of 1° and 89°, no significant performance degradation is observed. At an orbital altitude of 10 km, the method achieves a motion direction estimation accuracy of approximately 0.03°, enabling precise direction-of-motion for navigation filter.

A lightweight autonomous lunar orbiter positioning method based on crater visual matching was studied. The goal was to reduce dependence on groundbased tracking systems and improve positioning autonomy and timeliness. Traditional methods relied on ground stations to process radio tracking data, which led to high costs and limited autonomy. To address this, a visual matching algorithm based on neighboring crater clusters was proposed. After dynamically adjusting the onboard camera focal length, geometric information extracted from images was matched with known crater data. The matching results were then used to estimate the orbiter's pose. A filtering process refined the positioning results. Instead of using full crater images, the method built a database using geometric matrices of crater centroids. It matched geometric data from captured images to reduce data load. A lunar-orbiter system model was built. The simulation results show that the proposed crater visual matching algorithm achieves an overall average matching success rate of over 93.24% at different altitudes. The localization error increases with the variance of the added noise. However, after dynamically adjusting the focal length and applying filtering, the localization performance remains robust under various noise conditions. Overall, 92.59% of the localization errors are under one kilometer, and the average positioning error is 0.2727km. These results show that the method enables autonomous positioning using onboard images. It reduces reliance on ground systems and performs well in both matching accuracy and positioning error. The approach shows promise for future autonomous lunar orbiter navigation.

As one of the missions under China's Space Exploration Science Satellite Program, the Hongmeng project aims to deploy multiple small satellites in lunar orbit to conduct the first high-resolution ultra-long-wavelength sky survey on the lunar farside, opening the last observational window of the radio spectrum. To evaluate the feasibility of imaging under practical engineering conditions, an end-to-end parallel simulation framework capable of supporting tens of billions of baselines and processing hundreds of millions of pixels is required. An end-to-end simulation framework based on single-machine parallel computing is developed, covering available-baseline selection, visibility data generation, Earth-Moon occultation determination, and image reconstruction. Targeted data partitioning strategies are introduced for the generation and processing of large-scale observational data, and an engineering feasibility evaluation method is established for the full imaging chain. Imaging performance is further analyzed for both full-sky and partial-sky scenarios under nominal observations and multiple satellite failure conditions. Simulation experiments preliminarily show that low-resolution full-sky imaging achieves SSIM=0.9985 and PSNR=57.9568, while high-resolution partial-sky imaging achieves SSIM=0.8399 and PSNR=23.9138. As the number of available baselines increases, SSIM and PSNR improve steadily and become stable after sufficient observation time. When up to two low-frequency satellites fail during the later stages of observation, imaging quality doesn't degrade. The proposed data-partitioning and parallel strategies enable visibility generation and large-scale linear system solving without exceeding single-machine memory limits. The proposed end-to-end parallel simulation framework effectively supports imaging performance evaluation for the Hongmeng project under both nominal and partial sub-satellite failure conditions, demonstrating strong engineering applicability. The framework provides a solid technical foundation for future migration to high performance GPU clusters and is expected to be extendable to other large scale radio-interferometric arrays and deep space electromagnetic imaging missions.

Non-independent and identically distributed (Non-IID) data across clients remains a fundamental challenge in federated learning. A critical gap exists: the lack of a universal metric capable of both quantifying distributional differences across diverse Non-IID scenarios and fairly evaluating algorithmic robustness. This work addresses this gap by developing a generic metric for the degree of Non-IIDness among distributed nodes. We propose a Domain-shift-based Metric (DSM). The core idea is to circumvent the intractability of measuring divergence in high-dimensional raw data by leveraging a pre-trained feature extractor. DSM transforms the problem into estimating domain shift within a learned feature space. Specifically, it quantifies the Non-IID degree as theweighted sum of Wasserstein distances between client feature distributions and the global feature distribution. We validated DSM on MNIST and Fashion-MNIST datasets, simulating five canonical Non-IID scenarios. Our experiments demonstrate that: DSM effectively differentiates bias levels both within and across these five scenarios, showing superior sensitivity compared to four conventional metrics (e.g., Euclidean, Cosine distances); After calibrating different scenarios to an equivalent Non-IID degree using DSM, we conducted a fair comparison of four federated classification algorithms and four federated generative algorithms. The evaluation consistently identified Scaffold as the top performer for classification and BGAN for generation, validating DSM's utility for fair cross-scenario algorithm assessment. The proposed DSM metric establishes the first unified, quantitative benchmark for Non-IIDness across scenarios in federated learning. As a model-agnostic tool, it provides a principled basis for algorithm evaluation and selection. Furthermore, it offers a crucial quantitative foundation for designing collaborative learning algorithms in distributed systems with inherent Non-IID data, such as satellite constellations in aerospace applications.

The aerospace information network architecture jointly constructed by data link terminals and satellites can effectively expand communication coverage. In order to meet the requirements of multi-user flexible access and anti-destruct and endurance of data link communication networks, the spaceborne phased array spatial anti-jamming technology is studied, and an adaptive beam iterative algorithm combined with power inversion algorithm and despread respread algorithm is proposed. Firstly, the power inversion method is used to suppress the high-power suppressive interference , ensuring the receiver can achieve reception synchronization; Then, the coarse synchronization information such as time delay and frequency offset is obtained through despread respread processing, so that the local reference signal is constructed; After that, serial interference cancellation is introduced to eliminate the impact of user multiple access interference in the received array signals, thereby minimizing the error between the beamforming weights and the actual incident steering vector of the signal; Finally, the adaptive anti-jamming beam weights are fast and robust iterated through the second-order least mean square (LMS) iteration. Simulation verification was carried out under the scenario of a 6-element uniform linear array (ULA), strong interference and multi-user incidence. The results show that the output signal-to-interference-plus-noise ratio (SINR) improvement of the proposed algorithm is close to the theoretical gain value, which is significantly better than the performance of the existing algorithms. Through comparison, the proposed adaptive anti-jamming receiving beam design algorithm can not only ensure reliable reception under strong interference incidence, but also effectively resist the impacts of multiple access interference and system frequency offset estimation errors. It can iteratively update the spatial multi-user beam weights in real-time and adaptively, exhibiting superior anti-jamming multi-user reception performance, which fully meets the anti-destruct and dynamic adaptive requirements of aerospace information network.

Anomaly detection is vital for spacecraft health in orbit. Existing algorithms rely on high-quality training data and suffer marked performance loss on typically incomplete spacecraft data. This study examines the impact of incomplete spacecraft data on detection performance. First, three granular levels of missingness metrics are proposed based on missing values' effect on model inputs. Then, a generalization performance measure using these metrics is designed, and an upper bound for detection model degradation is theoretically proven. Finally, the prediction algorithm ADForecast is developed from this measure; it accurately forecasts detection accuracy at a given missing ratio and integrates with various detection algorithms. Experiments show ADForecast efficiently and accurately predicts the performance of multiple algorithms under most missing ratios; when pretrained with historical data from similar spacecraft, the prediction error stays below 5%.

Aiming at the challenges of multiple nodes, complex topology and large amount of calculation in the spacecraft formation flight system, the traditional centralized state estimation is difficult to apply due to the high pressure of communication and calculation and low fault tolerance. An interval state estimation scheme is proposed based on distributed observer network. Each local observer only uses part of the output information, interacts with the neighbor observer with a given communication topology, and completes the joint estimation of the global state through a cooperative mechanism. The theoretical criterion for ensuring that the true state of the system is always included in the estimation interval is established based on the positive system theory. Furthermore, by combining Lyapunov stability theory, Riccati equation and regional synchronization theory, the sufficient conditions for ensuring the uniform bounded stability of the observation error dynamic system are given.Numerical simulations verify the effectiveness and feasibility of the proposed distributed interval estimation strategy. This method can significantly reduce the system overhead while ensuring that the theory is rigorous and easy to implement : compared with similar distributed methods, the communication traffic is reduced by more than 70%; compared with the centralized method, the computational complexity can be reduced by more than 90% with the increase of scale, which greatly improves the scalability, robustness and practical application potential of the system.

To address the issue of insufficient ionization caused by rapid propellant diffusion in Planar Hall Thruster (PHT), a modified PHT with a shallow gas chamber (PHT-C) was designed. A comparative experimental study was conducted to investigate the discharge characteristics, thrust performance, and beam properties of the PHT-C and the conventional PHT. The results show that the shallow gas chamber effectively concentrates the propellant, leading to a lower ignition voltage for the PHT-C. The thrust and specific impulse of the PHT-C outperform those of the PHT, reaching maximum values of 15.8mN and 1828.0s, respectively, at a power below 500W. Under high anode voltage and low-to-medium anode flow rates, the PHT-C achieves higher propellant utilization and beam divergence efficiency, resulting in a maximum relative improvement in anode efficiency of 35.0% compared with the conventional PHT. Additionally, its beam transitions from the triple-peak structure of the conventional PHT to a more focused double-peak structure, which helps reduce sputtering on components at large angles. This study introduces a shallow gas chamber into the PHT, which mitigates the excessive propellant diffusion in open space and enhances performance, providing a novel method for the optimization of PHTs.

The temperature distribution significantly influences the operational stability and reliability of the high-power Hall thruster(HPHET). To investigate the thermal dissipation and temperature distribution of LHT-200E Hall thruster under rated power conditions, finite element analysis (FEA) is employed. The thermal model of the thruster is first validated and calibrated under a 12.5kW operating condition. Subsequently, thermal characteristic analysis and thermal design optimization are conducted for the 15kW rated condition. Through simulations, the temperature field distribution under three thermal design approaches, i.e., changing the material of the discharge chamber support, adding heat sinks or heat plates at different positions, and segmenting the magnetic base, is analyzed to verify the effectiveness of the thermal designs. The results show that, under the 12.5kW condition, the total heat dissipation is 2510W, accounting for 20.1% of the total power, and the simulated temperature results are the closest to the measured values with a maximum error of 6.2% occurring in the inner coil, primarily attributing to inaccuracies in contact thermal resistance settings, which are within the permissible range of thermal model establishment. Comparative simulations for the 15kW condition demonstrate that, when the three thermal design approaches are appropriately applied, the temperature of the magnetic base can be reduced by approximately 50℃, and the temperature of the inner coil can be reduced by approximately 40℃.Among the three thermal design methods, adding heat plates is the most effective cooling approach, whereas changing the discharge-chamber support material and segmenting the magnetic base produce only moderate improvements. Comparing the three methods shows that combining a high-thermal-conductivity bracket for the discharge chamber with a heat-plate design effectively lowers the temperatures of critical thruster components, evens out their temperature distribution and enhances mission reliability.

To address the degradation of landing accuracy resulting from thrust magnitude uncertainty in the lander's engine, a method integrating Powered Explicit Guidance (PEG) with Recursive Quadratic Programming (RQP) is proposed. The descent trajectory was divided into two phases with distinct thrust levels. PEG was applied in each phase to generate the corresponding guidance law, with the altitude and velocity at the thrust-switching point treated as optimization variables. These parameters were optimized using RQP framework, in which the Hessian matrix was approximated via a variable-metric method to compute the search direction. To further mitigate convergence to local minima, gradient clipping and stochastic parameter perturbation were introduced. Monte Carlo simulations were carried out to validate the effectiveness and robustness of the proposed method.  The results demonstrate reliable convergence across a range of test conditions, including variations in the desired downrange, initial parameters, and thrust deviation. Furthermore, compared with the conventional PEG approach, the proposed method significantly reduces both downrange error and fuel consumption. The proposed method effectively improves the lander’s pinpoint landing accuracy in the presence of thrust uncertainty, offering a reliable and technically feasible approach for future lunar soft-landing missions.

In response to the demand for the in-orbit autonomous operation of ultra-high agility, stability, and precision(ASP) spacecraft, this paper proposes a fully autonomous high-precision in-orbit identification method for structural modal parameters. This approach is designed to overcome the limitations of traditional ground-based processing methods which suffer from poor real-time performance and require significant manual intervention. The proposed method utilizes actuator frequency sweep data and employs a Savitzky-Golay filter to denoise the frequency response data, which significantly suppresses high-frequency noise while preserving key peak features. A novel peak detection algorithm, based on the velocity of motion in the complex plane, is introduced to identify insignificant modes. Subsequently, admittance circle fitting theory is used to calculate the frequency, damping ratio, and gain of each mode. The accuracy of the parameter estimation is comprehensively improved through a segmented frequency band least-squares optimization method. Numerical simulations demonstrate that the proposed method can accurately extract modal parameters even in the presence of noise and disturbances, and the optimized frequency response curve shows a high degree of consistency with the theoretical model. The method's efficacy in a realistic noise environment is validated through a physical experiment, which successfully identifies the resonance peaks of insignificant modes. The resulting identified structural transfer function aligns well with the measured data, providing critical technical support for the high-performance autonomous control of ASP spacecraft.

In response to the demand for miniaturization and lightweight design of rendezvous and docking products, a LiDAR system based on a MEMS two-dimensional scanning drive unit was proposed. To meet the requirements for long-range rapid acquisition and stable tracking, the optical system was designed to determine energy parameters, the MEMS scanning drive method and search-capture strategy were developed, and a ground-based long-distance search-capture validation test was designed. Firstly, the MEMS-based LiDAR optical system was designed, and based on the analysis of the spatial cooperative target echo energy model, the key parameters of the fiber laser, APD detector, MEMS scanning mirror, optical transceiver system, and laser cooperative target were determined to meet the requirements of long-distance detection at the 30km level. Secondly, the Lissajous single-frame scanning curve for the MEMS unit and the square-ring multi-frame scanning search and acquisition strategy were designed. Finally, the influence of atmospheric two-way transmittance on the maximum ranging capability under ground conditions was analyzed, along with the effects of light intensity fluctuation and spot drift under turbulent atmospheric conditions on ground-based testing. A ground-based long-distance search and acquisition experimental platform was established, and both ground-based static power tests and dynamic captive-carry flight tests were designed. At a distance of 28.6km, the target was rapidly acquired within 15 seconds while meeting dynamic performance requirements of ±5(°)/s. Experimental results verify that the optical system design of the MEMS LiDAR satisfies the 30km-level ranging capability in orbit, and the search and capture strategy design meets the requirements for rapid acquisition and stable tracking. This lays a foundation for the application of miniaturized and lightweight LiDAR products in future rendezvous and docking missions.

Cable prestress is a critical parameter for finite-element modeling of cable-net structures. Due to the strong coupling among cables in large-scale cable-net systems, conventional modal-based methods have difficulty in accurately measuring prestress and suffer from low identification efficiency. A multi-experiment sensitivity-based prestress correction algorithm was proposed. Compared with single-case identification, multiple experiments were used to enrich sensitivity information, break near collinearity among sensitivity columns, alleviate rank deficiency and improve identification accuracy, while noting that it may also introduce redundancy in the sensitivity matrix, increase the computational burden, or lead to noise amplification under ill-conditioned sensitivity matrix. Photogrammetric measurements were employed to obtain measured nodal displacements, and the correction objective was defined as the minimization of the RMS error between finite-element computed displacements and experimental displacements. Sensitivity matrices were constructed by finite differences under multiple loading cases and assembled for identifiability analysis. A parameter-aware Tikhonov regularization was introduced to suppress ill-posed amplification and out-of-bound updates, and Leave-one-out cross-validation (LOOCV) was used to adaptively adjust the update step size. The proposed algorithm was applied to two test cases: a single planar segment of a radial-rib cable net antenna and a complex three-dimensional spatial cable net. After five iterative corrections, the prestress estimation accuracy was improved by 96.73% for the planar segment and by 85.74% for the complex spatial net, respectively. The method achieves high accuracy and provides a reliable tool for online prestress calibration of large-scale cable-net structures.

There are some advantages of terahertz communication system such as large transmission capacity, small terminal size, good transmission security and abundant frequency resources, which is irreplaceable in special cases of black barrier and solar eclipse. This paper presents a comprehensive overview of domestic and international developments in the field. The terahertz space communication system with HEO and MEO relay satellites is constructed in 220GHz.The calculation results of link budget indicate that the terahertz communication system has the feasibility of high-speed data relay between satellites and massive date transmission between satellites and ground station. Finally, the technological development trends of future terahertz satellite communication systems are discussed.

When performing very long baseline interferometry using weak signals in deep space exploration or high-dynamic arcs of detectors, a high-precision interferometry time delay model is required. A theoretical analysis of the impact of the time delay rate model on correlation processing was conducted, whose results showed that the longer the integration period, the higher the accuracy requirement for the time delay rate model. Based on the initial time delay model, a high-precision time delay rate model refinement method based on multi-integration period cross-spectral phase least squares processing was proposed. The least squares calculation was performed on the cross-spectral phases of multiple integration periods to obtain the residual time delay rate and correct the initial time delay rate model; further, an evaluation method for the accuracy of the time delay rate model was presented. Monte Carlo simulations and measured data from China deep space Network were used to process and verify both radio source signals and detector signals. The results show that after the correction of the time delay rate model, the accuracy of time delay rate model is better than 0.2 ps/s, the residual delay estimation accuracy of the radio source is improved by up to approximately 56%, and the residual time delay accuracy is improved by nearly two orders of magnitude in scenarios where the detector's predicted ephemeris is inaccurate.The proposed method is conducive to improving the interferometric measurement accuracy of weak signals in deep space exploration and high-dynamic arcs of detectors, and has certain reference significance for subsequent data processing of deep space exploration.

Aiming at the fact that the error detection and retransmission method is not suitable for reliable transmission in inter-satellite broadcast or multicast communication of small satellites, a reliable data transmission method for inter-satellite networks is proposed. By utilizing the original 2～3 byte error control field of the application-layer space packet, the original error detection code is replaced with an error correction code, constructing a correctable space packet. Based on the analysis of the error data model, for a space packet with a length of 512 bytes, a BCH error correction method capable of correcting double-bit errors is adopted, and encoding and decoding methods suitable for satellite implementation are provided. The new algorithm not only eliminates the need for a bidirectional channel, making it suitable for broadcast or multicast while saving volume, weight, power consumption, and cost, but also effectively reduces the packet error rate. When the bit error rate is 10-4, the packet error rate decreases by approximately two orders of magnitude; when the bit error rate is 10-7, the packet error rate decreases by approximately five orders of magnitude.