Xiao Chen

The Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) technique enables cislunar spacecraft to obtain accurate position and velocity information, allowing full state estimation of two vehicles using only inter-satellite range (ISR) measurements when both their dynamical states are unknown. However, its stand-alone use leads to significantly increased orbit determination errors when the orbital planes of the two spacecraft are nearly coplanar, and is characterized by long initial convergence times and slow recovery following dynamical disturbances. To mitigate these issues, this study introduces an integrated navigation method that augments inter-satellite range measurements with line-of-sight vector angles relative to background stars. Additionally, an enhanced Adaptive Robust Cubature Kalman Filter (ARCKF) incorporating a chi-square test-based adaptive forgetting factor (AFF-ARCKF) is developed. This algorithm performs adaptive estimation of both process and measurement noise covariance matrices, improving convergence speed and accuracy while effectively suppressing the influence of measurement outliers. Numerical simulations involving spacecraft in Earth–Moon L4 planar orbits and distant retrograde orbits (DRO) confirm that the proposed method significantly enhances system observability under near-coplanar conditions. Comparative evaluations demonstrate that AFF-ARCKF achieves faster convergence compared to the standard ARCKF. Further analysis examining the effects of initial state errors and varying initial forgetting factors clarifies the operational boundaries and practical applicability of the proposed algorithm.

Fewer isolated pulsars are available for X-ray pulsar navigation, and they are unevenly distributed spatially. In contrast, the number of available binary pulsar for navigation is promising. However, the challenges of using binary pulsars as navigation pulsars is significant time-varying systematic errors. Therefore, to develop a measurement model suitable for both binary pulsars and isolated pulsars, while effectively mitigating timevarying systematic errors, achieving significant navigation accuracy, we propose a second-differenced measurement model based on the phase and Doppler frequency shift of binary pulsars. To linearize the measurement model and reduce the impact of distance on systematic errors, we developed a first-differenced measurement model based on phase difference and Doppler frequency shift. To further suppress time-varying systematic errors, we propose a second-differenced measurement model, which is the difference between the first-differenced measurement model at the neighboring filtering time. For deep space spacecraft, time-varying systematic errors are of significant magnitude but change slowly over the filtering period. Therefore, the second-differenced measurement model effectively mitigates the majority of these errors. In addition, to address the issue of increased random errors caused by the seconddifferenced model, we derived a differential noise covariance matrix that can effectively suppress random errors within the traditional Extended Kalman Filter (EKF) framework. The simulation results demonstrate that the proposed method can simultaneously utilize binary pulsars and isolated pulsars for navigation. It effectively suppresses the impact of time-varying systematic errors, including pulsar direction error and linearization error, leading to improved navigation accuracy.

The Moon is the closest celestial body to the Earth. Its rich unique resources are an important supplement to the Earth’s resources and have a profound impact on the sustainable development of human society. As large-scale exploration missions gradually progress, demands for communication, navigation, surveying and other services of lunar-space probes have significantly increased. Constellation navigation and orbit determination technology will become an indispensable part of future lunar exploration infrastructure. This article systematically analyzes the current status of lunar relay navigation satellite networks at home and abroad, summarizes the technical principles of single-satellite and constellation navigation and orbit determination, discusses the technical difficulties in lunar navigation constellation orbit determination and navigation, and analyzes possible solutions. Finally, the development trend of research on high-precision orbit determination and navigation methods for lunar navigation constellations is proposed.

In celestial spectral velocimetry methods, when the solar spectra are stable, highly accurate velocity information of spacecraft can be derived from the Doppler frequency shift. However, solar activity can cause a frequency shift in the solar spectra, greatly affecting the accuracy of velocimetry. Due to limitations of spacecraft payload and computing resources, we propose a celestial spectral velocimetry compensation method that only uses single-frequency band solar images and solar spectra. In addition to a spectrometer used by traditional celestial spectral velocimetry methods, we only add one optical imaging sensor. We conduct a gray correlation analysis between single-frequency band solar image sequences and velocimetry bias induced by solar activity, which demonstrates a strong correlation between the two. Based on the above results, the velocimetry bias estimation can be modeled as a sequence regression problem. To address the regression issues, we develop a novel hybrid framework that combines semi-supervised regression generative adversarial networks (SRGANs) and long short-term memory (LSTM). The role of SRGAN is to improve the generalization ability of the regression model and extract features from the single-frequency band solar image sequences. LSTM receives the extracted feature sequences to capture temporal dependencies within the spectral sequences, thereby providing accurate velocimetry bias estimation. The experimental results indicate that SRGAN-LSTM accurately estimates the velocimetry bias caused by solar activity. After compensation, the velocity error decreases from 0.3242 to 0.0327 m/s.

To suppress the systematic errors of the X-ray pulsar navigation system (XPNAV) based on the phase and Doppler frequency shift, and eliminate singularity phenomena, a double-differenced autonomous navigation method is proposed. By considering the intrinsic spin phase and time propagation delay of the pulsar, the observation pulse phase models on the spacecraft and Mars were established. To linearize the measurement model, a phase-differenced model was developed by subtracting between the two phase models. To suppress the systematic errors in the phase-differenced model, a double-differenced model based on phase and Doppler frequency shift is proposed, which is the difference between the phase-differenced model at the neighbor filtering time. For a deep-space spacecraft, the magnitude of the systematic error is significant but changes slowly over the filtering period. Therefore, the double-differenced model can suppress the majority of systematic errors. In order to solve the problem of correlation between process and measurement noise, an improved extended Kalman filter (IEKF) method is proposed. The simulation results reveal that the proposed method can effectively suppress the impact of systematic errors, including the pulsar direction error and linearization error.

Autonomous celestial navigation has been exploited for orbit determination of deep space exploration. Geometric constraints in celestial measurement are the inherent attributes in actual comprehensive autonomous celestial navigation physical systems; they are usually neglected in autonomous navigation systems which causes a loss of information in measurement. For the purpose of high-precision autonomous celestial navigation, the geometric constraints should be utilized as fully as possible. This paper proposes a geometric coplanar constraint for the mutually dependent celestial measurement (line of sight or vectors), and the geometric coplanar constraint model is established. The sequence quadratic program (SQP) algorithm based on the geometric coplanar constraint is put forward to eliminate the dependence of multiple celestial measurements, and suppress the noises in celestial measurement geometrically. Taking both geometry coplanar constraints of celestial measurement and the nonlinear characteristics of system models into account, cubature Kalman filter with measurement optimization is proposed for decreasing the random noise in measurements geometrically and statistically. Simulations demonstrate that the proposed geometric coplanar constraints-aided autonomous celestial navigation method can effectively eliminate the measurement noise geometrically and statistically, and achieve high-precision performance.

Traditional autonomous celestial navigation usually uses astronomical angle as measurement, which is a function of spacecraft’s position and can’t resolve the spacecraft’s velocity directly. To solve this problem, velocity measurement by stellar spectra shift is proposed in this paper. The autonomous celestial integrated navigation method is derived by combining velocity measurement with angle measurement, which can ensure the long-term high accuracy, real-time and continuous navigation performance for deep space exploration (DSE) missions. The observability of the integrated navigation system is analyzed. Moreover, the design of doppler navigator and hardware in-the-loop simulation system are described. Finally, a simulation example is employed to demonstration the feasibility and effectiveness of the proposed navigation algorithm.