The high accuracy and reliability of the navigation system is the “multiplier” of the unmanned-aerial-vehicle performance. Conventional integrated navigation systems are mostly based on Kalman filtering and adopt customized system solutions, which do not have the ability of “plug-and-play” processing of asynchronous and heterogeneous navigation information. This can have serious consequences. Factor graphs are capable of meeting the needs of all-source autonomous navigation in complex flight environments due to their “plug-and-play” characteristics, and have a wide range of application prospects. This paper firstly describes the necessity, importance and significance of factor map fusion theory in ensuring the stable, reliable and high-precision operation of aircraft navigation system, discusses the existing architectural solutions of factor map fusion, and analyzes the key technologies such as inertial pre-integration, sensor model construction and probability density function calculation in factor graph information fusion, and finally points out the challenges of factor graph for integrated navigation.

A numerical method for computing Nash equilibrium strategies (NES) of the spacecraft time-optimal orbit pursuit-evasion game (TOOPEG) with continuous thrust reachable domain (RD) analysis is proposed. Through theoretical derivation and Monte Carlo validation, the equivalence among the minimum time of the TOOPEG problem with NES, the minimum time of a virtual single spacecraft for a time-optimal approach to the origin, and the minimum time required for the envelope of the pursuer’s RD to enclose that of the evader is established. First, the necessary conditions for NES are derived using Pontryagin’s maximum principle (PMP), converting the original bilateral optimal control problem into a 7-dimensional two-point boundary value problem (TPBVP). Then, the TOOPEG is transformed into a virtual single-spacecraft time-optimal approach problem, with the above necessary conditions. By exploiting the evolutionary characteristics of the continuous-thrust RD, the problem is further reduced to a 3-dimensional nonlinear differential equation. An improved Broyden quasi-Newton iterative (IBQNI) algorithm is employed to obtain high-precision numerical solutions, and an iterative initial value construction method based on a linearized orbit dynamic model is proposed. Furthermore, a set of criteria is developed to assess the relative spatial configuration between the RD of different spacecraft. Numerical simulations demonstrate that the proposed method achieves excellent convergence and remarkable computational efficiency.

With the expansion of the size of multi-beam radar arrays, the progress of system miniaturization, and the gradual improvement of high-precision geographic elevation databases, the application of multi-beam lidar has significant advantages such as anti-interference, high precision, and high sensitivity. Further research on 3D terrain point cloud mapping technology for aircraft has important theoretical and practical significance, which is one of the important research directions for future high-precision and highly reliable navigation solutions for aircraft. Combined with the working characteristics of the aircraft, this paper focuses on the study of the 3D terrain point cloud map matching technology based on multi-beam radar for aircraft, analyzing the feasibility of applying 3D terrain point cloud map matching technology for aircraft navigation. A robust model for point cloud feature extraction and registration based on deep learning is constructed. Meanwhile, the paper investigates the advantages of the deep-learning-based 3D terrain point cloud map matching technology as well as inspects the effective impact of the 3D point cloud matching technology based on deep learning on the matching accuracy. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Mammals have the ability to sense exogenous information and self-motion information according to the navigation cells in the brain for self-positioning and navigation,which provides a good biological model for the development of intelligent and adaptive UAV(unmanned aerial vehicle)navigation methods.In this paper,we study the neural mechanism of key navigation cells and the information fusion modelling method,and propose a brain-inspired navigation method based on place cell and grid cell information fusion to address the problems of low real-time loop detection and sparse detection points in the traditional vision-based brain-inspired cognitive map construction method.Firstly,we use continuous attractor neural network and isotropic Gaussian network to model grid cell and position cell respectively,and achieve path integration and position measurement,based on which we propose grid cell zeroing algorithm to improve the efficiency of grid cell wide range calculation.Secondly,the connection weight matrix of the two cell networks is obtained by Hebb-learning rule,which realises the real-time correction process of the position cell to the grid cell path integral.Finally,the 3D position of the UAV is obtained based on the neuron population vector weighted average as well as the grid cell vertex position processing decoding method.The experimental results show that the method proposed in this paper can accurately decode the three-dimensional position of the UAV in a wide range of space,which improves the accuracy compared with the traditional navigation and positioning algorithms,and further expands the application scope of the three-dimensional brain-inspired navigation method for UAVs.

To address the problem that the predictive control parameters of the model are fixed and set according to experience during satellite rendezvous and docking trajectory tracking control, a DQN (Deep Q Network) optimized MPC (Model Predictive Control) method is proposed. A relative motion model of the satellite based on the ROE (relative orbit element) is established, considering the thrust constraints. Then DQN is used to improve the MPC so that the satellite can independently select the appropriate control parameters according to the current environment, which has stronger robustness. Through the theoretical study and simulation analysis of the satellite orbit motion model, the feasibility of the DQN-optimized MPC control scheme is verified. The simulation analysis compares the trajectory tracking control effects of using only MPC and DQN-optimized MPC algorithm, which validates the efficiency and excellence of the DQN-optimized MPC, and the simulation results show that the control accuracy has been improved by 9.8

The growing number of non-cooperative targets in space poses a threat to the safety of spacecraft in orbit. However, in angles-only and range-only tracking scenarios, the relative orbital state may exhibit limited observability or even become completely unobservable. Meanwhile, non-Gaussian noise induced by the complex space environment may lead to filter divergence or even failure. In response to these challenges, this paper proposes a robust adaptive asynchronous federated filter (AF-RVBACKF) for high-precision space target tracking (STT), which combines space-based angle and range observations. First, the one-step prediction and measurement likelihood probability density functions (PDFs) are modeled using a Gaussian-inverse-Wishart (GIW) distribution. Variational Bayesian (VB) inference is employed to minimize the Kullback-Leibler divergence (KLD) between the true and approximate posterior PDFs, thereby estimating both the states and parameters. Next, following the variational update, a fading adaptive factor improved through multidimensional adaptation is introduced to further mitigate the impact of outliers on state estimation. Finally, considering the time-varying and non-uniform update intervals of heterogeneous sensors, a non-feedback asynchronous federated filtering framework is designed to facilitate cooperative tracking between angle and range sensors. This enhances the observability of STT and enables globally optimal estimation. The results show that, compared to angles-only or range-only tracking, the proposed combined observation model significantly improves the observability of STT. Moreover, under non-Gaussian noise conditions, the proposed AF-RVBACKF achieves the highest estimation accuracy.

A large number of sensors carried by spacecraft are facing the risk of irradiation, which may lead to the failure of sensors and affect the mission of the spacecraft. Therefore, it is significant to make the sensor work safely by attitude maneuvers. This article proposes a guidance algorithm for the attitude reorientation of rigid spacecraft, which aims to reduce the conservativeness of the traditional potential function and to solve the problem of the goal being non reachable with obstacles nearby (GNRON). While the rationality of the form design of the potential function is analyzed from the view of numerical calculation, a modified inverse-proportional potential function is designed based on it. Additionally, the anti-unwinding attitude error function is established to avoid the unwinding phenomenon of quaternions. In this paper, a set of weight assignment schemes for the potential function is proposed to obtain the maneuver path close to the edge of the attitude-forbidden zone, which reduces the conservativeness and energy consumption compared with the traditional method. Finally, the scheme can also solve the GNRON phenomenon. In the fourth section, the form design of the potential function is studied by numerical simulation, and the performance of the proposed algorithm is shown by comparative experiments.

Due to the sensitivity of the relative orbital elements model to the measurement noise, the non-stationary heavytailed noise(NSHT) induced by the time-varying environment during the relative navigation usually leads to filter divergence. To address this problem, a new nonlinear filter based on Gaussian-Student's-Multivariate K(GSK) mixture distribution is proposed in this paper. A Dirichlet stochastic mixture vector fusing Gaussian, Student's t, and Multivariate K distributions is introduced, thus proposing a GSK mixture distribution modeling measurement likelihood; then the Kullback-Leibler Divergence (KLD) of the true posteriori probability density function(PDF) and the approximate posteriori PDF are minimized by a variational Bayesian(VB) technique to solve for the state and parameter approximate a posteriori estimations, and finally a new nonlinear filter based on the GSK mixture distribution is derived for angles-only relative navigation in time-varying environments. Simulation outcomes indicate that the filter can realize state estimation in non-stationary states effectively with 45.16% higher estimation accuracy than the existing advanced filters.

The number of space targets in the near-Earth orbit has greatly increased, and space-based radar has the advantage of high resolution and high accuracy tracking to enhance the tracking efficiency of space extended targets (SET). We propose a gamma Gaussian inverse Wishart based on a matched linearization-Poisson multi-Bernoulli mixture (GGIWML-PMBM) filter to estimate the motion state and shape size of the SET. For the random matrix that can only describe the distribution under which the measurements are linear, the measurements of the spatial target are linearized using matched linearization, and the extended information is preserved in the second-order central moments. The transfer density and likelihood function of GGIW are nonlinear for Poisson measurements with nonlinear Gaussian spatial distributions, and the single-target densities and normalizing constants of the PMBM filter are not closed form. The prediction and update of PMBM include Gaussian-weighted integral calculation, for which different nonlinear approximation methods are used to calculate the weighted integral and derive the closed form of GGIWML-PMBM. Finally, the simulation scenarios of low-orbit single-radar sensor tracking near SET and group SET are established, and the results show that the tracking accuracy can reach 2.6 m for near SET and 6.6 m in group SET.

In order to address the issues of poor demonstration effects and difficulties in analyzing algorithms effectiveness in real-time during the research process of navigation algorithms for unmanned systems, and to facilitate the design of navigation algorithms and improve the professionalism of their demonstrations, this paper proposes a method for designing an unmanned system integrated navigation simulation demonstration system. Firstly, the carrier motion simulation scene is designed based on the Gazebo simulation platform to generate the necessary navigation parameters in real-time. Secondly, a visual display interface is designed based on ROS and Qt, which displays the carrier's navigation parameters, motion trajectories, and other information in real-time by publishing and subscribing to related topics. In addition, the system has extensible functionality to support secondary development according to user needs. The system has been validated to have good demonstration effects and is helpful for the research and demonstration of navigation algorithms for unmanned systems.

In this paper, a multi-prior mixture (MPM) distribution and arithmetic average (AA) fusion-based Student’s t filter (MPMAASTF) is proposed for the problem of non-stationary heavy-tailed noises filtering with only rough prior information available. Firstly, a MPM distribution is proposed to model the joint probability density function (PDF) for one-step prediction and measure likelihood, then the Kullback-Leibler Divergence (KLD) minimization technique and Jensen’s inequality are used to derive approximate posterior PDFs for states and parameters. A finite number of Student’s t PDF fusion algorithm based on AA fusion is developed to guarantee the closure of the filtering posterior PDF, and finally existing high precision moment matching technique is embedded. The proposed filter improves the filtering accuracy of non-stationary heavy-tailed noises by adaptive learning of the degrees of freedom (dof), the one-step prediction error scale matrix and the measurement noise scale matrix. Simulations validate the effectiveness and superiority of the proposed method.

In Kalman filter-based spacecraft autonomous celestial navigation, Inertial/Celestial integrated navigation system and asynchronous multi-sensor data fusion, complex environments and sensor alignment errors are likely to lead to inaccurate statistical priors for the noise covariance matrices and the non-zero measurement noise mean vector (MNMV). To address this issue, this paper firstly proposes a MultiNormal-Inverse Wishart (MNIW) mixture distribution modelling the joint probability density function (PDF) for one-step prediction and measure likelihood, then the MNIW mixture distribution is decomposed into a Gaussian hierarchy, and finally the posterior estimates of the state and variables are obtained using variational Bayesian technique. In this paper, a Multi-Normal-Inverse Wishart mixture distributionbased variational Bayesian extended Kalman filter (VB-EKF) is proposed, in which a first-order Taylor expansion is used to address the non-linear problem. The proposed filter can be used to address nonlinear filtering problem with inaccurate noise covariance matrices and measurement bias. Simulations of spacecraft autonomous celestial navigation validate the effectiveness and superiority of the proposed filter.

An adaptive learning pigeon-inspired optimization based on mutation disturbance (ALPIO) is proposed for solving the problems of fuel consumption and threat avoidance in spacecraft cluster orbit reconstruction. First, considering the constraints of maintaining a safe distance between adjacent spacecraft within the spacecraft cluster and of avoiding space debris, the optimal performance index for orbital reconfiguration is proposed based on the fuel consumption required for path planning. Second, ALPIO is proposed to solve the path planning. Compared with traditional pigeon-inspired optimization, ALPIO uses the initialization of chaotic and elite backward learning to increase the population diversity, using a nonlinear weighting factor and adjustment factor to control the speed and accuracy of prepopulation convergence. The Cauchy mutation was implemented in the map and compass operator to prevent the population from falling into local optima, and the Gaussian mutation and variation factor were utilized in the landmark operator to prevent the population from stagnating in the late evolution. Through simulation experiments using nine test functions, ALPIO is shown to significantly improve accuracy when obtaining the optimum compared with PSO, PIO, and CGAPIO, and orbital reconfiguration consumes less total fuel. The trajectory of path planning for ALPIO is smoother than those of other optimization methods, and its obstacle avoidance path is the most stable.

针对特定区域覆盖并密集重访的卫星星座优化设计问题,采用回归轨道和共星下点轨迹星座的设计方案,提出特定区域内重点地区权值排序覆盖并融合遗传蚁群算法优化求解卫星星座轨道参数的方法.分析区域覆盖星座的设计需求,建立回归轨道覆盖区域模型,利用遗传蚁群算法计算出最优轨道根数,使用共星下点轨迹星座求解算法求出所有星座参数.仿真实验结果表明优化设计的星座满足对于区域目标的覆盖时间和重访次数需求,并对重要地点按照权值排序进行了侧重性覆盖和重访,验证了算法的可行性.

Existing robust filters under generalized nonstationary noises conditions are difficult to choose suitable prior parameters, this brief proposed a Pearson-type VII distribution with adaptive parameters selection based interacting multiple model (IMM) Kalman filter (IMMPVII KF). In the model conditional filtering process, both the one-step prediction and the measurement likelihood are modeled as Pearson-type VII distributions. They are decomposed into Gaussian-Gamma Hierarchies (GGH), which are then matched to the time-varying heavy-tailed properties of the noises by pre-selecting the sets of shape and rate parameters and the variational Bayesian (VB) technique. Finally, a new model probability update method for filter under non-Gaussian conditions is derived. Simulation results show that the filter proposed in this brief has better robustness and adaptability to generalized non-stationary noises than the existing filters.

The design of formation configuration is a key issue for SAR satellite formation flight control, which determines the baseline direction and length of SAR satellite formation system, and the direction and length of baseline will directly affect the earth observation performance of the system. According to the GMTI mission requirements of SAR satellite formation system in low earth orbit, based on the relative motion model of relative E/I vector, this paper takes the measurable speed ratio and time effective ratio of ground moving target detection as the joint optimization objective function, establishes the relationship between the objective function and the satellite formation mixed baseline vector, and optimizes the two configurations of along-track formation and space elliptical formation through genetic algorithm. The simulation results show that it can meet the basic requirements of GMTI mission of SAR satellite formation.

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope (CMG) is employed to provide a strong moment. However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated. When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

Estimating noise covariance matrices and suppressing outliers simultaneously is a huge challenge because they are coupled. In order to solve the nonlinear filtering problem with unknown non-Gaussian noise, the maximum correntropy criterion (MCC) is used to suppress the outliers, while the variational Bayesian (VB) technique is used to estimate the one-step prediction error covariance matrix (PECM) and the measurement noise covariance matrix (MNCM), and the nonlinear problem is solved by the third-order spherical radial cubature rule. In this paper, nominal measurement is constructed to eliminate the influence of outliers on the recursive estimation of MNCM. Through these operations, the variational Bayesian and maximum correntropy based cubature Kalman filter (VBMCCKF) and the maximum correntropy cubature Kalman filter (MCCKF) are derived. The interacting multiple model (IMM) fusion framework is used to promote the collaborative work of VBMCCKF and MCCKF, thus a novel filter is proposed in this paper. The simulation verifies the validity and universal applicability of the proposed filter. The estimation error of the proposed filter in spacecraft autonomous celestial navigation is about 30% less than that of the existing filter with the best performance.

As an emerging form of combat, UAV swarm operations are an important part of future systematic operations. In order to carry out mathematical modeling and effectiveness evaluation of the UAV swarm combat mode, the main indicators and factors affecting the UAV swarm combat effectiveness were analyzed through the OODA combat loop. The relevant indicators are identified, the weight of the indicators is determined by the AHP method, and the final evaluation value of the UAV swarm combat effectiveness is obtained by the comprehensive evaluation method of AHP-FCE. The results show that this method can reasonably reflect the characteristics of UAV swarm combat, effectively evaluate the combat effectiveness of UAV swarms, and provide a theoretical reference for the subsequent evaluation of UAV swarm combat effectiveness.

A multi-satellite co-tracking method for a single non-cooperative target is proposed to extend the arc of observation as well as to improve the accuracy of tracking. Firstly, the motion of the target is considered to be affected by J2 perturbation, and the model of multi-satellite co-tracking a single space target is designed with only measured angles. Then, a multi-satellite co-tracking method for a single space target based on an adaptive distributed spherical simplex information-weighted consensus filter (ADSSICF) is proposed. The spherical simplex is used to reduce the computational cost of the information filter, and to improve the efficiency of tracking. The angle-only measurement equation is linearized by the statistical linear regression method, and linearization errors are compensated for by updating measurement noise. By designing an adaptive consensus algorithm, only a small number of iterations are needed to achieve network consensus, to improve the convergence speed of the consensus algorithm, and prove the stability of ADSSICF. Finally, a simulation of four low-orbit satellites tracking a single space target is established. The focus of this paper is on the real-time performance and tracking accuracy of the multi-satellite co-tracking a single space target with angle-only based on ADSSICF. The performance of ADSSICF is verified from three indicators: the consensus and convergence of algorithm, the accuracy of state estimation.