The establishment of a digital parallel battlefield that integrates the functions of "research, combat, testing, practical operation, and training" serves as an effective and essential supporting measure for enhancing combat command and joint training capabilities, which address future intelligent high-end warfare among major powers. In the air defense and anti-missile realm, constructing a digital parallel battlefield faces several formidable challenges, including configuring complex scenarios, facilitating interactions between virtual and real forces, and simulating combat behaviours. To tackle these issues, the paper employed a digital twin modelling approach grounded in Model-Based Systems Engineering (MBSE) to enable the precise configuration of complex scenarios. Based on the Live-Virtual-Constructive (LVC) concept, a distributed simulation architecture combining virtual and real elements was established to realise seamless virtual-real interactions and efficient coordination. In addition, an Agent modelling methodology based on data/rules dual-driven was introduced to simulate intelligent combat behaviours in air defense and anti-missile operations. A multi-branch simulation deduction and auxiliary decision-making framework tailored for the parallel battlefield was constructed, achieving the organic integration of situation analysis, plan formulation, and evaluation for optimal selection. The system development was accomplished by applying the software-defined method, enabling dynamic scheduling of system resources, flexible reconfiguration, and agile deployment. The research results indicate that the newly developed digital-intelligent parallel battlefield for air defense and anti-missile, constructed by the concept of the digital twin, provides robust support for simulation applications across multiple scenarios, including equipment testing, combat experiments, joint training, and command decision-making within the domain of air defense and anti-missile.

The digital parallel battlefield represents a precise mapping from the physical to the digital space, transcending the traditional capability boundaries of simulation and facilitating cross-domain, cross-level, and more efficient applications. Based on the critical requirements for building the digital parallel battlefield, this paper studied overseas and domestic research status. Through comparative analysis of the gaps between current capabilities and actual needs, the paper deeply analysed the current challenges' root causes, which were characterised by “diverse constructions, difficult sharing, and high costs”. In addition, several key technologies were discussed in detail, including the overall architectural design, the multi-branch quick deduction, the counter-design of the blue team with game strategy, the integration of virtual-real parallel systems, the experiment design and comprehensive evaluation, etc. Finally, the paper proposed recommendations for future practical explorations, emphasising directions including “physical-digital synergy, co-evolution, collaborative operations, and sustainable development”.

Parallel simulation enables rapid prediction, decision support, and performance evaluation of future evolution via creating a simulation mirror system parallel to the exact system. However, parallel simulation faces challenges such as large scale, complex virtual and real interaction, and multi-level resolution model fusion, which affect its credibility evaluation. This paper discussed the challenges faced by the credibility evaluation of parallel simulation systems and provided recommendations, in order to provide ideas for researching and applying credible evaluations of parallel simulations.

With the rapid development of information technology, modern warfare is transforming towards digitalisation, networking, and intelligence. As an advanced stage of the digital battlefield, the digital parallel battlefield leverages physical and virtual systems integration to provide innovative solutions for situational awareness, element coordination, and decision optimisation. This paper systematically reviewed the latest research on the digital parallel battlefield, analysing its theoretical foundations, military value, technical architecture, and practical applications. Key challenges within the field were identified, and future development trends were explored. The study highlighted the significant role of the digital parallel battlefield in enhancing joint operational capabilities, optimising command and control efficiency, and innovating military training models. In addition, challenges such as a lack of unified theoretical frameworks, delayed technical standards, and insufficient cross-domain coordination were given. In conclusion, with the continuous integration of artificial intelligence, big data, and other emerging technologies, the digital parallel battlefield will achieve broader applications in intelligence, collaboration, and service-oriented development.

Focusing on the problems existing in the traditional behaviour tree in multi-aircraft air combat cooperative decision modelling, such as the syntax structure being too flexible, lack of a standardised model, and in sufficient communication cooperative simulation support, this paper proposed a customised communication behaviour tree method for multi-aircraft air combat cooperative decision modelling. The tailored design of generic communication action nodes and communication coordination subtree provided the corresponding customised behaviour tree code framework, allowing the user to quickly standardise and implement the dual aircraft air combat coordination strategy's behaviour tree representation. The experiments based on a typical combat simulation and rehearsal platform show that compared with the classical strategy provided by the platform, the proposed method is highly readable, acquires better combat effectiveness and scalability, and improves the efficiency and fidelity of modelling multi-aircraft air combat cooperative decision-making.

In air combat decision-making, effectively identifying the key states and improving the decision-making ability of intelligent bodies in these states is the key research direction of reinforcement learning algorithms. In this paper, a dynamic strategy switching framework built by deep reinforcement learning was proposed for the intelligent body problem in air combat decision-making, aiming at increasing the decision-making quality of the intelligent body in the complex environment. This study identified critical states using dimensionality reduction and classification of high-dimensional state space through representation learning and cluster analysis techniques in the non-critical state, a deep reinforcement learning algorithm was employed for decision-making; in the critical state, an inverse dynamics model was adopted to generates the target state's corresponding action sequence and a parallel simulation strategy was utilized to execute the action sequence in multiple simulation environments to approximate the target state rapidly. At the end of the simulation, the optimal decision path was determined by advantage value evaluation. The experimental results show that the method can improve the decision-making ability of the intelligent body in critical states, providing a new solution for intelligent decision-making in complex air combat environments.

To overcome the challenges faced in simulation assessment, such as the intense subjectivity of assessment results, the lack of assessment analysis in simulation model resources, the difficulty in implementing traditional confidence verification steps for simulation models, and the difficulty in quantifying assessment indicators, a set of verification and validation and accreditation(VV&A) methods for simulation models based on mixed data from internal and external fields was proposed in this paper. The proposed method had the advantages of strong operability and quantifiability. By dividing the assessment object into different functional modules, using internal and external field test data to verify the simulation model, and conducting an assessment from the perspective of model data sources and modelling methods, experts were organised to review and confirm the confidence assessment process and report, which ultimately presenting a quantified confidence assessment result of the simulation model.

Urban combat is a focal point in intelligent warfare, and constructing high-fidelity 3D models of battlefield environments is critical for enhancing situational awareness. Traditional modelling methods face challenges, including oblique photogrammetry, low reconstruction efficiency and stringent data acquisition requirements. This paper studied the theory and application of 3D Gaussian splash technology using the 3D modelling of the urban combat environment. It outlined two technical concepts for multi-source heterogeneous data integration and object-oriented modelling employing 3DGS as future research directions. First, sparse point clouds were initialised via Structure from Motion (SfM) technology, combined with Gaussian Splatting to optimise scene representation, enabling high-precision point cloud rendering. Second, the proposed method was compared with traditional oblique photogrammetry to validate its advantages in modelling efficiency, memory utilisation, and lighting simulation capabilities. Finally, two technical frameworks were introduced: a multi-source heterogeneous data fusion scheme and a building-and-vegetation object-oriented modelling approach, giving novel solutions for 3D modelling in urban combat environments.

The drone swarm confrontation is built based on the OODA decision loop and employs multi-agent deep reinforcement learning for algorithm design to find the optimal collaborative defence strategy for drone swarm. Specifically, a QMIX-based single-layer decision algorithm is developed to tackle contribution allocation and high-dimensional space challenges in drone cooperation. In this paper, a hierarchical decision-making model integrating rule-based methods and reinforcement learning was proposed. This model first adopted a decision layer with rule-based or HMM intention recognition to analyze combat scenarios and schedule drones, followed by an action layer utilizing the QMIX algorithm to output actions. To verify the performance of the proposed algorithms, this study established a controllable and observable simulation platform using Python and Unity and produced a challenging defensive game problem. Experiments quantitatively evaluated defence strategies in perspectives of cooperation effectiveness, resource efficiency, and generalisation. The results show that each index of hierarchical decision-making is significantly better than that of single-layer decision making, and the winning rate has been dramatically improved. The HMM-based hierarchical strategy shows the best performance, offering a promising new approach to drone swarm defence.

To solve the resource optimisation problem in the modular design of complex systems, a hybrid optimisation method combining fuzzy C-means clustering, genetic algorithm, simulated annealing, and immune selection mechanism was proposed in this study. This method first used the fuzzy C-means clustering algorithm to analyse the correlation between component functional structures, generating initial module partitions. Then, it optimised the module partitions using an improved genetic algorithm. The integration of simulated annealing significantly enhanced the local search ability of the algorithm. At the same time, the immune selection mechanism maintained population diversity through operations including elite retention, gene exchange, and insertion mutation, further improving the algorithm's global search ability and stability. The results show that the proposed method significantly optimises the cohesion and coupling of modules and can effectively improve the quality and efficiency of modular design. In addition, the process presents an ideal balance between calculation speed and optimisation accuracy, which is particularly suitable for industrial scenarios having high requirements for independence, scalability and cost control.

This paper proposed a cooperative deployment algorithm for naval fleet detection nodes based on constrained reinforcement learning to address the coordinated deployment of detection nodes in naval fleet formations. First, the method of dividing grids with regular hexagons was employed to design the grid. The battlefield space was modelled based on the battlefield space feature expression optimisation model of the graph neural network. Then, taking the formation's overall detection range and interception depth as the main optimisation objectives and considering constraints such as formation combat damage, deployment formation, ship orientation, and communication range, an intelligent agent model for the collaborative deployment of detection nodes was produced. Finally, the collaboration deployment intelligent agent model is trained in the air defense combat scenario of the US naval vessel formation. The simulation results show that the fleet deployment positions are optimized by the cooperative deployment algorithm proposed in this paper and the overall interception effectiveness of the fleet is improved by 13.1%.

This paper proposed a Mercator transformation-based planning method for the online trajectory planning of cruise vehicles subject to no-fly zone constraints. By directly incorporating the planned trajectory's heading angle variation into the planning plane's higher-order derivatives, this approach explicitly characterised the energy expenditure of the trajectory without introducing dynamic constraints. The proposed method leverages quadratic programming (QP) optimisation properties to improve efficiency. It formulated the online trajectory planning problem under the QP framework, simultaneously addressing energy consumption and no-fly zone constraints. This formulation significantly enhanced computational efficiency and solution optimality. Simulation results demonstrate that the method can efficiently generate smooth, energy-efficient, and conveniently trackable trajectories while strictly complying with no-fly zone restrictions, achieving effective online trajectory planning for cruise vehicles.

Target state estimation is a key problem of collaborative detection. Traditional model-based state estimation algorithms perform poorly under partially known state-space models. In contrast, existing neural network-based state estimation algorithms have low interpretability, making it difficult for them to effectively apply in real-world scenarios (e.g., collaborative detection). This paper proposed a highly interpretable neural network-based state estimation and fusion framework to address the above problems. First, a Kalman filter neural network model was employed to obtain high interpretability by approximating the model-based state estimation algorithm. Second, a learnable weighted robust fusion framework was introduced to improve the fusion accuracy under partially known state space models. Experimental results show that the proposed method performs high target state estimation accuracy and robustness in simulation environments and real datasets, significantly outperforming traditional methods.

The trajectory of hypersonic vehicles during unpowered high-speed gliding flight within the atmosphere is a complex nonlinear multi-constraint optimisation problem. To address trajectory optimisation under different objective functions for the unpowered gliding phase of hypersonic vehicles, the dynamics equations for the gliding phase were established, simplified, and improved in this study. A trajectory optimisation method based on the hp-adaptive Chebyshev pseudo-spectral method was employed, and the analytical gradients of the objective functions in numerical form were derived. The trajectory optimisation problems for minimum flight time and minminm heat generation under specified conditions were solved. The results demonstrate that this method can solve trajectory optimisation problems for hypersonic vehicles with high computational accuracy. Besides, the correctness of the provided gradient calculation formulas was verified in this study, which could improve the computational efficiency of the algorithm to a certain extent.

An illuminator resource scheduling method based on tabu search was proposed to solve the illuminator resource scheduling problem to illuminate targets intercepted by semi-active guided missiles after completing the allocation of missile firepower to incoming targets by naval formations at sea. This paper addressed the naval air and missile defence scenario. First, a mathematical model was built for task group illuminator resource allocation based on missile firepower scheduling and the available illuminator resources of the fleet. Then, a collaborative illuminator strategy was introduced within the framework of a tabu search algorithm, where the tabu list was used to improve the efficiency of the objective function's solution. After that, different-scale simulation scenarios of naval task group air and missile defence operations were set up. Finally, experiments were conducted to validate the effectiveness of the proposed method.