The digital twin is becoming the most promising emerging technology in the field of unmanned combat and has the potential to innovate future combat styles. Online battlefield learning is one of the key technologies for supporting the successful application of digital twin in unmanned combat. Since there is an urgent need for effective algorithms for online learning the battlefield states in real time, a new random finite set- (RFS-) based algorithm is proposed in the presence of detection uncertainty including clutters, missed detection, and noises. The system architecture and operational mode for implementing the digital twin-enabled online battlefield learning are provided. The unmanned ground vehicle (UGV) is employed as the experimental subject for systematically describing the proposed algorithm. The system architecture for implementing the digital twin-enabled online battlefield learning is firstly given, and its operational mode is also described in detail. The RFS-based digital twin models including the battlefield state model, UGV motion model, and sensor model are designed. The Bayesian inference is adopted, and the probability hypothesis density (PHD) filter is modified to implement the online learning process. At last, a group of experiments are conducted to verify the performance and effectiveness of the proposed algorithm. The research work in this paper will provide a good demonstration of the application of digital twin in unmanned combat.

The adoption of unmanned vehicles brings both great autonomy and new technical challenges to modern warfare. Unmanned vehicles such as unmanned ground vehicles (UGVs) hold great promise for future combat operations and have already been used in several recent military conflicts in Syria and Afghanistan [

Due to the data separation between the real battlefield and its models, it is difficult to achieve the automatic flow of information in a closed loop. Digital twin provides a new and effective way to solve this problem. It can enable the real-time bidirectional interoperability between the real world and virtual simulation space and is also an effective way to enable efficient real-time data sharing throughout the entire operational process including intelligent monitoring, prediction, digital representation, evaluation, decision support, and battlefield learning [

Battlefield refers to the environment constituted by all the objective factors in the battlespace except the combatants and weapons. All kinds of combat operations are inseparable from the specific battlefield. Battlefield has an important influence on the course and outcomes of combat operations. Combat entities can receive inputs from and provide outputs to the battlefield. The combat intention of the combat entity is realized through its interaction with the battlefield.

Battlefield learning means sensing the entities on the battlefield rapidly, understanding the current situation comprehensively, and predicting future status accurately before decision-making [

Based on the classical definition of battlefield learning, online battlefield learning is the process of perceiving an existing battlefield and anticipating how it may evolve in the future. It is useful for obtaining knowledge of the previously unknown battlefield while the real combat process is proceeding simultaneously [

In the military simulation, computer-generated force (CGF) is the virtual combat force object which is created by a computer and can control or guide all or part of its action and behavior [

In recent years, the digital twin has become a hot topic, as well as the representative intelligence in all fields from military to people’s livelihood [

In this paper, we focus on learning the battlefield states that consist of significant environmental cues and the UGV states. In order to explore how to implement the digital twin-enabled online battlefield learning, we propose a random finite set- (RFS-) based algorithm which can support real-time interaction, as well as the deep integration and mutually beneficial symbiosis between the virtual and real battlefield. It is the necessary foundation for the successful application of the digital twin in unmanned combat. Our main contribution is designing and implementing a new online battlefield learning algorithm by using the RFS-based Bayesian theory and modifying the probability hypothesis density (PHD) filter [

The rest of the paper is structured as follows. A literature review on the recent digital twin and random finite set (RFS) is given in Section

The digital twin has important research and application value in every stage of online battlefield learning. In the design and demonstration stage, the digital twin can help to improve the evaluation capability of system performance by enabling the equal two-way interaction between the simulation system and the real system. Through the semiphysical simulation, digital twin enhances the ability to quickly locate the design defect, optimize system design, and test the practicability of an online battlefield learning algorithm in execution.

In order to apply the digital twin-enabled online battlefield learning in the operation stage, it is important to realize the bidirectional interaction between the simulation space and the real space. Tao gives the five-dimensional structure models of digital twin and presents six application principles [

Online battlefield learning needs autonomy in the operation stage. A decentralized multiagent system is also a new approach for implementing online battlefield learning, such as blockchain and CGF. Some researchers have discussed how to use blockchain to overcome the cybersecurity barriers for achieving intelligence in Industry 4.0 and introduced eight cybersecurity issues in manufacturing systems. Some researchers have surveyed the ability of blockchain for overcoming the barriers and examined the literature on the manufacturing system perspective and the product lifecycle management perspective. Ali et al. provided a survey of all aspects of multiagent systems, starting from definitions, features, applications, challenges, and communications to evaluation. They also gave a classification on multiagent system applications and challenges along with references for further studies [

RFS provides a novel unified probabilistic way for fusing real-time battlefield data [

With the rapid development of emerging information technologies, such as artificial intelligence (AI), cloud computing, edge computing, digital twin, and Internet of Things (IoT), the combat style has also been undergoing profound changes. New information technologies have facilitated the birth, development, and application of unmanned combat. Just as it is shown in Figure

The relationship between new information technologies and unmanned combat.

The operational mode of the digital twin-enhanced online battlefield learning consists of five elements, i.e., computing services, physical entities, simulation models, connected data, and the connection between them. As shown in Figure

The operational mode of digital twin-enabled online battlefield learning in unmanned combat.

The battlefield considered in this paper consists of all the significant environmental cues and the states of UGVs. Since GPS and topographic map in actual combat are most likely be disabled, location and mapping for unmanned vehicles can only be obtained with the help of the equipped sensors. The RFS-based online battlefield learning algorithm plays a central role in the virtual space. It provides simulated battlefield information to the decision support system to train the deep learning network system. It can also generate real-time battlefield information to the unmanned combat simulation system and helps to evaluate the possible outputs of available COAs.

For combat simulation, the battlefield provides spatial-temporal constraints for all participating actors. The simulated combat objects are deployed and controlled in the virtual space. They learn the battlefield that consists of other combat objects and significant environmental cues by using the proposed algorithm. The combat simulation system in the virtual space is used as a decision-making aid tool that assists the commanders to evaluate all the available COAs. It is in charge of choosing the optimal COA. The proposed online battlefield learning algorithm aims at analyzing and understanding operational activity in the real space at a given time. It can help to make the right decision and predict the future situation. It is the key technology for enabling and implementing digital twin-enabled online battlefield learning in unmanned combat.

Corresponding to the operational mode, the system architecture of digital twin-enabled online battlefield learning in unmanned combat is shown in Figure

The system architecture of digital twin-enabled unmanned combat simulation.

The digital twin-enabled battlefield modeling consists of three aspects. The first one is modeling the battlefield states including cues (or landmarks). The second one is modeling the UGV movement. The third one is modeling the sensors equipped on the UGV. In order to overcome the data association uncertainty problem under high clutters and measurement noises, the RFS-based modeling method is employed to fully integrate data association uncertainty into battlefield learning. The key of the proposed algorithm is to represent the battlefield states by using RFS. The derivation of the simulation models depends on RFS. RFS is the theory proposed by Mahler for implementing RFS in engineering applications [

The vector-based representation of the battlefield has been demonstrated to have some mathematical consequences, such as the ordering of significant environmental cues, data association problems, and element management problems. In addition, for the dynamic random scene, how to quantify the errors of the learned results generated by the vector-based Bayesian inference is also a great challenge. The abovementioned problems are usually solved by augmenting or truncating vectors outside of the Bayesian inference process. This will lead to the problem that the Bayesian optimality can only be achieved on the subset of the battlefield that is defined in advance. In this section, we give the RFS-based models which can solve these problems systematically.

The difficulty of RFS-based Bayesian inference is its computational complexity. To solve this problem, Mahler proposed the PHD (probability hypothesis density) filter. The PHD of the posterior probability density

Here,

We adopt the RFS-based battlefield representation; here,

Here,

The location of UGV can be represented by the state vector

In this paper, the specific mathematical expression of

Here,

Given the current UGV state RFS

Here, _{k}.

The detection RFS

Depending on

Here,

In this paper, the range and bearing sensor is used. The detection generated by the two-dimensional environmental cues at location

Here,

In this section, we give the basic principles, design, and implementation of the proposed algorithm. The process of the proposed algorithm relies on sequentially propagating the joint posterior probability density of the RFS-based battlefield and the UGV state as detection arrives.

With the RFS-based battlefield modeling, the RFS-based Bayesian inference is used to jointly learn the environmental cues’ locations and UGV state at every time step. The battlefield RFS can be characterized as follows:

In this paper, we use

Predict the battlefield state by using the previous battlefield states and input parameters:

Update the battlefield state depending on the received detection RFS

Here,

In this paper, the PHD filter is employed to implement the RFS-based Bayesian recursion [

The online battlefield learning process based on Gaussian mixture-based PHD filter.

The main challenge of online battlefield learning is how to learn the number and location of environmental cues while estimating the UGV state at the same time. In this paper, we partition the battlefield state into two kinds:

Here, the Gaussian mixture PHD filter is applied to propagate each PHD that depends on the UGV state. The location of environmental cues in the battlefield is characterized by the Gaussian components of the mixture, and the number of cues in the battlefield is characterized by masses of all the Gaussian components. In this paper, the PHD at time

In this paper,

Here,

The components of equation (

Here,

We assume that the number of clutters in

The posterior UGV state

The weights should be normalized as

By assuming that there is only one environmental cue

Here,

According to the learning process given above, we give the concrete realization method of the proposed algorithm in this section. We use C++ to write the experimental program for this algorithm. The C++ library dependencies such as Eigen (version 3.0.0), Boost (version 1.5.3), and gtest are also used. In order to detail the implementation of the proposed algorithm, the flow diagram of the proposed algorithm is presented in Figure

The flow diagram of the RFS-based online battlefield learning algorithm.

The computational complexity of the proposed algorithm is

for

Generate the particles for the UGV state,

Get predicted battlefield PHD through the predict step of PHD filter;

Get updated battlefield PHD through the update step of PHD filter;

Get predicted PHD mass

Get updated PHD mass

Select a given battlefield state

Get updated UGV state weight

end for

Initialize the learned battlefield state

Determine the maximum weight component

Update UGV state with

Update battlefield state according to the related PHD:

for

if

Generate new battlefield state by

end if

end for

Return

In this section, a group of experiments are conducted to quantitatively verify the effectiveness and analyze the performance of the proposed algorithm. The virtual machine we used to run our experiments has 4 G of RAM and 6 3.40 GHz Intel CPUs and runs on Unbuntu 14.04 OS. The experimental data used to support the findings of this study are included within the article. The parameters used in this experiment are given in Section

As shown in Figure

The real and learned battlefield states.

Partial experimental parameters.

Parameter | Velocity input std. (m/s) | Steering input std. (deg) | Detection probability | Clutter rate | Particle number | Landmark existence threshold |
---|---|---|---|---|---|---|

Value | 2 | 2 | 0.90 | 0.0001 | 100 | 0.5 |

The sensor used in this experiment is the range-bearing sensor that can detect landmarks with distances of 5 m to 30 m in any direction. The range measurement standard deviation (std) is 1 m and the bearing measurement std is 2 deg. The maximum FoV of the sensor used by the UGV is 10 m and 360 deg.

The experimental results are shown in Figure

In order to quantitatively evaluate the performance of the proposed algorithm, we give the errors of the learned battlefield states in Figures

The errors of the learned number and locations of landmarks. (a) The learned and observed number of landmarks. (b) The OSPA errors of the learned landmarks.

The errors of the learned UGV states. (a) Euclidean errors of the learned UGV states. (b) Orientation errors of the learned UGV states.

Consider two sets

The errors of learned UGV states are shown in Figures

In order to analyze how detection parameters affect the proposed algorithm, the averaged errors of the UGV states and landmarks are generated with different probabilities of detection _{D} decreases. The increase of

The performance for varying values of probability of detection and clutter intensity. (a) Averaged errors for the learned UGV states. (b) Averaged COLA errors for learned landmarks.

In order to apply the proposed algorithm in real unmanned combat applications, the time cost should be fully evaluated. As shown in Figure

Time cost for varying values of detection probability and clutter intensity. (a) Averaged time cost of the algorithm. (b) Averaged time cost of CPU while the algorithm running.

Digital twin technology enables real-time dynamic interaction between the real battlefield and the simulation system. Our main contribution is proposing a new online battlefield learning algorithm based on RFS to enable the application of the digital twin in unmanned combat. The digital twin has a broad application prospect in unmanned combat and greatly promotes the innovation of unmanned combat mode. Since the implementation of the digital twin in unmanned combat depends on battlefield understanding, an effective battlefield learning algorithm is quite important. By adopting the RFS-based representation of the battlefield, the proposed algorithm can overcome the limitations of the traditional vector-based representation. The performance of the proposed algorithm is verified by using two groups of experiments. This paper is the first attempt for applying the digital twin to the unmanned combat area and has practical significance for implementing the digital twin in many other areas.

Computer-generated force

Courses of action

Cardinalized optimal linear assignment

Extended Kalman filter

Field of view

Internet of things

Optimal subpattern assignment

Probability hypothesis density

Random finite set

Unmanned ground vehicle.

The experimental data used to support the findings of this study are included within the article.

The authors declare no conflicts of interest.

Peng Wang conceived, designed, and performed the simulations and wrote the manuscript. Jiancheng Zhu and Yong Peng provided the basic ideas and analyzed the experimental results. Mei Yang helped to perform the experiments. Ge Li and Yong Peng reviewed the manuscript.

The authors would like to acknowledge the support of the Young Elite Scientists Sponsorship Program of China Association of Science and Technology.