In recent years, unmanned aerial vehicle (UAV) technology has advanced rapidly, leading to widespread applications in civilian domains such as disaster rescue, aerial photography, and environmental monitoring, as well as in military operations including reconnaissance, precision strikes, and missile interception. However, the misuse of UAVs poses significant threats, including terrorist attacks, disruptions to aviation safety from unauthorized flights, and illicit surveillance by large military drones. These concerns have spurred global interest in developing effective countermeasures, making anti-UAV systems a critical area of research. Current anti-UAV methods encompass diverse technical approaches, such as radio frequency jamming, GPS spoofing, microwave interference, laser-based directed energy attacks, and kinetic strikes using projectiles. Each method relies on distinct technological frameworks, resulting in a variety of anti-UAV equipment. In complex battlefield environments, the threat level posed by UAVs can change dynamically, necessitating the selection of appropriate countermeasures based on mission objectives and requirements. Relying solely on a single anti-UAV approach may lead to resource inefficiency or inadequate response, undermining overall operational effectiveness. Moreover, the combination of multiple combat scenarios and weapon systems presents challenges for command decision-making, highlighting the importance of rapidly identifying optimal disposal strategies. Existing decision-making methods for anti-UAV operations have been explored through fuzzy mathematics, case-based matching, genetic algorithms, dynamic programming, and association rules. From a systemic combat perspective, a layered approach integrating soft-kill and hard-kill measures, with coordinated deployment of various anti-UAV assets, is essential to leverage the technical advantages of different systems. This study focuses on UAV threats involving close-range reconnaissance and attacks on specific guarded areas. By analyzing the threat态势 posed by combinations of UAV behavioral states and the applicability of different disposal methods, we construct a decision-making model for anti-UAV operations based on dynamic Bayesian networks (DBNs). This model aims to effectively support command personnel in the decision-making process by considering the probabilistic characteristics of multiple UAV state factors and their temporal evolution, thereby inferring the likelihood of various disposal actions.
The core of our approach lies in probabilistic reasoning, which allows for handling uncertainty in dynamic threat environments. Bayesian methods form the foundation, where prior knowledge and conditional probabilities are used to update beliefs about events. Formally, if a set of events \(B_1, B_2, \ldots\) satisfies the following conditions:
$$B_i \cap B_j = \emptyset \quad \text{for} \quad i \neq j,$$
$$\bigcup_{i=1}^{\infty} B_i = \Omega, \quad \text{with} \quad P(B_i) > 0 \quad \text{for} \quad i=1,2,\ldots,$$
then for any event \(A\) with \(P(A) > 0\), Bayes’ theorem states:
$$P(B_i | A) = \frac{P(B_i) P(A | B_i)}{\sum_{j=1}^{\infty} P(B_j) P(A | B_j)}.$$
When there are \(n\) events \(B_i\), the denominator sums over \(n\) terms. Building on this, Bayesian networks (BNs) are probabilistic graphical models that represent random variables as nodes and their conditional dependencies as directed edges in an acyclic graph. Conditional probability tables (CPTs) quantify these dependencies, enabling inference under uncertainty. For anti-UAV decision-making, static BNs may fall short in capturing temporal dynamics, which is where dynamic Bayesian networks (DBNs) extend the framework by incorporating time slices. A DBN models sequences of observations over time, enhancing the rationality and accuracy of reasoning by accounting for inter-factor relationships across time steps. The inference in a DBN can be expressed as follows for hidden nodes \(x\) and observed nodes \(y\) over time slices \(h = 1, 2, \ldots, w\):
$$P\left(x_{11}, x_{12}, \ldots, x_{1n}, y_{11}, y_{12}, \ldots, y_{1m} \mid x_{w1}, x_{w2}, \ldots, x_{wn}, y_{w1}, y_{w2}, \ldots, y_{wm}\right) = \frac{\prod_{h} \prod_{l} P(x_{hl} \mid \text{pa}(x_{hl})) \prod_{q} P(y_{hq} \mid \text{pa}(y_{hq}))}{\sum \prod_{h} \prod_{l} P(x_{hl} \mid \text{pa}(x_{hl})) \prod_{q} P(y_{hq} \mid \text{pa}(y_{hq}))},$$
where \(\text{pa}(\cdot)\) denotes the parent nodes, \(l = 1,2,\ldots,n\), \(q = 1,2,\ldots,m\), and the summation is over all possible hidden states. This formulation allows for updating beliefs as new observations arrive, which is crucial for real-time anti-UAV operations.
To apply DBNs to anti-UAV disposal decision-making, we first identify the key factors influencing the threat posed by UAVs. Based on analysis of UAV behavior and operational contexts, we select five observable factors: UAV action, UAV speed, dangerous payload carriage, UAV quantity, and UAV distance from the protected area. These factors collectively determine the threat level and guide the choice of disposal methods. The disposal process is divided into discrete time slices, each representing a decision point. Our DBN model, as illustrated below, incorporates seven nodes per time slice: five observation nodes corresponding to the UAV factors, one decision node for the anti-UAV weapon disposal method, and inter-slice dependencies to capture temporal evolution. The model structure ensures that decisions at time \(T(n-1)\) influence those at \(T(n)\) through a state transition probability matrix, while current observations at \(T(n)\) jointly compute the probability distribution for the disposal decision.
The variables and their state sets are defined as follows:
| Variable | State Set |
|---|---|
| UAV Action (Behave) | {Away, Hover, Circle, Access} |
| UAV Quantity (Number) | {Small (n < 3), Middle1 (3 ≤ n ≤ 10), Large (n > 10)} |
| UAV Distance (Distance) | {Outer (inner警戒区), Middle2 (middle警戒区), Inner (outer警戒区)} |
| Dangerous Payload (Load) | {Loaded, Unloaded} |
| UAV Speed (Velocity) | {High, Low} |
| Weapon Disposal (Disposal) | {Alert, Disturb, Directed Energy (DE), Fire Strike (FS)} |
Note: The distance states are defined relative to the protected area, with “Inner” being closest and “Outer” farthest, reflecting layered defense zones. In anti-UAV operations, these factors are monitored continuously to assess threat escalation.
To operationalize the DBN model, we must specify the prior probabilities and conditional probabilities. Through analysis of historical data and expert elicitation, we derive the state transition probabilities for disposal decisions across time slices, as shown in Table 1. This matrix encapsulates how the choice of anti-UAV action evolves based on previous decisions, reflecting the persistence or escalation of responses. Additionally, we define the conditional probabilities for each observation node given the disposal decision state, presented in Table 2. These probabilities quantify the likelihood of observing specific UAV behaviors under different disposal scenarios, aiding in threat inference. While these values incorporate some subjectivity, they are grounded in experimental data and domain knowledge, and can be refined with more实战 data to improve accuracy for robust anti-UAV applications.
| \(T(n+1) \backslash T(n)\) | Alert | Disturb | Directed Energy (DE) | Fire Strike (FS) |
|---|---|---|---|---|
| Alert | 0.65 | 0.2 | 0.1 | 0.05 |
| Disturb | 0.2 | 0.45 | 0.25 | 0.1 |
| Directed Energy (DE) | 0.1 | 0.2 | 0.4 | 0.3 |
| Fire Strike (FS) | 0.05 | 0.15 | 0.3 | 0.5 |
| Disposal Decision | UAV Action Probabilities | UAV Quantity Probabilities | |||||
|---|---|---|---|---|---|---|---|
| Away | Hover | Circle | Access | Small (n<3) | Middle1 (3≤n≤10) | Large (n>10) | |
| Alert | 0.15 | 0.4 | 0.4 | 0.05 | 0.7 | 0.2 | 0.1 |
| Disturb | 0.08 | 0.35 | 0.35 | 0.22 | 0.3 | 0.5 | 0.2 |
| Directed Energy (DE) | 0.06 | 0.17 | 0.17 | 0.6 | 0.1 | 0.5 | 0.4 |
| Fire Strike (FS) | 0.05 | 0.1 | 0.1 | 0.75 | 0.1 | 0.2 | 0.7 |
| Disposal Decision | Dangerous Payload Probabilities | UAV Speed Probabilities | UAV Distance Probabilities | ||||
|---|---|---|---|---|---|---|---|
| Loaded | Unloaded | High | Low | Inner | Middle2 | Outer | |
| Alert | 0.1 | 0.9 | 0.1 | 0.9 | 0.1 | 0.5 | 0.4 |
| Disturb | 0.2 | 0.8 | 0.2 | 0.8 | 0.1 | 0.7 | 0.2 |
| Directed Energy (DE) | 0.8 | 0.2 | 0.8 | 0.2 | 0.5 | 0.3 | 0.2 |
| Fire Strike (FS) | 0.9 | 0.1 | 0.7 | 0.3 | 0.7 | 0.2 | 0.1 |
These tables are pivotal for the DBN inference engine. For instance, when the disposal decision is “Alert,” there is a high probability of observing UAVs in a hovering or circling state, with low speed, no dangerous payload, and at outer distances—indicative of a low threat level. Conversely, “Fire Strike” is associated with high probabilities of access actions, loaded payloads, high speed, and inner distances, signaling an imminent threat. The transition matrix in Table 1 shows that decisions tend to persist (e.g., Alert to Alert with probability 0.65) but can escalate based on evolving threats, which is common in anti-UAV operations where responses must adapt to UAV behavior.
To validate our model, we conduct a simulation experiment representing a UAV threat scenario involving close-range incursion into a protected area. We consider six consecutive time slices, labeled Time1 to Time6, with observed values for each UAV factor as detailed in Table 3. This scenario mimics a gradual escalation: starting with benign behavior and progressing to aggressive intrusion, testing the model’s ability to recommend appropriate anti-UAV measures over time. The observations are based on synthetic data designed to reflect realistic UAV tactics, such as initial reconnaissance followed by attack maneuvers.
| Time Slice | UAV Action (Behave) | UAV Quantity (Number) | Dangerous Payload (Load) | UAV Speed (Velocity) | UAV Distance (Distance) |
|---|---|---|---|---|---|
| Time1 | Circle | Small | Unloaded | Low | Outer |
| Time2 | Circle | Middle1 | Unloaded | Low | Outer |
| Time3 | Hover | Middle1 | Unloaded | Low | Middle2 |
| Time4 | Access | Middle1 | Loaded | High | Middle2 |
| Time5 | Access | Large | Loaded | High | Middle2 |
| Time6 | Access | Middle1 | Loaded | High | Inner |
Using the DBN model with the specified probabilities, we perform inference to compute the probability distribution for disposal decisions at each time slice. The results are presented in Table 4, which shows the inferred probabilities for each anti-UAV action. This output serves as a decision support tool, where command personnel can select the action with the highest probability or consider a weighted combination based on risk tolerance. The simulation demonstrates how the model dynamically adjusts recommendations as the threat evolves, aligning with layered defense strategies in anti-UAV operations.
| Time Slice | Alert | Disturb | Directed Energy (DE) | Fire Strike (FS) |
|---|---|---|---|---|
| Time1 | 0.87 | 0.128 | 0.0017 | 0.00021 |
| Time2 | 0.527 | 0.454 | 0.0177 | 0.00089 |
| Time3 | 0.321 | 0.672 | 0.0055 | 0.00097 |
| Time4 | 0.0045 | 0.0908 | 0.7 | 0.204 |
| Time5 | 0.0017 | 0.0276 | 0.426 | 0.544 |
| Time6 | 0.00013 | 0.0015 | 0.271 | 0.727 |
Analyzing the results, we observe a clear progression in recommended anti-UAV actions. At Time1, with UAVs circling at outer distance, low speed, no payload, and small quantity, the Alert action has the highest probability (0.87). This suggests a low-threat situation where monitoring via radar or electro-optical sensors is sufficient, aligning with standard anti-UAV protocols for early detection. By Time2, as the UAV quantity increases to the Middle1 range while other factors remain similar, the probability for Alert decreases to 0.527, and Disturb rises to 0.454. This indicates a moderate threat, prompting the use of radio frequency jamming or GPS spoofing as soft-kill measures to disrupt UAV control links, while maintaining surveillance. At Time3, with UAVs hovering at middle distance, the Disturb probability peaks at 0.672, reinforcing the need for干扰 in response to closer proximity, even without payload threats.
The scenario escalates at Time4, where UAVs exhibit access actions with loaded payloads, high speed, and middle distance. Here, the Directed Energy (DE) probability jumps to 0.7, advocating for hard-kill methods like laser or microwave weapons to neutralize high-threat targets with precision and minimal collateral damage—a key advantage in anti-UAV engagements. At Time5, with a large swarm of loaded UAVs accessing at high speed, Fire Strike becomes dominant at 0.544, supported by DE at 0.426. This reflects a high-threat scenario requiring kinetic strikes, such as guns or missiles, combined with directed energy for area defense. Finally, at Time6, with UAVs penetrating the inner zone, Fire Strike probability soars to 0.727, emphasizing the urgency of lethal force to eliminate imminent dangers. Throughout, the model’s temporal dependencies, via the transition matrix, ensure smooth decision transitions, avoiding abrupt changes unless warranted by observations.
This simulation underscores the model’s capability to support layered anti-UAV strategies. By integrating multiple factors and their temporal dynamics, the DBN approach provides a probabilistic framework that enhances decision-making under uncertainty. For instance, the model can handle incomplete data by marginalizing over unobserved variables, using the formula:
$$P(\text{Disposal} \mid \text{Observed}) = \sum_{\text{Hidden}} P(\text{Disposal}, \text{Hidden} \mid \text{Observed}),$$
where “Hidden” represents unobserved UAV states. This is particularly useful in real-world anti-UAV operations where sensor data may be noisy or partial. Moreover, the model allows for what-if analysis by setting evidence on specific nodes and observing changes in disposal probabilities, aiding in contingency planning. The use of DBNs also facilitates learning from new data; parameters like the conditional probabilities can be updated via Bayesian inference as more operational data becomes available, improving the model’s accuracy over time for adaptive anti-UAV systems.
In practice, implementing this model requires integration with sensor networks for real-time data feeds. For example, radar systems can provide distance and speed estimates, electro-optical/infrared (EO/IR) sensors can identify payloads and actions, and signal intelligence can detect control signals. The DBN engine would process these inputs at each time slice, compute disposal probabilities, and present recommendations to command centers. This aligns with trends in automated decision support for anti-UAV operations, where speed is critical due to UAVs’ agility. However, human oversight remains essential, as the model’s outputs should inform rather than replace commander judgment, especially in complex ethical or tactical situations.
Further refinements to the model could include additional factors such as weather conditions, terrain, UAV type (e.g., fixed-wing vs. multi-rotor), and counter-countermeasures employed by adversaries. Expanding the state spaces or incorporating continuous variables via hybrid DBNs could enhance realism. Additionally, the cost-effectiveness of disposal methods could be integrated into the utility function, leading to decision-theoretic extensions where the goal is to maximize expected utility in anti-UAV engagements. For instance, one might define a utility function \(U(\text{Disposal}, \text{Threat})\) that balances threat neutralization against resource consumption and collateral damage, then select the action maximizing expected utility:
$$\text{Expected Utility} = \sum_{\text{Threat}} P(\text{Threat} \mid \text{Obs}) \cdot U(\text{Disposal}, \text{Threat}).$$
This would align with economic models of defense, where anti-UAV resources are allocated efficiently across multiple threats.
In conclusion, our research demonstrates the viability of dynamic Bayesian networks for anti-UAV disposal decision-making. By modeling the probabilistic relationships between UAV behaviors and disposal actions over time, the DBN approach offers a robust tool for threat assessment and response recommendation. The simulation results show that the model effectively guides command personnel through escalating threat scenarios, from initial警戒 to hard-kill interventions, supporting layered defense strategies. This contributes to the broader field of anti-UAV technology by addressing the decision-making gap, complementing existing hardware-focused solutions. Future work will involve validating the model with real-world data, enhancing computational efficiency for real-time use, and exploring integration with multi-agent systems for coordinated anti-UAV operations. As UAV threats continue to evolve, such probabilistic frameworks will be increasingly valuable for safeguarding critical areas and ensuring security in both civilian and military domains.