Efficiency Evaluation of Anti-Drone Swarm Operations

In recent years, with the rapid advancement of technologies such as networking, artificial intelligence, autonomous systems, and big data, unmanned combat systems have developed swiftly. Drone swarm operations are transitioning from concept to reality, moving from theory to practice. For instance, in March 2019, a large-scale exercise in the Persian Gulf involved dozens of drones flying over long distances to destroy targets, highlighting the imminent security threats posed by drone swarms. This underscores the critical need for effective anti-drone swarm strategies. The complexity of anti-drone measures, involving multiple手段 and equipment, can lead to command confusion and resource waste if not properly coordinated. Therefore, rational integration of作战手段 and selection of optimal作战方案 can enhance cost-effectiveness and reduce command-and-control difficulties, ultimately improving system作战 efficiency. This paper focuses on evaluating the effectiveness of anti-drone swarm operations, aiming to establish a comprehensive evaluation index system for electronic countermeasures against drone swarms and propose a practical assessment approach for优选作战方案.

Currently, various countries are actively developing anti-drone technologies, which can be broadly categorized into detection and tracking,干扰对抗, and destruction打击. Based on these, the effectiveness evaluation model for anti-drone swarm operations is constructed from four criteria: reconnaissance, deception, soft kill, and hard destroy. The index system is illustrated in a hierarchical structure, with detailed explanations provided for each indicator. For example, taking “DJI” drone swarms as targets, the indicators are defined as follows.

Anti-Drone Swarm作战效能评估 Index System

The evaluation system includes 12 primary indicators under four criteria, each with sub-indicators. Below is a summary table of the指标体系 for anti-drone swarm operations.

Criteria	Primary Indicators	Sub-Indicators	Description
Reconnaissance	Radar Reconnaissance	Maximum Detection Distance	The farthest distance at which the radar can detect the drone swarm. Larger distance is beneficial for defense. Formula: $$ R_{a_{max}} = \left[ \frac{P_t G_t^2 n_{\sigma} \lambda^2}{(4\pi)^3 P_{a_{min}}} \right]^{\frac{1}{4}} $$ where \( P_t \) is transmit power, \( G_t \) is antenna gain, \( n_{\sigma} \) is effective cross-section for n drones, \( P_{a_{min}} \) is minimum detectable signal power.
		Target Tracking Number	Number of individual drones in the swarm that can be simultaneously tracked. More is better.
		Equipment Quantity	Number of radar units deployed. More units improve reconnaissance effectiveness.
	Radio Reconnaissance	Direction-finding Accuracy	Accuracy of direction-finding equipment. Higher accuracy is beneficial.
		Frequency Range	Covered frequency bands. Wider range is better.
		Equipment Quantity	Number of radio reconnaissance units. More units enhance effectiveness.
	Electro-Optical/Infrared Reconnaissance	Maximum Detection Distance	Maximum warning distance for small drones. Larger distance is advantageous.
		Equipment Quantity	Number of electro-optical/infrared units. More units improve效果.
Deception	Camouflage Deception	Camouflage Area	Effective area covered by camouflage devices. Larger area is beneficial.
		Deception Type Quantity	Number of enemy reconnaissance types that can be防护. More types improve deception.
	Decoy Deployment	Decoy Quantity	Number and types of decoys deployed. More is better.
		Frequency Range	Frequency bands covered by decoys. Wider range enhances诱骗效果.
Soft Kill	Radio Interference	Equipment Quantity	Number of radio干扰 units. More units improve干扰效果.
		Interference Distance	Maximum distance for jamming drone command communications. Larger distance is beneficial. Formula: $$ K_j \leq \frac{P_j G_j q_{r_j}(\theta) \gamma_j \phi_k R_j \Delta f_r}{P_t G_t q_{r_t} \phi_t R_t \Delta f_j} $$ where \( P_j, G_j \) are jammer power and gain, \( P_t, G_t \) are enemy communication power and gain, \( R_j, R_t \) are干扰 distance and enemy communication distance, \( K_j \) is jamming suppression coefficient.
		Interference Frequency Band	Frequency coverage of interference. Wider range is better.
		Interference Power	Transmit power of the equipment. Higher power improves效果.
	Navigation Interference	Equipment Quantity	Number of navigation干扰 units. More units enhance effectiveness.
		Interference Distance	Maximum distance for jamming drone navigation signals. Larger distance is beneficial.
		Interference Type Quantity	Number of navigation systems that can be干扰 (e.g., GPS, BeiDou). More types are advantageous.
		Interference Power	Transmit power. Higher power improves效果.
	Link Seizure Control	Equipment Quantity	Number of link seizure units. More units are beneficial.
		Seizure Number	Number of drones that can be simultaneously seized. More is better.
		Seizure Mode	Mode of seizure: forced landing or control. Control is more favorable for defense.
	Net-based Weapon Capture	Equipment Quantity	Number of net-based weapon units. More units improve effectiveness.
		Effective Distance	Maximum distance for launching nets or foam. Larger distance is beneficial.
		Effective Area	Area covered by launched nets or foam. Larger area is advantageous.
Hard Destroy	Laser Strike	Effective Strike Distance	Maximum distance for effective damage to drones. Larger distance is beneficial.
		Single Emission Duration	Maximum duration of laser emission per shot. Longer duration increases success rate.
		Fire Transfer Time	Minimum time between strikes. Shorter time allows more drones to be engaged per unit time.
		Equipment Quantity	Number of laser weapon units. More units improve打击效果.
	High-Power Microwave Attack	Beam Width	Width of microwave beam, determining defense area. Wider beam is beneficial under same power.
		Transmit Power	Power of electromagnetic pulse. Higher power is advantageous.
		Frequency Range	Targeted frequency bands for attack. Wider range is better.
		Equipment Quantity	Number of microwave attack units. More units enhance effectiveness.
	Firepower Strike	Cost-Effectiveness Ratio	Ratio of defense cost to destroyed drone cost. Higher ratio is favorable for defense.
		Fire Transfer Time	Minimum time between火力打击 shots. Shorter time increases engagement rate.
		Equipment Quantity	Number of firepower strike units. More units are beneficial.

This comprehensive index system forms the basis for evaluating anti-drone swarm作战效能. Each indicator is quantified based on equipment parameters or battlefield data, enabling a systematic assessment of various anti-drone measures.

Determination of Indicator Weights Using Fuzzy Analytic Hierarchy Process (FAHP)

To assign weights to the indicators, the Fuzzy Analytic Hierarchy Process (FAHP) is employed due to its ability to handle imprecision and hierarchical structures. Common methods like AHP,德尔菲法, and direct scoring have limitations in precision for反无人机蜂群作战效能评估. FAHP involves constructing triangular fuzzy number complementary judgment matrices, calculating expectation matrices, and performing consistency checks. The process for determining weights from criteria layer to indicator layer is outlined below.

First, for the criteria layer B relative to the target layer A, a triangular fuzzy number complementary judgment matrix is established:

$$ \tilde{A} = \begin{bmatrix}
(0.50,0.50,0.50) & (0.15,0.20,0.25) & (0.25,0.30,0.35) & (0.35,0.40,0.45) \\
(0.75,0.80,0.85) & (0.50,0.50,0.50) & (0.65,0.70,0.75) & (0.55,0.60,0.65) \\
(0.65,0.70,0.75) & (0.25,0.30,0.35) & (0.50,0.50,0.50) & (0.35,0.40,0.45) \\
(0.55,0.60,0.65) & (0.35,0.40,0.45) & (0.55,0.60,0.65) & (0.50,0.50,0.50)
\end{bmatrix} $$

The expectation matrix E is computed by taking the average values of the triangular fuzzy numbers:

$$ E = \begin{bmatrix}
0.5000 & 0.2000 & 0.3000 & 0.4000 \\
0.8000 & 0.5000 & 0.7000 & 0.6000 \\
0.7000 & 0.3000 & 0.5000 & 0.4000 \\
0.6000 & 0.4000 & 0.6000 & 0.5000
\end{bmatrix} $$

Then, the positive reciprocal matrix H is derived from E:

$$ H = \begin{bmatrix}
1 & 0.2500 & 0.4286 & 0.6667 \\
4 & 1 & 2.3333 & 1.5 \\
2.3333 & 0.4286 & 1 & 0.6667 \\
1.5 & 0.6667 & 1.5 & 1
\end{bmatrix} $$

The maximum real eigenvalue \( \lambda_{max} \) of H is calculated as 4.0725. Consistency is checked using the consistency index \( IC \), random index \( IR \), and consistency ratio \( RC \):

$$ IC = \frac{\lambda_{max} – k}{k – 1} = \frac{4.0725 – 4}{4 – 1} = 0.0091 $$

With \( IR = 0.9 \), \( RC = \frac{IC}{IR} = 0.0269 < 0.1 \), indicating acceptable consistency.

Next, fuzzy evaluation values and expectations are computed for each criterion. For criterion 1:

$$ \tilde{u}_1 = (0.2849, 0.3250, 0.3716) $$

$$ E(\tilde{u}_1) = 0.3266 $$

Similarly, for others: \( E(\tilde{u}_2) = 0.1762 \), \( E(\tilde{u}_3) = 0.2640 \), \( E(\tilde{u}_4) = 0.2389 \).

After normalization, the weight vector for criteria layer B is:

$$ \alpha_A = (0.3248, 0.1752, 0.2858, 0.1370) $$

Following the same FAHP process, weight vectors for indicator layers are determined. For example, for雷达侦察 under reconnaissance:

$$ \alpha_{B1} = (0.4893, 0.2888, 0.2220) $$

Similarly, other weights are computed. The final weights for all sub-indicators are aggregated. A summary table of weights is provided below.

Indicator Layer	Sub-Indicator	Weight
Radar Reconnaissance	Maximum Detection Distance	0.1589
	Target Tracking Number	0.0938
	Equipment Quantity	0.0721
Radio Reconnaissance	Direction-finding Accuracy	0.0963
	Frequency Range	0.0789
	Equipment Quantity	0.0821
Electro-Optical/Infrared Reconnaissance	Maximum Detection Distance	0.1035
	Equipment Quantity	0.0608
Camouflage Deception	Camouflage Area	0.0394
	Deception Type Quantity	0.0426
Decoy Deployment	Decoy Quantity	0.0563
	Frequency Range	0.0381
Radio Interference	Equipment Quantity	0.0653
	Interference Distance	0.0494
	Interference Frequency Band	0.0442
	Interference Power	0.0454
Navigation Interference	Equipment Quantity	0.0271
	Interference Distance	0.0208
	Interference Type Quantity	0.0379
	Interference Power	0.0342
Link Seizure Control	Equipment Quantity	0.0530
	Seizure Number	0.0433
	Seizure Mode	0.0473
Net-based Weapon Capture	Equipment Quantity	0.0316
	Effective Distance	0.0195
	Effective Area	0.0277
Laser Strike	Effective Strike Distance	0.0113
	Single Emission Duration	0.0236
	Fire Transfer Time	0.0181
	Equipment Quantity	0.0336
High-Power Microwave Attack	Beam Width	0.0142
	Transmit Power	0.0296
	Frequency Range	0.0169
	Equipment Quantity	0.0243
Firepower Strike	Cost-Effectiveness Ratio	0.0196
	Fire Transfer Time	0.0109
	Equipment Quantity	0.0162

These weights reflect the relative importance of each indicator in anti-drone swarm作战效能评估, derived through FAHP to ensure精度 and consistency.

Case Study for Anti-Drone Swarm作战方案 Evaluation

To validate the effectiveness evaluation model, a case study is conducted using实兵模拟演练 data.假设 a smart command system exists to handle the complexity of numerous anti-drone方案 combinations. Three representative作战方案 are selected, targeting a swarm of 10 “DJI” drones. The indicator values for each scheme are collected and normalized for comparison.

First, the raw indicator values for the three schemes are tabulated. These include parameters such as maximum detection distances, equipment quantities, interference distances, etc., based on actual equipment性能.

Indicator	Sub-Indicator	Scheme 1	Scheme 2	Scheme 3
Radar Reconnaissance	Maximum Detection Distance (km)	20.3	0	19.5
	Target Tracking Number	6	0	5
	Equipment Quantity	2	0	1
Radio Reconnaissance	Direction-finding Accuracy (°)	0	6.65	5
	Frequency Range (MHz)	0	80	150
	Equipment Quantity	0	2	1
Electro-Optical/Infrared Reconnaissance	Maximum Detection Distance (km)	6	5.5	0
	Equipment Quantity	2	1	0
Camouflage Deception	Camouflage Area (m²)	10	10	10
	Deception Type Quantity	2	1	1
Decoy Deployment	Decoy Quantity	0	0	0
	Frequency Range (MHz)	0	0	0
Radio Interference	Equipment Quantity	0	2	1
	Interference Distance (km)	0	8	10
	Interference Frequency Band (MHz)	0	80	150
	Interference Power (kW)	0	0.15	0.3
Navigation Interference	Equipment Quantity	1	0	1
	Interference Distance (km)	50	0	30
	Interference Type Quantity	1	0	1
	Interference Power (kW)	10	0	8
Link Seizure Control	Equipment Quantity	0	1	0
	Seizure Number	0	1	0
	Seizure Mode	0	2	0
Net-based Weapon Capture	Equipment Quantity	1	0	0
	Effective Distance (m)	2	0	0
	Effective Area (m²)	75	0	0
Laser Strike	Effective Strike Distance (m)	5	0	0
	Single Emission Duration (s)	200	0	0
	Fire Transfer Time (s)	6	0	0
	Equipment Quantity	1	0	0
High-Power Microwave Attack	Beam Width (°)	0	0	3
	Transmit Power (kW)	0	0	100
	Frequency Range (MHz)	0	0	500
	Equipment Quantity	0	0	2
Firepower Strike	Cost-Effectiveness Ratio	0	0	0
	Fire Transfer Time (s)	0	0	0
	Equipment Quantity	0	0	0

Next, normalization is applied to standardize the indicator values. For benefit-type indicators, the formula is: $$ z_{ij} = \frac{y_{ij}}{\left( \sum_{i=1}^{m} y_{ij}^2 \right)^{1/2}} $$ For cost-type indicators, the formula is: $$ z_{ij} = \frac{1/y_{ij}}{\left[ \sum_{i=1}^{m} (1/y_{ij})^2 \right]^{1/2}} $$ Since all indicators here are benefit-type (higher values are better), the first formula is used. The normalized values are computed and summarized in the following table.

Indicator	Sub-Indicator	Scheme 1 (Normalized)	Scheme 2 (Normalized)	Scheme 3 (Normalized)
Radar Reconnaissance	Maximum Detection Distance	0.7212	0.0000	0.6928
	Target Tracking Number	0.7682	0.0000	0.6402
	Equipment Quantity	0.8944	0.0000	0.4472
Radio Reconnaissance	Direction-finding Accuracy	0.0000	0.7993	0.6010
	Frequency Range	0.0000	0.4706	0.8824
	Equipment Quantity	0.0000	0.8944	0.4472
Electro-Optical/Infrared Reconnaissance	Maximum Detection Distance	0.7372	0.6757	0.0000
	Equipment Quantity	0.8944	0.4472	0.0000
Camouflage Deception	Camouflage Area	0.5774	0.5774	0.5774
	Deception Type Quantity	0.8165	0.4082	0.4082
Decoy Deployment	Decoy Quantity	0.0000	0.0000	0.0000
	Frequency Range	0.0000	0.0000	0.0000
Radio Interference	Equipment Quantity	0.0000	0.8944	0.4472
	Interference Distance	0.0000	0.6247	0.7809
	Interference Frequency Band	0.0000	0.4706	0.8824
	Interference Power	0.0000	0.4472	0.8944
Navigation Interference	Equipment Quantity	0.7071	0.0000	0.7071
	Interference Distance	0.8575	0.0000	0.5145
	Interference Type Quantity	0.7071	0.0000	0.7071
	Interference Power	0.7809	0.0000	0.6247
Link Seizure Control	Equipment Quantity	0.0000	1.0000	0.0000
	Seizure Number	0.0000	1.0000	0.0000
	Seizure Mode	0.0000	1.0000	0.0000
Net-based Weapon Capture	Equipment Quantity	1.0000	0.0000	0.0000
	Effective Distance	1.0000	0.0000	0.0000
	Effective Area	1.0000	0.0000	0.0000
Laser Strike	Effective Strike Distance	1.0000	0.0000	0.0000
	Single Emission Duration	1.0000	0.0000	0.0000
	Fire Transfer Time	1.0000	0.0000	0.0000
	Equipment Quantity	1.0000	0.0000	0.0000
High-Power Microwave Attack	Beam Width	0.0000	0.0000	1.0000
	Transmit Power	0.0000	0.0000	1.0000
	Frequency Range	0.0000	0.0000	1.0000
	Equipment Quantity	0.0000	0.0000	1.0000
Firepower Strike	Cost-Effectiveness Ratio	0.0000	0.0000	0.0000
	Fire Transfer Time	0.0000	0.0000	0.0000
	Equipment Quantity	0.0000	0.0000	0.0000

Using the weights from the FAHP analysis, the overall evaluation value for each anti-drone scheme is computed by summing the weighted normalized values. The results are as follows:

Scheme	Evaluation Value
Scheme 1	0.4058
Scheme 2	0.2682
Scheme 3	0.3818

Based on the evaluation values, Scheme 1 demonstrates the highest effectiveness among the three, followed by Scheme 3 and then Scheme 2. This outcome aligns with实兵验证 results, where Scheme 1’s combination of radar reconnaissance, electro-optical/infrared侦察, navigation interference, net-based weapons, and laser strike capabilities provides a balanced anti-drone defense. However, it is important to note that Scheme 1 is optimal only within this subset; a smart command system would evaluate all possible combinations to identify the absolute best anti-drone作战方案 for real-time battlefield conditions.

Conclusion and Future Directions for Anti-Drone Swarm Operations

This paper presents a comprehensive efficiency evaluation model for anti-drone swarm operations, focusing on electronic countermeasures. By constructing an index system based on reconnaissance, deception, soft kill, and hard destroy criteria, and applying the Fuzzy Analytic Hierarchy Process to determine indicator weights, a method for assessing and优选作战方案 is developed. The case study validates the model’s practicality, showing that it can effectively compare different anti-drone schemes and support command decision-making. The integration of such models into intelligent command systems, leveraging cloud computing and big data, can enhance real-time optimization of anti-drone measures, improving作战 efficiency and resource allocation.

Looking ahead, the evolution of drone technology suggests that drone swarms will play increasingly significant roles in future warfare, not only in骚扰 and reconnaissance but also in integrated network-centric operations. Drones may form networks with manned aircraft, satellites, ground vehicles, and naval vessels, potentially realizing scenarios akin to science fiction. Therefore, it is imperative to advance anti-drone swarm technologies and build integrated joint defense systems. Emphasis should be placed on enhancing the intelligence level of武器装备, utilizing various models and algorithms to provide optimal作战方案 for command authorities. This will elevate overall作战 efficiency in countering the growing threat of drone swarms.

Future research could refine the evaluation指标体系 to account for dynamic factors such as target types, battlefield environments, and weather conditions. Additionally, incorporating machine learning algorithms for adaptive weight adjustment could further improve the accuracy of anti-drone效能评估. As anti-drone measures evolve, continuous updates to the model will ensure its relevance and effectiveness in safeguarding against emerging drone swarm threats.