A TARGET THREAT ASSESSMENT METHOD FOR APPLICATION IN AIR DEFENSE COMMAND AND CONTROL SYSTEMS Текст научной статьи по специальности «Компьютерные и информационные науки»

Radar and Navigation

UDC 621.391 Original article

https://doi.org/10.32603/1993-8985-2023-26-3-90-98

A Target Threat Assessment Method for Application in Air Defense Command and Control Systems

Xuan Truong Nguyen 1EI, Kim Phuong Phung1, Quang Hieu Dang1, Xung Ha Vo2, Hoa Tien Vu1

1Le Quy Don Technical University, Hanoi, Vietnam 2National Institute of Science and Technology, Hanoi, Vietnam

Eltruongnx.isi@lqdtu.edu.vn

Abstract

Introduction. This paper presents a solution for threat assessment of air targets using the fuzzy logic inference method. The approach is based on the Sugeno fuzzy model, which has multiple inputs representing target trajectory parameters and a single output representing the target threat value. A set of IF-THEN fuzzy inference rules, utilizing the AND operator, is developed to assess the input information.

Aim. To develop and test an algorithm model to calculate the threat value of an air target for use in real-time automated command and control systems.

Materials and methods. An algorithm model was developed using a fuzzy model to calculate the threat value of a target. The model is presented in the form of a flowchart supported by a detailed stepwise implementation process. The accuracy of the proposed algorithm was evaluated using the available toolkit in MATLAB. Additionally, a BATE software testbed was developed to assess the applicability of the algorithm model in a real-time automated command and control system.

Results. The efficiency of the proposed fuzzy model was evaluated by its simulation and testing using MATLAB tools on a set of 10 target trajectories with different parameters. Additionally, the BATE software was utilized to test the model under various air defense scenarios. The proposed fuzzy model was found to be capable of efficiently computing the threat value of each target with respect to the protected object.

Conclusion. The proposed fuzzy model can be applied when developing tactical supporting software modules for real-time air defense command and control systems.

Keywords: fuzzy logic, fuzzy model, threat value, air defense, command and control system

For citation: Xuan Truong Nguyen, Kim Phuong Phung, Quang Hieu Dang, Xung Ha Vo, Hoa Tien Vu. A Target Threat Assessment Method for Application in Air Defense Command and Control Systems. Journal of the Russian Universities. Radioelectronics. 2023, vol. 26, no. 3, pp. 90-98. doi: 10.32603/1993-8985-2023-26-3-90-98

Conflict of interest. The authors declare no conflicts of interest. Submitted 26.03.2023; accepted 28.04.2023; published online 29.06.2023

© Xuan Truong Nguyen, Kim Phuong Phung, Quang Hieu Dang,

Xung Ha Vo, Hoa Tien Vu, 2023

Introduction. Automatic evaluation of the air situation and information updates in automated command and control systems (ACCS) plays a pivotal role in ensuring the effectiveness of combat operations (as depicted in Fig. 1). The threat level of targets with respect to the protected object can be assessed based on target data from radar sources and higher-level information processing. These values are aggregated and filtered to serve as a crucial input parameter for target distribution requests and selection of appropriate combat means, enabling informed decision making using air defense systems [1, 2].

Automatic evaluation of the air situation is a continuous, real-time process that determines the threat value of targets to the protected objects. Calculating the threat value is a challenging task due to the need for high processing performance, information synthesis from multiple sources, and real-time requirements. The information used for situation assessment is frequently obtained from various heterogeneous, uncertain, and interfered sources [3, 4]. Therefore, to ensure reliability, it is necessary to employ estimation algorithms capable of inferring from incomplete or unreliable information sources. Currently, fuzzy logic and Bayesi-an probability networks are widely used for assessing the threat of air targets [5-9]. In this paper, considering the priority of real-time approaches, we develop a method for automatic target threat assessment based on fuzzy logic methods.

The threat value is evaluated based on the inference ability of fuzzy systems, including linguistic variables, fuzzy sets, fuzzy rules, defuzzifica-tion mechanisms, etc. The outstanding advantage

of this method consists in its similarity with natu- Fig- 2. Schematic diagram of the basic structure of a fuzzy model A Target Threat Assessment Method for Application in Air Defense Command and Control Systems

ral inference mechanisms, thus enabling users to participate in the design processing of inference systems and use their expert knowledge to propose suitable fuzzy rules. At the same time, the fuzzifi-cation process contributes to smoothing threat value variations at uncertainty boundaries.

Research methods.

Basic structure of a fuzzy model. The fuzzy set theory proposed by Lotfi A. Zadeh includes fuzzy logic, fuzzy arithmetic, fuzzy mathematical programming, fuzzy topological geometry, fuzzy graph theory, and fuzzy data analysis. This theory aims to introduce the concept of fuzzy sets. Mathematically, a fuzzy set a on a basic space x is defined as a=|[(ia (jc)/jc]|jc gx|. In which,

is a membership function that quantifies the degree to which elements a: belong to the basic set x, expressed as: ¡1^: x —»[0, l],

The structure of a typical basic processing model conventionally includes an input, an output, and a processor. The processor is essentially a mapping that reflects the dependence of the output variables on the input variables in the system. In a fuzzy model, a certain numerical value can be taken as an input, a fuzzy set or an unambiguous numerical value can be taken as an output. The output-input mapping relationship of a fuzzy model is described by a set of fuzzy rules, rather than by an explicit function. As a rule, a general fuzzy model has numerous inputs and outputs. However, a multi-output model can always be divided into a set of single-output models. In this work, we consider the case of a multiple-input one-output system. Specifically, the basic structure of a fuzzy model consists of five components [10] (Fig. 2).

In Fig. 2, the rule set is a site where the IF-THEN fuzzy rules are stored. This is a set of

statements or human-understandable rules, which describe the behavior of the system. With an n input-one output fuzzy model, each fuzzy rule can be described as follows:

IF^is 4)

AND.AND

(x„is 4)]

THEN [(y is lK)(ffl?)],

where Aji_ with k =\...,n and B are the language values defined on the input and output variables of the model, respectively;

xj-is A4=1,...,«.

The hypothesis part of the rule is formed from the intersection (performed by fuzzy AND) between the linguistic statements, referred to as component premises. The conclusion of the rule is mapped from the hypothesis part by fuzzy inference (IF-THEN). Corresponding to each rule, there is a rule confidence <o2j-fc[0,l] The reliability of the rule reflects the correctness of m^- 0 ,

showing that the rule does not participate in determining the output of the model. Each rule base is a combination of fuzzy OR selection of all fuzzy rules. Rules can be formed from human expert knowledge or obtained from empirical samples. The rule base is the most important component of any fuzzy model.

The model parameter set specifies the shape of the membership function of the linguistic value used to represent fuzzy variables and fuzzy rules. The parameter values can be evaluated by either expert experience or knowledge mining process from an experiment. The rule base and the model parameter set are commonly referred to as the knowledge base. The reasoning mechanism is responsible for performing a fuzzy inference procedure based on the knowledge base and input values to give a predicted value at the output. The fuzzifi-cation interface performs the conversion of explicit inputs into degrees of belonging to language values. The defuzzification interface converts the fuzzy inference result into a clear output value.

Constructing a fuzzy model to assess the target threat level. The fuzzy model is constructed as a multiple-input one-output model, with the input data comprising the target trajectory information

and the protected object information. The target trajectory information is obtained from processing and merging the data retrieved from the measuring system, including distance, speed, altitude, flight direction, etc. The protected object information includes position, scope, protected direction, etc. The correlation between the target Tt and the protected object Oj is illustrated in Fig 3.

The target trajectory information can be used to determine the vicinity of the target to the protected

object, where the CPA distance of the target

is the shortest distance to the protected object. The closest point of approach (CPA) is an important parameter for evaluating the target threat level. The target is especially dangerous when its CPA distance is equal to 0. In the case of n targets attacking m protected objects, the closest approach time parameter is calculated as follows:

where i/cPAj" 's t'lc distance from the target i to

the CPA of the protected object j and v, is the target velocity i. The value of the approaching flight direction 0^- ranges within [0°,180°], determined through the azimuth and flight direction. When the target approaches the protected object, the approach flight direction ranges within . The larger the flight direction, the lower

the threat level. A fuzzy model to evaluate the threat of a target is constructed following the steps outlined in Fig. 4.

Step 1. Based on the information about the target derived by radar sources and that about the

Tab. 2. Fuzzy inference rule set in the form of IF-THEN to evaluate input data by AND operator based on expert knowledge

No. Reliability Ю; AND Target threat value

Range, m Altitude, m Speed, m/s Distance dCPA, m Flight Direction ег, Time to CPA Tij s CPA' s

1 1.0 L L H L L L H

2 1.0 H H L H H H L

3 1.0 M M M M M M M

4 0.5 H L H L L M M

5 0.5 M L H L L M H

6 0.5 L H M H H H L

7 0.1 H H M L L H H

8 0.1 M M H M L M M

9 0.1 L L L L L H L

rule, e[0,i] is built as shown in Tab. 2.

Tab. 2 shows that each evaluation rule for determining the target threat value is the minimum value of the membership level of the fuzzy set for each input. According to Tab. 1, the linguistic expression l of the input information n is defined as nl and the relative degree of the target x is lnl (x), then the satisfaction Hk for each input clearly value vector is calculated as follows:

Hi = min{m3( x), |23(x), |31( x), |43( x), M.53C x), |g3( x)}; H2=min{mi( x), |21( x), I33( x), |41( x), |51( x), |gi( x)};

H9=min{|i3( x) ,|23( x) ,I33( x) ,|43( x) ,|53( x) ,|61( x)}.

Step 4. Each evaluation rule in Tab. 2 generates a satisfaction Hk . In case where all the rules in Tab. 2 are activated at the same time, there will be rules that produce the same satisfaction Hk . For example, rules 1, 5 and 7 generate the target threat level with the language expression High (H); rules 3, 4 and 8 generate the threat level with the language expression Medium (M); rules 2, 6, and 9 produce a hazard level with the language expression Low (L). Therefore, it is necessary to integrate the rules that produce the same linguistic expression of the threat level, using the fuzzy U operator ProbOR according to the following formula:

Pi = U Hk ®i,

Vk

where H kl is the satisfaction corresponding to a linguistic expression of threat level l (l = 1: High (H);

94

l = 2: Medium (M); l = 3: Low (L)). Then, for the rules in Tab. 2, their combined members are:

pi = hiffli + h505 + h707 -h101h505 -—H505 H 707 — h7 07 hiff>i + h101h505 h707;

p2 = h303 + h404 + h808 — h303 h404 — —H404h808 — h808h303 + h303h404h808;

p3 = H2 02 + h606 + H909 — H202h606 — —h606h909 — h909 h202 + h202 h606h909.

Step 5. Defuzzification and the target threat value is calculated using the Center of Gravity (CoG) method. CoG is the most prevalent and physically appealing of all the defuzzification methods [Sugeno, 1985, Lee 1990]. The membership function at the model output with three linguistic expressions (High, Medium, Low), corresponding to the target threat value is vn e [0,1.0]. To calculate a specific value, it is necessary to combine the relevant members (Pi, P2, P3) followed by its conversion to a scalar value, through a truncation to remove the uncertain components and the final form of the membership function lC (vn) to the determined threat level.

This method returns a precise value depending on the CoG of the fuzzy set. The overall area of the membership function distribution is divided into a number of sub-areas (such as triangle, trapezoidal etc.) in Fig. 6. Let Si and vi denote the area and CoG of i-th sub-region. Where, Sj = Jic (v)dv and n is the number of geometrical

components. The threat value of the air target T to the protected object Oj is calculated as follows:

Tab. 3. Trajectory parameter details

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Threat value

Fig. 6. Output membership function of the fuzzy model after clipping the center of gravity

Target, no. Distance, km Azimuth, deg Altitude, m Speed, m/s Course, deg

T 134.40 43.5 4500 305.6 245.0

T2 70.43 51.3 3200 250.0 250.0

T3 54.92 79.5 5800 333.3 220.0

T4 116.81 122.1 7300 244.4 350.0

T5 56.57 135.0 9500 261.1 315.0

T6 80.22 140.1 8200 241.7 265.0

T7 114.02 307.9 5200 305.6 80.0

T8 101.07 296.4 6200 319.4 95.0

T9 59.42 247.8 2700 194.4 75.0

T10 100.12 236.0 9140 216.7 105.0

I Stv

Vi

CoG _ 7=1

V

I Si

7=1

jvc(v)vdv jvc (v)dv

Simulation testing and result evaluation.

Input data. Fig. 7 depicts an air defense scenario used to test the proposed fuzzy model when evaluating and comparing the threat levels of different targets. This scenario simulates an air situation with 10 tracks (Tj,T2,...,T10) with different parameters and the protected object O. The horizontal axis Ox has a positive direction pointing to the East, and the vertical axis Oy pointing to the North.

The trajectory parameters of the targets at the testing time are presented in Tab. 3. Here, the CPA

y, km 100

60

40

III,

y

20

—I-1-1-1 it- '-*

-100 ,-80■ -60 -40 -201 0

TV-

'10

-20

-40 --

-60

r-

•h 1 т 1 T3

- \ I

'20■■ /Ю■■ 60,1 80 ; 100, ^ km

^ У t / I . ) 5

\ ;

!■ T4

-100

Fig. 7. Air defense scenario for evaluation testing of the proposed model

distance dCpA

approach flight direction вц and

flight time Tcpa of the target over the approach

point are calculated by (1) based on pre-processing of the input data.

Simulation testing and result evaluation. Experiment 1. In the first test, to evaluate the accuracy of the proposed fuzzy model based on the Sugeno model and the proposed fuzzy rules in Tab. 2, we use the FIS Edition toolkit in MATLAB. Fuzzy rules are established according to the values of the input information (Fig. 8). Following the establishment of fuzzy rules, the Simulink toolkit in MATLAB is used to construct a fuzzy model for calculating the threat level of the targets in Tab. 3. The testing results of this model with the target trajectory parameters are presented in Fig. 10.

Experiment 2. To evaluate the computational performance of the proposed fuzzy model, we developed a BATE software testbed, which simulates the real-time ACCS. BATE is implemented in Microsoft Visual Studio C++, capable of simulating and displaying an air situation picture [11] on a digital map (Fig. 9). Then the calculation time complexity of the proposed method is estimated. We created various air defense scenarios with increasing complexity to calculate execution time.

Comments. According to Fig.10, the threat value of target T5 is the highest V5 j = 0.783, the threat

value of target T7 is the lowest V7j = 0.213. From

the calculation results of the threat value, it is possible to arrange the targets in terms of their threat levels from high to low, which is convenient for imple-

T

7

T

T

5

T

6

Fig. 8. Testing simulation of the proposed fuzzy model using the FIS EDITOR tool

Fig. 9. Air defense scenario for evaluation testing of the proposed model

л

H

0.8

0.6 0.4 0.2 0

1 1 ■

1 1

1 1 , 1

1 ll 1 1 1

T T2 T3 T4 T5 T6 T7 T

T9 T10

'6

Air target

Fig. 10. Threat level values of the target in the testing of an air defense scenario

menting the function of automatically distributing the target data to firing units in an ACCS [12, 13].

Fig. 9 presents the proposed algorithm model calculated and updated for the threat values of dozens of targets in each data update cycle (less than 1 s) [14, 15]. The threat values are displayed directly on a digital map. This confirms that the proposed algorithm model can be applied in real-time ACCS.

Conclusion. This paper presents a method for solving the issue of calculating the threat value of air targets based on the fuzzy logic inference method. The proposed model utilizes the Sugeno fuzzy model, which features multiple inputs (target trajectory pa-

rameters) and a single output (target threat value). A fuzzy inference rule in the IF-THEN format is established to evaluate input information using the AND operator, incorporating expert knowledge. The fuzzy rules and defuzzification, implemented through the clipped center of gravity method, are combined to determine the clear threat value of a target.

The proposed fuzzy model was simulated and tested using MATLAB tools on a scenario involv-

ing 10 target trajectories with varying parameters. Additionally, the BATE software is used to test the model via different air defense scenarios. The testing results suggest that the proposed fuzzy model is capable of timely calculating the threat value of each target to the protected object, thus being suitable for developing tactical supporting software modules for real-time air defense command and control systems.

Author's contribution

Xuan Truong Nguyen, synthesize and analyze approaches to solving the threat assessment problem in automated command and control system; building and evaluating an algorithm model to calculate the threat value of the air target based on fuzzy model. Developing a testbed software BATE in Microsoft Visual Studio C++, that simulates the real-time automated command and control system.

Kim Phuong Phung, scientific support including: evaluating fuzzy algorithm model to calculate the threat value of the air target that can be applied in a real-time automated command and control system.

Quang Hieu Dang, scientific support including: programming the software module to display the air situation picture in Microsoft Visual Studio C++, simulation and evaluation of the results.

Xung Ha Vo, scientific support including: simulation model by the MATLAB and evaluation of results.

Hoa Tien Vu, scientific guidance, scientific consulting on mathematical models in the field of radar data processing; target tracking, guidance in conducting experimental studies.

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Information about the author

Xuan Truong Nguyen, Master's degree in "Radar Engineering" (2013) of the Russian Federation Armed Forces Army Air Defence Military Academy named after Marshal of the Soviet Union A. M. Vasilevsky. Postgraduate student, Researcher of Institute of System Integration / Le Quy Don Technical University. The author of 5 scientific publications. Area of expertise: radar and radio navigation; telecommunications. Address: Le Quy Don Technical University, 236, Hoang Quoc Viet, Hanoi, Vietnam E-mail: truongnx.isi@lqdtu.edu.vn

Kim Phuong Phung, Master's degree in "Computer science " (2014) of the Military Academy of Air and Space Defence named after Marshal of the Soviet Union G. K. Zhukov. Postgraduate student, Lecturer of the Department of Electronic Technologies of Institute of System Integration/Le Quy Don Technical University. The author of 3 scientific publications. Area of expertise: electronic technology; computer science. Address: Le Quy Don Technical University, 236, Hoang Quoc Viet, Hanoi, Vietnam E-mail: phuongpk.isi@lqdtu.edu.vn

Dang Quang Hieu, PhD (2022), Senior Researcher of the Institute of System Integration/ Le Quy Don Technical University. The author of 7 scientific publications. Area of expertise: radar and radio navigation; telecommunications.

Address: Le Quy Don Technical University, 236, Hoang Quoc Viet, Hanoi, Vietnam E-mail: Hieudq@lqdtu.edu.vn

Xung Ha Vo, Master's degree in "Radar System Engineering" (Le Quy Don Technical University (LQDTU), Vietnam, 2007), PhD student in "Radar Systems Engineering". Head of System and Antenna Design/National Institute of Science and Technology. The author of 5 scientific publications. Area of expertise: system engineering; radar data processing; control and automation.

Address: National Institute of Science and Technology, 17, Hoang Sam Str. Cay Giay, Hanoi, Vietnam E-mail: voxungha@amst.edu.vn

Vu Hoa Tien, PhD in "Radio Electronica and Control Automation" (2005), Associate Professor (2014), Visiting Lecturer of Department of Aerospace Control Systems; a specialist in systems engineering control and automation. Author of 57 publications. Area of expertise: systems automatic control for UAV; electronic technology, systems engineering.

Address: Le Quy Don Technical University, 236, Hoang Quoc Viet, Hanoi, Vietnam E-mail: hoatien57@lqdtu.edu.vn