信息支援条件下协同空战态势评估研究*

安超，李战武，2，常一哲，杨海燕

（1.空军工程大学航空航天工程学院，西安710038；2.西北工业大学电子信息学院，西安710072；3.空军工程大学空管领航学院，西安710051）

信息支援条件下协同空战态势评估研究*

安超1，李战武1，2，常一哲1，杨海燕3

（1.空军工程大学航空航天工程学院，西安710038；2.西北工业大学电子信息学院，西安710072；3.空军工程大学空管领航学院，西安710051）

针对现有空战态势评估方法表现形式不够直观、模型简单的问题，提出一种将威力场与遗传神经网络相结合的态势评估方法，并将其应用于信息支援条件下的协同空战态势评估。分别从攻击能力、探测能力、电子干扰能力、生存能力、通信能力、告警能力、协同能力以及决策能力等方面构建威力势模型。利用遗传算法优化BP神经网络，并将其应用于编队作战能力评估。最后利用具体算例进行仿真验证，结果表明该方法是正确可行的。相比于传统态势评估方法，该方法在信息支援条件下的超视距协同空战态势评估中具有全面性、直观性、准确性等优势。

信息支援，协同空战，威力场，态势评估

0 Introduction

As the important resources of combat system，information has significant meanings of the cooperative air combat.A new cooperative air combat emerges that the fighter formation fights with the information of airborne early-warning aircraft（AEW）［1］.The rationality and accuracy of situation assessment will directly influence the decision maker to grasp the battlefield situation and implement the decision［2］.Consequently，researching situation assessment on cooperative air combat with information support has important meanings of modern air combat.

Aiming at the situation assessment problem about cooperative air combat，the domestic and international experts all carried on a great deal of researches［3-8］.Currently，the literatures of situation assessment mostly make use of the non-parameter model or improvement model.In the air combat，the influence of the battlefield and opposite side should embody on the fighter's power，which should not be a simple superposition of the weapon material characteristic and situation advantage，but combining material function and situation factors，such as distance and angle.

Aiming at this problem，the paper leads power field and genetic neural network（GNN）into situation assessment on cooperative air combat.The method can not only make use of power field to describe a formation situation in the air combat with information support，but also show the influence of whole war power and battle sky from information support.It is vivid and real-time，so it provides a new way for situation assessment of air combat.

1 Power field model for situation assessment with information support

1.1 Model of formation air combat capability

In the modern air battle，both parties fighting capability is the whole formation power.Consequently，the model includes the fighter，AEW and cooperation capability.

Where EFis the power of the fighter；EAWACSis the power of AEW；ECOis the cooperation capability.

1.2 Model of the fighter’s power

The model of the fighter’s power mainly considers aspects of attack，detection，survivability，communication，electronic countermeasures and alert.The model is as follows：

Where EDis detection，EWis attack，EEis electronic countermeasures，ESis survivability，ECis communication，EAis alert.

1.2.1 Attack

The main way of the modern air combat with information support is beyond visual range air combat，whose main weapon is the medium-range air-to-air missile. On these grounds model is built as follows［10］：

Where AMis the attack factor of the missile.

Where N is the quantity of the missile，PKis the kill probability of a single missile，φ is the scope of missile attack angle，nmaxis the missile maximum available overloads，ωmaxis the largest missile tracking angular velocity，ψ is the missile off-axis angle，KDis the correction coefficient of guidance system，r is the distance between carrier aircraft and calculated point，rmaxis the missile launch maximum distance，rminis the missile launch minimum distance，θ is the relative calculation point advance angle.

1.2.2 Detection

Detectionequipmentmainlyconsidersradarandinfraredsearch-trackdevice.Modelisbuiltasfollows［11］：

Where ADRis the detection factor of the radar，ADIRis the detection factor of infrared search-track device.

Where STRis the radar maximum found target distance，θRis the radar search total azimuth，PTRis the radar target probability，K2is the radar measure coefficient，m1is the number of tracking targets at the same time，m2is the number of attacking targets at the same time.

Parameter meanings are basically consistent with（7）.where K2'is the measure coefficient of infrared system.

1.2.3 Electronic countermeasures

Aiming at the characteristic of electronic jammer，the model is built as follows［12］：

Where ADISis the factor of electronic countermeasures.

Where Pjis the jammer transmission power，Gjis the jamming antenna gain，θ'is the antenna beam width，Ω is the antenna biggest point range in space，n is the multiple radar jamming capability，Pfis the coverage rate of jammer to interference radar.Δtjis the guide time，it is the time from jammer receiving radar signals to launch interference signals.Δf is the frequency guided error，Δθ is the azimuth guided error，the sum of the two is guided error.KEis the gain factor.The paper assumes that radar axis of suppression area is same with the airplane.

1.2.4 Survivability

Aircraft survivability is the capability that airplane dodges or bears artificial hostile environment.The model is built as follows［13］：

Where ASis the factor of survivability.

Where W is the airplane span，L is the airplane length，RCS is the radar effectively reflects area，Aviis the airplane surface area of vulnerability parts，Avis the airplane surface area.

1.2.5 Communication

The model is built from the radio communication capability and data-link communication capability［9，14］.

1.2.6 Alert

According to related literatures［9，14］，the model is built on infrared warning，ultraviolet warning and radar warning.

Where Alis the factor of infrared warning，AUis the factor of ultraviolet warning，ARis the factor of radar warning.

Where Daiis the maximum alarm distance，Pdriis the detection probability，Pfaiis the false alarm rate，φiis the cover airspace，diis the angular resolution.

Where Dauis the maximum alarm distance，Pdruis the detection probability，Pfauis the false alarm rate，φuis the cover airspace，duis the angular resolution.

Where Darthe maximum alarm distance，Pdrris the radar sensitivity，Pfauis the false alarm rate，μuis the accuracy of direction，tris the response time of radar warning，fmaxis the upper limit of frequency measurement，fminis the lower limit of frequency measurement.

1.3 Model of the AEW’s power

The AEW is very important in the formation cooperative air combat.According to related literatures［15-16］，the model is built on detection guide，communication transmission，threat warning，survivability and decision making.

Where EAWACSis the power of AEW，EA'is the threat warning of AEW，ED'is the detection guide，EDM'is the decision making，ES'is the survivability，EC'is the communication transmission.

1.3.1 Detection guide

According to related literatures［15-16］，the model is built on detection capability，tracking capability and guide capability.

Where AD'is the factor of detection，AT'is the factor of tracking，AG'is the factor of guide.

Where K is the radar system coefficient，Dris the radar maximum detecting distance，θR'is the radar search total azimuth.

Where m is the number of attacking targets at the same time，PT'is the probability of accurate tracking.

Where n is the number of guiding airplane at the same time，PG'is the probability of successful guide，the model is in literature［16］.

1.3.2 Decision making

As the core of the formation，decision making of the AEWisveryimportant.Generally，decisiontimeishelpful toimprovetheaccuracyofdecisionmaking，butifdecision time exceeds the time of battle reaction，it will cause the failureofdecision［17］.ThepaperusestheGaussdistribute todescribedecisionmaking.Themodelisasfollows:

Where t'is the allowing decision time of the AEW.

The mode of the AEW about communication transmission，threat warning and survivability is similar with that of the fighter.

1.4 Cooperation

The paper combines cooperative subject with cooperative time as cooperation ability.If the two aircrafts are apart from more far，the difficulty of cooperative communication and maneuvering will more.The model is as follows:

Where KCOis the coefficient of cooperative structure.PC1iand PC1jare the reliability of radio station in the i th airplane and j th airplane.PC1iand PC1jare respectively the maximum affecting distance of radio station in the i th airplane and j th airplane.PC2iand PC2jare respectively the reliability of data link in the i th airplane and j th airplane，dmaxiand dmaxjare respectively the maximum affecting distance of data link in the i th airplane and j th airplane，t'is the allowing decision time of the AEW.

1.5 Determining weight

Determining weight adopts the method of information entropy.Details see the literature［15］.So the weightsareasfollows：ω1=0.45，ω2=0.18，ω3=0.13，ω4=0.17，ω5=0.07.

2 Designing genetic neural network

2.1 Building genetic neural network

The BP nerve network has strong parallel processing mechanism as well as the function approximation and generalization capability.It has special advantage in operating speed on the great sample problem about assessing air combat situation.But the BP nerve network has a salient weakness that is easy to fall into local minimum.The characteristic，strong capability of global search，can be used to optimize BP nerve network and enhance the efficiency and precision of solving problems.The detailed process is as Fig.1.

Fig.1 Process of genetic neural network

2.2 Parameter determination

The parameter determination of genetic neural network is as follows.The BP network number is set to 3.Inconsideration of each network training sample has 6 input values，which are attack，detection，survivability，communication，electronic countermeasures and alert，therefore node point number of inputs layer is 6.The node point number of output layer is 1 for air combat capability.The node number of the hidden layers is ensured by empirical formula.Where l is the node number of the hidden layers，n is the node number of the inputs layer，m is the node number of the outputs layer，a is the adjusting number between 1-10.The initial node number of hidden layers is 3，then the node number will increase gradually，and the maximum error is set as 0.01.When the error is at its minimum，the node number of hidden layers will be chosen.The population of genetic algorithm is set to 40，the crossover probability is 0.3，the mutation probability is 0.01，the maximum number of evolution is 100.

3 Data normalization

The results of the training will be used to calculate the relative close degree（pij）of theth aircraft of the red side and theth aircraft of the blue side according to formula（24）.

Where Eijis the power of the i th aircraft of the red side to the j th aircraft of the blue side，Ejiis the j th aircraft of the blue side to the i th aircraft of the red side.If pij＞0.5，it indicates that the i th aircraft of the red is superior to the j th aircraft of the blue side，and bigger of the numerical value，more obvious of the superiority.If pij=0.5，it indicates two sides are neck and neck.If pij＜0.5，it indicates that the i th aircraft of the red has disadvantages to the j th aircraft of the blue side，and smaller of the value，more obvious of the disadvantage.

4 Simulation analyses

Each of the red and blue side has 3 fighters in the air combat，among which the red side has information support of the AEW.The warning and detecting range of the AEW is vast，but that of the fighter is limited，so in the process from the blue formation entering the detecting range of the AEW to reach the fighters of the red side，the red formation has absolute advantage than the blue formation.The specific situation is referred in Fig2. Therefore in the simulated example，we only consider the situation after the fighters of two sides meeting，the initial position is shown in Table 1.

Table 1 Initial position

Fig.2 Situation in the distance R=77.8 km

Fig.2 indicates the situation of the red and blue formations in the initial position.In the case，specific parameters of fighters in both sides consult literature 7. In the decision making，the support of AEW can enhance fighting capabilities.In Fig.3，the formation includes the support of AEW.

Fig.4 Error evolution curve for nerve network training

Tab 2 Situation in the distance R=77.8 km（red to blue）

Fig.4 describes the evolution process of the error in neural network training.We can see the error is re strained when it evolves to the 80th generation.Through using neural network to train the situation information of the red and blue sides，and calculating the relative close degree with formula（24），we can get the mutual advantage of both the red and blue sides，which is shown in Table 2.The mutual advantage order of both sides is p13＞p12＞p23＞p33＞p11＞p12＞p32＞p21＞p31.In the Fig.4，fighter formation of blue side is totally surrounded in the power range of the red side，and its power range is weakened due to the effect of the power range of the red side.So the red side has advantage to the blue side from the distribution of power，which accords with the results of neural network in Table 2.From the results of neural network assessment and the distribution of the power，accuracy of method in this paper is verified and it proves that information support can improve air battle capacity of the formation to a large extent.

5 Conclusions

A new method of assessment that combines power field with genetic neural network is proposed to solve the situation assessment problems in cooperative air combat with information support.The result of simulation indicates that the method，proposed in this paper，can not only use power field to describe the formation situation with information support，but also reflect the improvement of the formation fight capability with information support.It provides a new thinking and method for air combat situation assessment.

［1］XIA Q J，ZHANG A，ZHANG Y Z.Study on effectiveness evaluation of fighter plane formation cooperative combat［J］. Journal of System Simulation，2010，22（9）：2182-2189.

［2］LI C，DUANMU J S，LEI Y J，et al.Situation assessment based on cognitive maps and intuitionistic fuzzy reasoning［J］.Systems Engineering and Electronics，2012，34（10）：2064-2068.

［3］XIAO L，HUANG J，XU Z S.Modeling air combat situation assessment based on combat area division［J］.Journal of Beijing University of Aeronautics and Astronautics，2013，39（10）：1309-1313.

［4］LIAO H X，LUO J X，WANG Y.On threat assessment algorithm of multi-formation air combat under command of AWACS［J］.Electronics Optics&Control，2008，15（10）：55-88.

［5］GUO H，XU H J，LIU L.Target threat assessment of air combat based on support vectormachines for regression［J］.Journal of Beijing University of Aeronautics and Astronautics，2010，36（1）：123-126.

［6］SANDEEP M，GERARD R，CHRISTINE I，et al.OLIPSA：On-line intelligent processor for situation assessment［C］//Proc.of the second annual symposium and exhibition on situation awareness in the tactical air environment，1997：440-448.

［7］NARAYANA R P，SUDESH K K，GIRIJA G.Situation assessment in air-combat：a fuzzy-bayesian hybrid approach［C］//Proc.Of the international conference on aerospace science and technology，india institue of science，bangalore，2008：63-68.

［8］NGUYEN X T.Threat assessment in tactical airborne environments［C］//Proc.of the Fifth International conference on information fusion，2002：1300-1307.

［9］ZHOU T，REN B，YU L.Modeling of air combat analysis based on combat power field［J］.Journal of System Simulation，2008，20（2）：738-745.

［10］JIN L，ZHANG S G，SUN J B.Air combatability and sensitivity analysis of modern fighter aircraft［J］.Journal of Beijing University of Aeronautics and Astronautics，2009，35（1）：82-86.

［11］BARTON D K.Radar system analysis and modeling［M］. Beijing：Publishing House of Electronics Industry，2007：284-307.

［12］SARKAR T K，WANG H，ADVE R S.A deterministic least squares approach to space time adaptive processing（STAP）［J］.IEEE TransAntennas Propagat，2001，49（1）：91-103.

［13］BALL E.The fundamentals of aircraft combat survivability analysis and design［M］.New York：American Institute of Aeronautics and Astronautics Inc，1985：100-131.

［14］ZHU B L，ZHU R C，XIONG X F.Assessments of effectiveness for aircraft［M］.Beijing：Aviation Industry Press，1993.

［15］GUO H，XU H J，LIU L.Measurementof combat effectiveness of early-warning aircraft based on interval number［J］.Systems Engineeringand Electronics，2010，32（5）：1007-1010.

［16］ZHANG Y，JIANG Q S.Effectiveness evaluation of earder-actuatedreentry vehicle.Under-actuated systemrequiresless control input mechanism compared with fully actuatedsystem，sothe methodproposedcan ly-warning aircraft based on hierarchy TOPSIS［J］.Systems Engineering and Electronics，2010，32（5）：1007-1010.

［17］ZHENG B H，ZHANG Z F，FANG G T，et al.Influence factor analysis of command and control cooperation efficiency in operating system［J］.Fire Control&Command Control，2012，37（7）：70-73.

Situation Assessment on Cooperative Air Combat with Information Support

AN Chao1，LI Zhan-wu1，2，CHANG Yi-zhe1，YANG Hai-yan3
（1.Aeronautics and Astronautics Engineering College，Air Force Engineering University，Xi’an 710038，China；
2.College of Electronic Communication，North western Polytechnical University，Xi’an 710072，China；
3.ATC navigation College，Air Force Engineering University，Xi’an 710051，China）

Considering on the remaining problem in current situation assessment of air combat，such as lack of visualization and crude of the model，a situation method，which is consist of combat power field and neural networks，is proposed and applied in the cooperative air combat with information support. Optimized by genetic algorithms，the BP neural networks is applied in situation assessment on formation air combat ability.The method is verified by the simulation and the result shows the method in the paper has advantages of visualization，figurativeness and integrity compared with former situation assessment methods.

information support，cooperative air combat，combat power field，situation assessment

V221.91

A

1002-0640（2016）12-0009-06

2015-11-17

2015-12-29

国家自然科学基金资助项目（61472441）

安超（1987-），男，山东泰安人，硕士研究生。研究方向：先进航空火力控制原理与技术。