Taget Aocation Study fo Fomation Ship-ToAi Missie System Based on the Missie Fie Zone Division Jihua Dou and Shouquan Dong 667#, Jiefang Road, Zhongshan Distict, Daian City, China Emai: doujihua@6com Abstact Based on the poposed definition method of singe ship-to-ai missie fie zone, hoizonta secto division methods of fomation ship-to-ai missie fie zone in typica odes ae poposed, the singe missie fie zone can be divided and detemined Aftewads, the fomation taget aocation methods based on the missie fie zone division ae poposed, incuding the fomation taget aocation method based on the singe type missie fie zone division, the fomation taget aocation method based on the mutitypes missie fie zone division, which can be used to assist the fomation missie taget aocation decision suppot Index Tems ship-to-ai missie, fomation, taget aocation I fie zone A Hoizonta Secto of Singe Ship-To-Ai Missie Fie Zone The paametes of hoizonta secto of the singe missie fie zone ae the secto numbe, and the stating side ange, temination side ange, maximum distance of the secto Based on the hoizonta secto division methods of the fomation missie fie zone in typica odes, the paametes of hoizonta secto of the singe missie fie zone in typica odes can be detemined Assume that be the maximum distance of the secto, Lys be the maximum hoizonta pojection vaue of the sope distance of the missie ki zone, Tf be the missie system combat eaction time, Vm be the maximum taget speed can be cacuated by division, INTRODUCTION =Lys+VmTf Taget aocation fo fomation ship-to-ai missie system is the decision-making pocess of assigning aiving tagets to the missie system Because the ai defense capabiity of the fomation missie system is detemined by the fomation missie fie zone, taget aocation fo the fomation missie system shoud be based on the missie fie zone Pio methods ae used fo taget aocation fo the fomation missie system, such as genetic agoithms, impoved hybid genetic agoithm, adaptive chaotic patice swam optimization method, distibution estimation agoithm4, hybid patice swam optimization method5 the fomation missie fie zone isn t consideed by the above methods In this pape, definition method of the singe missie fie zone is poposed, the fomation taget aocation methods based on the missie fie zone division ae poposed, which can be used to assist the fomation missie taget aocation decision suppot B Paametes of Singe Ship-To-Ai Missie Ki Zone6 The fist paamete is the aveage sope distance of nea bounday of the singe missie ki zone, it is defined by Ds The second paamete is the maximum eevation ange of nea bounday of the missie ki zone, it is defined by β The thid paamete is the owe bound of the missie ki zone, it is defined by Hd The fouth paamete is the highe bound of the missie ki zone, it is defined by Hg The vetica pane pojection of the singe missie ki zone is shown in Fig, the missie ki zone can be obtained by otating Fig in the hoizonta secto H Hg Vm Hd II DEFINITION METHOD OF SINGLE SHIP-TO-AIR MISSILE FIRE ZONE Ds β L Figue Vetica pane pojection of singe ship-to-ai missie ki zone Singe ship-to-ai missie fie zone is a theedimensiona aispace, whose paametes ae as foows III Manuscipt eceived August, 0; evised Juy 8, 04 05 Engineeing and Technoogy Pubishing doi: 070/joace4-45 ( 4 HORIZONTAL SECTOR DIVISION METHODS OF FORMATION SHIP-TO-AIR MISSILE FIRE ZONE IN TYPICAL ORDERS
The fomation missie system must be of the same type when the hoizonta secto division is on Assume that the numbe of the ship of the fomation is thee A Singe Coumn Ode Thee is oveapping egion between the two adjacent missie fie zones fo the two missie systems onboad two adjacent ships in singe coumn ode, the est egion is the nonoveapping egion fo anyone of the two adjacent missie systems Foowing the pincipe of being esponsibe fo the haf of the oveapping egion fo the singe missie system, the hoizonta secto of the singe missie fie zone fo the singe missie system is its unoveapping egion pus the haf of the oveapping egion, which is shown in Fig with staboad case The potside case is the same as that of the staboad case In the end, the hoizonta secto of the fomation missie fie zone in singe coumn ode can be divided is the secto M4OM 5 whose ange inteva is [, ] B Singe Tansvese Ode Thee is oveapping egion between the two adjacent missie fie zones fo the two missie systems onboad the two adjacent ships in singe tansvese ode, the est egion is the nonoveapping egion fo anyone of the two adjacent missie systems Foowing the pincipe of being esponsibe fo age ight secto fo the missie system onboad the ightmost ship, and age eft secto fo the missie system onboad the eftmost ship, the hoizonta secto of the fomation missie fie zone in singe tansvese ode can be divided, which is shown in the soid ine of the Fig with staboad case The potside case is the same as that of the staboad case M P M B M 4 M B M 5 A A A A O O O Figue Hoizonta secto division figue of fomation ship-to-ai missie fie zone in singe coumn ode O O O M P N Assume that and be the minimum staboad ange and maximum staboad ange of the singe missie fie bounday, and be ship spacing, and the fa acs of the two adjacent ships (defined by O and O ae AB and AB espectivey, the two fa acs intesect at point P The ange POB is bisected by a staight ine (defined by OM, the ange POA is bisected by a staight ine (defined by OM Assume that M O B, M O A, PO O In the tiange POO, accos 7 Then, (accos, (accos The hoizonta secto of the missie fie zone fo each missie system of the fomation is shown in the soid ine of the figue The hoizonta secto of the missie fie zone fo the missie system onboad ship O is the secto AO M whose ange inteva is [, ] The hoizonta secto of the missie fie zone fo the missie system onboad ship O is the secto MOM whose ange inteva is [, ] The hoizonta secto of the missie fie zone fo the missie system onboad ship O Figue Hoizonta secto division figue of fomation ship-to-ai missie fie zone in singe tansvese ode The missie system onboad the ightmost ship O is esponsibe fo age ight secto, the hoizonta secto of its fie zone is keeping the oigina unchanged, it is the AO B whose ange inteva is [, ] secto The hoizonta secto of the missie fie zone fo the missie system onboad ship O is the nonoveapping egion pus the fouth of the oveapping egion between the two adjacent missie fie zones fo the two missie systems onboad ship O and ship O The fa ac of the hoizonta secto fo the missie system onboad ship O (defined by AB intesects with the hoizonta secto fo the missie system onboad ship O at point M and point N Then, MO P O N MO N 4 The hoizonta secto fo the missie system onboad ship O is the secto AO P pus secto OB Assume MO O, and NOO, that MO N Coodinate system of the poe is estabished, the position of the ship O is the coodinate poe, the B B 05 Engineeing and Technoogy Pubishing 4
positive diection is to the ight Assume that be the poa adius of any point in the coodinate system, the inea equation of the staight ine OA can be expessed as 7 sin[ ( ] sin( The O equation can be expessed as cos accos (, The inea equation of the staight ine OB can be expessed as ( sin( sin( cos (accos Then, the ange inteva, 4, the of the secto AO P is O B is ange inteva of the secto, 4 The hoizonta secto of the missie fie zone fo the missie system onboad ship O is the nonoveapping egion pus the fouth of the oveapping egion between the two adjacent missie fie zones fo the two missie systems onboad ship O and ship O, which can detemined by the same method as that of ship O C Oientation Ode A A M O R R Figue 4 Hoizonta secto division figue of fomation ship-to-ai missie fie zone in oientation ode Thee is oveapping egion between the two adjacent missie fie zones fo the two missie systems onboad N O B O B two adjacent ships in oientation ode, the est egion is the nonoveapping egion fo anyone of the two adjacent missie systems Foowing the pincipe of being esponsibe fo age ight secto fo the missie system onboad the ightmost ship, and age eft secto fo the missie system onboad the eftmost ship, the hoizonta secto of the fomation missie fie zone in oientation ode can be divided, which is shown in the soid ine of the Fig 4 with staboad case The potside case is the same as that of the staboad case The missie system onboad the ightmost ship O is esponsibe fo age ight secto, the hoizonta secto of its fie zone is keeping the oigina unchanged, it is the secto AO B whose ange inteva is [, ] The fa ac of the hoizonta secto fo the missie system onboad ship O (defined by AB intesects with the hoizonta secto fo the missie system onboad ship O at point M and point N Then, the hoizonta secto fo the missie system onboad ship O is the secto A O M pus secto NO B Coodinate system of the poe is estabished, the position of the ship O is the coodinate poe, the positive diection is OO Assume that the side ange of ship O ooking at ship O is, MO O R The inea equation of the staight ine OM can be expessed as sin( sin( R sin( The ange inteva of the secto A O M is [, ] R acsin (4 R Assume that O O N R, The inea equation of the staight ine ON can be expessed as sin( sin( R sin( acsin (5 R NO B is The ange inteva of the secto [, ] R The hoizonta secto of the missie fie zone fo the missie system onboad ship O can detemined by the same method as that of ship O D Heingbone Ode The heingbone ode can be seen as eft oientation ode and ight oientation ode Foowing the pincipe of being esponsibe fo the ight secto in the ight 05 Engineeing and Technoogy Pubishing 4
oientation ode, and fo the eft secto in the eft oientation ode, the hoizonta secto of the fomation missie fie zone in heingbone ode can be divided IV FORMATION TARGET ALLOCATION METHODS BASED ON SHIP-TO-AIR MISSILE FIRE ZONE DIVISION A Fomation Taget Aocation Method based on Singe Type Ship-To-Ai Missie Fie Zone Division When the fomation is of the singe type missie system, the fomation taget aocation method based on the singe type missie fie zone division is as foows Based on the definition method of the singe missie fie zone and the hoizonta secto division methods of the fomation missie fie zone in typica odes, the missie fie zone fo any missie system of the fomation can be detemined When any taget is within the missie fie zone fo any missie system, the taget is aocated to the missie system In the end, the fomation taget aocation esuts based on the singe type missie fie zone division can be obtained B Fomation Taget Aocation Method based on Muti-Types Ship-To-Ai Missie Fie Zone Division The fomation taget aocation method based on the muti-types missie fie zone division is as foows The fist step is to get the fomation taget aocation esuts fo the fomation singe type missie system though the fomation taget aocation method based on the singe type missie fie zone division The second step is to cassify the fomation missie system Based on the missie ange, the fomation missie systems incude the temina ange missie system, the shot ange missie system, the shot medium ange missie system, the medium ange missie system, the medium ong ange missie system, the ong ange missie system Fom the font pincipe to back pincipe, the fomation taget aocation esuts based on the muti-types missie fie zone division can be obtained ( Pioity fie pincipe of temina ange ship-to-ai missie system gives to temina ange taget Fo temina ange singe taget, it shoud be intecepted by the temina ange missie system, it shoudn t be intecepted by the shot ange missie system, the shot medium ange missie system, the medium ange missie system, the medium ong ange missie system, the ong ange missie system When the taget can be intecepted by the mutipe temina ange missie systems, it shoud be fied by the temina ange missie system with east tota numbe of the fied tagets ( Pioity fie pincipe of shot ange ship-to-ai missie system gives to shot ange taget Fo shot ange singe taget, it shoud be intecepted by the shot ange missie system, it shoudn t be intecepted by the shot medium ange missie system, the medium ange missie system, the medium ong ange missie system, the ong ange missie system When the taget can be intecepted by the mutipe shot ange missie systems, it shoud be fied by the shot ange missie system with east tota numbe of the fied tagets ( Pioity fie pincipe of shot medium ange shipto-ai missie system gives to shot medium ange taget Fo shot medium ange singe taget, it shoud be intecepted by the shot medium ange missie system, it shoudn t be intecepted by the medium ange missie system, the medium ong ange missie system, the ong ange missie system When the taget can be intecepted by the mutipe shot medium ange missie systems, it shoud be fied by the shot medium ange missie system with east tota numbe of the fied tagets (4 Pioity fie pincipe of medium ange ship-to-ai missie system gives to medium ange taget Fo medium ange singe taget, it shoud be intecepted by the medium ange missie system, it shoudn t be intecepted by the medium ong ange missie system, the ong ange missie system When the taget can be intecepted by the mutipe medium ange missie systems, it shoud be fied by the medium ange missie system with east tota numbe of the fied tagets (5 Pioity fie pincipe of medium ong ange shipto-ai missie system gives to medium ong ange taget Fo medium ong ange singe taget, it shoud be intecepted by the medium ong ange missie system, it shoudn t be intecepted by the ong ange missie system When the taget can be intecepted by the mutipe medium ong ange missie systems, it shoud be fied by the medium ong ange missie system with east tota numbe of the fied tagets (6 Pioity fie pincipe of ong ange ship-to-ai missie system gives to ong ange taget Fo ong ange singe taget, it shoud be intecepted by the ong ange missie system When the taget can be intecepted by the mutipe ong ange missie systems, it shoud be fied by the ong ange missie system with east tota numbe of the fied tagets V EXAMPLE Assume that fomation incudes thee ships equipped ship-to-ai missie system, the ships ae numbeed as the st ship, the nd ship, the d ship Assume that the fomation aigning ange is 60 º, and the fomation couse is 0 º, and the ongitude and atitude of the fomation cente ae 4 N and 4 E espectivey, and the fomation spacing is 6 km, and =0km, and =5, and =50 Assume that the fomation is of the singe type missie system, based on the poposed hoizonta secto division methods of the fomation missie fie zone in typica odes, the hoizonta secto division figues of the fomation missie fie zone in singe coumn ode, singe tansvese ode, oientation ode and heingbone ode ae shown in Fig 5, Fig 6, Fig 7 and Fig 8 espectivey Though the poposed fomation taget aocation method based on the singe type missie fie zone division, when any taget is within the missie fie zone fo anyone of the thee missie systems, the taget is aocated to the missie system 05 Engineeing and Technoogy Pubishing 44
zone division can be used to get the fomation taget aocation esuts when the fomation is of the muti-types missie systems REFERENCES [] Figue6 6 Figue Figue Figue 5 5 [] [] [4] Figue88 Figue Figue77 Figue st ship st ship st ship [5] Figue 5-8 Hoizonta secto division figues of fomation ship-to-ai missie fie zone in singe coumn ode, singe tansvese ode, oientation ode and heingbone ode espectivey [6] [7] VI CONCLUTION Based on the poposed definition method of singe ship-to-ai missie fie zone, and the poposed hoizonta secto division methods of the fomation missie fie zone in typica odes, the singe missie fie zone can be divided and detemined Aftewads, the poposed fomation taget aocation method based on the singe type missie fie zone division can be used to get the fomation taget aocation esuts when the fomation is of the singe type missie system, the fomation taget aocation method based on the muti-types missie fie 05 Engineeing and Technoogy Pubishing J Z Xu, Mutipe fuzzy objective pogamming fo weapon taget assignment based on genetic agoithm, Miitay Opeations Reseach and Systems Engineeing, no, pp 70-74, 00 Y Sun, Y Wang, and J Y Li, Ai defense taget aocation based on impoved hybid genetic agoithm, Jouna of Sichuan Odnance, no 9, pp -6, 0 Y Wang, J J Zhao, W W Feng, L W Fu, and L X Chen, Ai defense taget distibution based on adaptive chaotic patice swam optimization, Compute Engineeing, no 0, pp 44-47, 0 S Gao, An estimation of distibution agoithm appied to weapon-taget assignment pobem and its paamete design, Jouna of Southeast Univesity, no, pp 78-8, 0 X Y Wang and J S Chen, Weapon taget assignment fo ai defense based on hybid patice swam optimization, Teecommunication Engineeing, no, pp -6, 0 T J Li, Ai Defense Missie System Fie Efficiency, Beijing: Beijing Univesity of Aeonautics and Astonautics Pess, 987, pp -5 M Tang, Eementay Mathematics, Beijing: Univesity of Eectonic Science and Technoogy Pubishing House, 004, pp -88 Jihua Dou is a instucto at 667#, Jiefang Road, Zhongshan distict, Daian City, China He eceived his PhD degee in Daian Univesity of Technoogy in China, he has pubished sevea opeationa eseach atices in vaious intenationa jounas and confeences Shouquan Dong is a pofesso at 667#, Jiefang Road, Zhongshan distict, Daian City, China He eceived his PhD degee in Nothwesten Poytechnica Univesity in China, his eseach aeas incude opeationa effectiveness 45