Missile Guidance Using Dual-Mode Seeker

Transcription

1 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: Schollink Resech Institute Jounls, ISSN: 4-76 jetes.schollinkesech.og Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 Missile Guidnce Using Dul-Mode Seeke De-Ming M, Jw-Kuen Shiu nd In Ho Deptment of Aeospce Engineeing, Tmkng Uniesity Dnshuei, Tiwn 57, Republic of Chin Deptment of Compute Science nd Infomtion Engineeing, De-Lin Institute Technology Tucheng, Tiwn 654, Republic of Chin Coesponding Autho: De-Ming M Abstct This study deoped n nlyticl method to quntittiy nlye the dul-mode seeke guidnce pefomnce. The method deies the seekes mesuement mods nd implements the Klmn filte. The study tkes the RFIR dul-mode seeke, which is poposed fo dnced longmedium nge i-to-i missiles, s the emple. The two-dimensionl guidnce loop is used to illustte the methodology nd dimensionless equtions e deied fo genelity. Afte discussing seel missile-tget scenios, the esults show tht the deoped scheme poides sufficiently ccute tget infomtion fo missile guidnce, not only fo dul-mode seekes, but lso when one of the seekes is jmmed. The methodology deoped in the study cn lso be pplied to incese the ccucy of tget tcking. Keywods: dul-mode seeke guidnce, f seeke, i seeke, klmn filte, popotionl nigtion I TRODUCTIO Multi Senso Dt Fusion MSDF is used in mny diese fids, pticully in mility infomtion systems [Ceuti, : Benskeu nd Rheume, 7] nd utonomous obotics [Luo, Yih nd Su, ]. MSDF is equied to combine nd pocess the dt fom multiple sensos nd cn poide moe ccute nd ible infomtion thn using single senso [Chong, Moi, Chng, nd Bke, ; Wlt nd Llins, 99]. This hs tditionlly been pefomed by some fom of Klmn [Go nd His, ] o Byesin filte. In ecent yes, soft computing techniques such s fuy logic nd tificil neul netwoks ANNs he lso been discussed fo dt fusion [Muphy, ]. Etensie efeences fo the chitectues, computtionl methods, lgoithms, nd pplictions of the multi senso dt fusion techniques cn be found in [Hll nd Llins, 997] nd [Smith nd Singh, 6]. The cuent tend in guidnce technologies is the multi-mode guidnce system with multi-mode seeke. In [Mot nd Pjitno, ], neuo-fuy multisenso dt fusion bsed on tget tcking system ws pesented. This method poided the cpbility of minimiing the noise tht contmintes the senso mesuements nd of ecluding inlid mesuements fom being used in the estimtion pocess. A missile guidnce system with ideo cme on-bod, which eceies dt fom goundbsed d, is discussed in [Mlyej, Mncheste, nd Skin, 4]. A constuctie senso fusion lgoithm is pesented, which llows fo ey estictie bit-te constints on the dt sent fom 66 the gound sttion to the missile. The ppliction of neul netwok in n Infed-Rd Dul-mode Guidnce System with el time tcking cpbility is pesented in [Yng nd Zhu, 7], nd the method is demonstted by simultion. The ppliction of missile guidnce fo tget imge tcking with n on-bod fowd looking infed FLIR cme nd n on-bod millimete we d MMW pointed towd gound tget is discussed in [Qi nd Shi, 8]. A nonline filte using low-cost mesuements fom stpdown seeke, ided by n IMU, mgnetometes, nd bomete, is designed in [Yun, Ryoo nd Song, 8] fo tcticl missile guidnce. Fo the guidnce system of typicl long nge nd medium nge i-to-i missiles, mid-couse guidnce utilies the nigtion dt fom the onbod inetil nigtion system nd the updted tget infomtion down-linked fom the cie icft, nd the teminl guidnce utilies the tget infomtion fom the ctie dio fequency RF seeke to clculte the guidnce commnd. To counte the missile ttck, ectonic wfe tctics e implemented by the tget icft to confuse o jm the missile s seeke. To counte-counte the tctics, one ltentie fo the missile s guidnce system is to impoe the cpbility of the tget infomtion pocess o to use the dul-mode seeke to incese the ccucy of the tget cquisition nd educe the jmming effect. Fo emple, the infed IR seeke is dded to cquie the tget infomtion to einfoce tht of the ctie RF seeke. Bsiclly, the technique of dt fusion is used to blend the tget

2 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 infomtion fom the IR nd the RF seekes to impoe the ccucy of the tget dt. Howee, it fils to cquie the published nlytic infomtion on the dul-mode seeke, een if it is impotnt. Theefoe, the pupose of the study is to deop n nlyticl methodology to elute qulittiy nd quntittiy the implementtion the dul-mode seeke. In this pticul emple, the ctie RF nd IR seekes e specified. The study deops the seekes mesuement mods nd pplies the etended Klmn filte to design the methodology. The key to successfully implementing the Klmn filte is to know the system s dynmics befoehnd. To illustte the methodology, popotionl guidnce is used in the two-dimensionl missile-tget geomety. In ddition, the dimensionless goening equtions e deied to genelie the nlysis. MATHEMATICAL MODEL The tget s tie position ecto nd ocity tie to the missile e: R R T R M V VT VM whee the subscipt T epesents the tget, nd M the missile. Theefoe, the components of the line of sight ngle between the missile nd the tget e gien by: sin Ry R tn R R The closing ocity between the missile nd tget is detemined by the eqution: V V R R c Fo the ctie d seeke, the mesuements e the line of sight ngles,,, the tes of chnge of the line of sight ngles &, &, the tie position R, nd the closing ocity V c. The sttes of the missile-tget geomety e the components long the missile body es of the tie position, nd the closing ocity. Theefoe, the tionships between the sttes nd the mesuements e: ˆ % R ˆ % R y %& ˆ& R ˆ H RF hot ' s %& & V R% Rˆ V y V% c Vˆ V c 5 whee H RF is the mesuement mti fo the d seeke, gien s R Ry R RB RBy RB RB RBy RB VB VBy VB HRF & RB RBy RB VB VBy VB R R R RB RBy R B Vc Vc Vc Vc Vc Vc RB RBy RB VB VBy V B 6 Fo the IR seeke, the mesuements e the line of sight ngles, nd the tes of chnge of the line of sight ngles &, &. The sttes e the tie nge nd ocity. Thus, the tionships between the sttes nd the mesuements e: tn R R sin Ry R & sin V cos V R & cos sin V cos V sin sin V R y 7 R R Ry R Similly, lineiing the equtions yids: R B tn R R ˆ R % By sin Ry R ˆ % R B & sin V cos V R R ˆ H IR hot ' s %& & VB & cos sin V cos Vy sin sin V R %& ˆ V & By Vc VR VyRy VR R VB 4 8 Lineition the boe equtions, yids: whee H IR is the mesuement mti of the IR seeke: 67

3 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 RB RBy R B RB RBy RB H IR RB RBy RB VB VBy VB RB RBy RB VB VBy VB 9 Combining the mesuement mtices H RF nd H IR obtins the ugmented mesuement mti fo the dul-mode seeke: H IR H H RF This is X6 mti; hence, by using dul-mode seeke we he moe mesuements thn sttes. The pope utilition of the mesuements cn ccuty obtin the tget s infomtion tie to the missile een when one of the seekes is out of seice. To genelie the nlysis, dimensionless equtions e deied. The efeence quntities e defined s: Refeence length initil nge, R Refeence time initil estimted time-to-go, R V M Thus, the dimensionless quntities e: R R, R R, R R, by y y, τ R V, τ t τ, M d d &, &, dτ dτ V V, V V, V V, M y y M M c y y To demonstte the methodology, we implement the two-dimensionl missile-tget geomety Fig. whee tn & sin cos c nd the implementtion of the etended Klmn filte [Gb, 974] suggests tht the stte equtions e: & y & y & & n n sin γcos γcos sinγ sin n sin ψcos ψcos sinψ sin T c c & n n cos ψcos ψcos sinψ sin y Ty c & n n cos γcos γcos sinγ sin T c whee n T, n T e the inetil components of the tget ccetion. The missile s ccetion commnd pependicul to the line of sight n c cn be clculted fom the popotionl guidnce [Zchn, 994], nd is the missile s flight pth ngle: n &, n & c c c c γ tn m m, ψ tn my m 4 The lineied stte equtions e then: δ & δ δ & δ & & & & δ & δ δ & & & & & δ 5 whee the ptil deities & e gien in the Appendi. The dimensionless mesuement mods fo the two-dimensionl IR- nd RF-seekes e gien by: h RF c c c c 6 nd h IR 7 Similly, the deities e gien in the Appendi. Theefoe, the simultion block digm is gien in Figue. In this figue, h is the dimensionless ugmented mesuement mod, gien by Eq., 68

4 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 nd K is the Klmn gin mti gien by the following eqution: T T K k Pkh k [ hkpkh k R k ] 8 whee P is the coince mti, nd the updted lue is gien by: P [ I K h ] P 9 k k k k Its time popgtion is: T P& t F t, t P t P t F t, t Q t whee function F is the lineied function of Eq., o the 4X4 mti gien by Eq. 5. By djusting the lues of the seekes coince mtices P, we cn simulte the sttus of ech seeke. SIMULATIO RESULTS A D DISCUSSIO S Thee cses e discussed using the dimensionless equtions. Consideing the cses of side ttck, nd ssuming the tget does not pefom n esie mneue, the dimensionless speed of the missile is., the mimum ccetion is, the speed of the tget is.4, nd the initil dimensionless distnce between them is.. In the fist cse, thee is no noise fo both the RF nd IR seekes. This is the stndd cse nd the missile cn successfully intecept the tget. In Figue, the tjectoies of the missile _m nd the tget _t e shown nd the miss distnce is In Figue 4, the ccetion of the missile is gien. As epected, the ccetion jumps to its mimum lue when inception begins nd deceses gdully to eo t the point of inteception. Fo the second cse, we ssume % ndom noise le fo the IR seeke nd noise fee signl fom the RF seeke. Figue 5 shows the missile s ccetion histoy. It shows tht the ccetion of missile jumps to the high lue nd then deceses gdully in the fist cse. When the missile is bout to intecept the tget, the ccetion eches its limit m. Fom the simultion esult, we cn see tht the missile still intecepts the tget successfully with miss distnce of In the thid cse, the RF seeke is ssumed to be jmmed, nd the RF signl is gien noise le of %. In Figue 6, the ccetion of the missile is pesented. Comped to the second cse, the ccetion eches its limit s the missile ppoches the tget, which is chnging moe pidly. Agin, fom the simultion esult, the missile cn intecept the tget with miss distnce of.9-4. The thid cse shows tht by pplying the guidnce scheme we he deoped, the missile cn intecept the tget successfully een if the RF seeke filed. In the cses of side ttck, simil esults wee obtined t the beginning of the intecept. The diffeences ise fom the noise le imposed becuse the popotionl guidnce we he implemented equies the closing ocity infomtion. In the second cse, the noise comes fom the IR seeke nd the infomtion bout closing ocity is not ffected. In the thid cse, the ctie RF seeke is ssumed to be jmmed, which is the souce of the closing ocity infomtion. The simultion esults show tht dmtic ccetion contol is equied in the thid cse. CO CLUSIO S This study poides quntittie method fo eluting the guidnce fo dul-mode seekes. The deoped scheme poides sufficiently ccute tget infomtion fo missile guidnce, not only fo dul-mode seekes, but lso fo when one of the seekes is jmmed. In ddition, the scheme cn lso be used fo only one seeke, which inceses the ccucy of the tget infomtion fo guidnce puposes. ACK OWLEDGEME T The Ntionl Science Council, Republic of Chin, sponsoed this wok. The contct numbe is NSC REFERE CES Benskeu, A. R. nd Rheume, F., Adptie dt fusion nd senso mngement fo mility pplictions Aeospce Science nd Technology, Vol., Issue 4, My 7, pp.7-8. Ceuti, M.G., Dt Mngement Chllenges nd Deopment fo Mility Infomtion Systems, IEEE Tns. Knowledge nd Dt Eng., ol. 5, no. 5, pp , Sept.Oct.. Chong, C.-Y.; Moi, S.; Chng, K.-C nd Bke, W.H., Achitectues nd Algoithms fo Tck Assocition nd Fusion, IEEE Aeospce nd Electonic Systems, ol. 5, no., pp. 5-, Jn.. Go, J.B. nd His, C.J., Some Remks on Klmn Filtes fo the Multisenso Fusion, Infomtion Fusion Vol., pp. 9-,. Gb, A., edito, Applied Optiml Estimtion, The M.I.T. Pess, 974. Hll, D.L. nd Llins, J., An Intoduction to Multisenso Fusion, Poc. IEEE, ol. 85, no., Jn Luo, R.C.; Yih, C.C. nd Su, K.L., Multisenso Fusion nd Integtion: Appoches, Applictions, nd Futue Resech Diections, IEEE Sensos J., ol., no., pp. 7-9, Ap.. Mlyej, V.; Mncheste, In R, nd Andey V. Skin, A.V., Pecision Missile Guidnce using RdVideo Senso Fusion with Communiction 69

5 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 Constint 4 5th Asin Contol Confeence, Vol.,pp.87-85,DOI:.9ASCC Mot, N. nd Pjitno, P., A multisenso dt fusionbsed tget tcking system, IEEE Intentionl Confeence on Industil Technology, Vol., pp.47-4, DOI:.9ICIT Muphy, R.R, Senso Fusion, Hndbook of Bin Theoy nd Neul Netwoks, Bdfod Book,. Qi, L. nd Shi, Z., A Method fo FLIR Tget Tcking Bsed on Distnce Updting, 8 Congess on Imge nd Signl Pocessing, pp.5-9, DOI:.9CISP Smith, D. nd Singh, S., Appoches to Multisenso Dt Fusion in Tget Tcking: A Suey, IEEE Tnsctions on Knowledge nd Dt Engineein,, Vol. 8, NO., Dec. 6, pp Wlt, E. nd Llins, J., Multisenso Dt Fusion, Atech House, 99. Yng J. P. nd Zhu X.P., Appliction of neul netwok in Infed-Rd Dul-mode Guidnce System, 7 IEEE Intentionl Confeence on Contol nd Automtion, pp , DOI:.9ICCA Figue - Simultion block digm fo two dimensionl guidnce -. _t _m _m Yun, J.; Ryoo, C.-K nd Song, T.-L., Stpdown Sensos nd Seeke Bsed Guidnce Filte Design, 8 Intentionl Confeence on Contol, Automtion nd Systems, pp DOI:.9ICCAS _t _m Zchn, P., Tcticl nd Sttegic Missile Guidnce, nd ed., Pogess in Astonutics nd Aeonutics, Vol. 57, AIAA, _t Figue the tjectoies of the missile nd tget Figue Two-dimensionl missile-tget geomety 64

6 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: Figue 4 the missile s ccetion fo the stndd cse time Figue 6 the missile s ccetion fo the cse of RF seeke jmmed time Figue 5 the missile s ccetion fo the cse of % noise le dded to the IR seeke time Appendi - The deities of the stte equtions nd mesuement mods A. The deities of the lineied stte eqution n 4 n n 4 n 4 n n 64

7 Jounl of Emeging Tends in Engineeing nd Applied Sciences JETEAS 4: ISSN: 4-76 n 4 n B. The deities fo the seeke s mesuement mods 4 b b 4 b b c c c c 64