A NOVEL DWELLING TIME DESIGN METHOD FOR LOW PROBABILITY OF INTERCEPT IN A COMPLEX RADAR NETWORK

Transcription

1 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) A NOVEL DWELLING TIME DESIGN METHOD FOR LOW PROBABILITY OF INTERCEPT IN A COMPLEX RADAR NETWORK Z. ZHANG,2,3, J. ZHU & S. SALOUS 3 Scence and Technology on Electonc Infomaton, Contol Laboatoy, People s Republc of Chna. 2 College of Electonc Infomaton, JangSu Unvesty of Scence and Technology, People s Republc of Chna. 3 School of Engneeng and Computng Scences, Duham Unvesty, UK. ABSTRACT To acheve the mpotant tactcal equement of low pobablty of ntecept (LPI) n the complex ada netwo, dynamcally contollng the emsson of the adas s vey necessay. A novel ada dwellng tme contol stategy based on an nteactng multple model algothm s pesented n ths pape, whch contols the dwellng tme of ada accodng to pedcted covaance matx dung tacng, tang advantage of the elaton model between the dwellng tme and the tacng pefomance. Fst, the complex ada netwo s bult fo taget tacng. Secondly, the nfluence of the dwellng tme s consdeed n the tacng pefomance of the complex ada netwo. Fnally, a decson wll be made afte the dwellng tme fo evey ada s obtaned by patcle swam optmzaton, the ada wth the smallest dwellng tme wll be selected to tac taget. The tacng accuacy and LPI pefomance ae demonstated n the Monte Calo smulatons. The esults ae valdated though the compason wth othe methods. Keywods: dwellng tme, nteactng multple model, low pobablty of ntecept, taget tacng. INTRODUCTION As we now, the less the emtted tme of the ada, the moe the excellent pefomance of the low pobablty of ntecept (LPI) []. To acheve the mpotant equement of LPI, dynamcally schedulng and contollng the dwellng tme of the ada dung the senso management s vey necessay. The wo n [2] fomalzes the typcal woload of a moden-phased aay ada and poposes a ate-based appoach to schedule ada dwells n a eal-tme manne. The pape [3] develops a genealzed famewo fo the ada tas schedulng poblem as an optmzaton model, and all ada tas paametes ae teated as vaables, theeby allowng geate schedulng flexblty and the ablty to handle moe tagets usng a sngle ada. The schedulng of tac dwells to mnmze ada enegy and tme wth an agle beam ada s consdeed n [4], whee the tade between hghe enegy wavefoms and ada tme s futhe nvestgated. The algothm n [5] ntoduces tme wndows that specfy allowable ealness and lateness of ada tass, and poposes a channg pocess that combnes the dwell tmes and the tme wndows of tass wth consecutve potes. The wo of Seveson and Paley [6] pesents a dstbuted, consensus-based appoach to optmze ada esouce management fo ballstc mssle suvellance and tacng. Almost all of those wos concen the pefomance of the sngle ada, and thee ae few studes on the desgn of dwellng tme and adas selecton n the complex ada netwo fo excellent LPI pefomance. In ths pape, a novel schedulng algothm fo dwellng tme n ada netwos s poposed. The emande of ths pape s oganzed as follows. Sectons 2 and 3 descbe the nteactng multple model (IMM) algothm of taget tacng and patcle swam optmzaton (PSO), espectvely. Secton 4 pesents the dwellng tme schedulng method n senso netwo n detal. Smulatons of the poposed algothms and compason esults wth othe methods ae povded n Secton 5. The conclusons ae pesented n Secton WIT Pess, ISSN: (pape fomat), ISSN: (onlne), DOI: /DNE-V0-N

2 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) 3 2 TARGET TRACKING ALGORITHM BASED ON IMM IMM method s used fo tacng maneuveng taget n ths pape. Many dynamc models ae used fo matchng dffeent moton states, and the swtch pobablty of a dffeent model s a Maov chan. Kalman flteng s employed fo the estmaton of taget state and the update of model pobablty n the algothm, and all dynamc models ae paallel pocessed and the model pobablty epesents model swtch [7]. 2 All the dynamc models ae: M = { m, m,..., m }, m s the th model used at tme, the swtch pobablty fom model m to model m s Pm m + { + } = p, m m M,, p =, =,2,, + = m ( ) s the pobablty of model, m ( ) = P{ m ( ) = Z }. Let X() and Z() epesent the state vecto and the obsevaton vecto, espectvely; the state equaton and tansfe equaton at tme ae: and X ( + ) = f ( + ) X( ) + w( ) () Z( ) = H X ( ) + v ( ) whee w () and v () ae statonay whte-nose pocesses wth covaance matces Q () and W() of model, f () s the tanston matx and H s the obsevaton matx. Evey ecuence of the IMM algothm contans: nteactng of nput, model s flteng, update of model pobablty and nteactng of output. 2. Inteactng of nput Utlzng all the states and model pobabltes fom last ecuence, the computaton of nput state ˆ ( t ) and covaance P 0 ( t ) of model can be expessed as X 0 0 = Xˆ ( ) = Xˆ ( ) μ ( ) (3) P ( ) = P( ) + αα.. μ ( ) (4) T 0 = ˆ ˆ α = [ X( ) X 0 ( )] (5) (2) 2.2 Model s flteng μ = P M = M = Z = ( ) { ( ) ( ), } p μ ( ) = p μ ( ) (6) In the lght of step () and obsevaton data Z(), the Kalman flteng of evey model s as follows: The pedcton of state and covaance fo model has the fom of Xˆ ( ) = f ( ) Xˆ ( ) (7) 0 P ( ) ( ) 0 ( )( ( )) T = f P f + Q (8) The esdual eo epesented by obsevaton data and estmaton of last obsevaton s

3 32 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) ˆ v( ) = Z( ) HX ( ) (9) The vaance matx of the esdual eo s obtaned by the follow equaton: Computaton of the flteng gan s gven as Equaton of updated state s Estmaton of the covaance s S HP H W (0) ( ) ( )( ) T = + ( ) K P H S T ( ) = ( )( ) ( ( )) ( - ) () P( ) = I K ( ) H P ( ) (2) P ( ) I- K ( ) H P ( ) (3) = ( ) 2.3 Updatng of the model pobablty The model pobablty s ecusvely updated as Λ μ Λ ( ) p μ ( ) = ( ) = = = ( ) s the lelhood functon of model at tme. Λ ( ) p μ ( ) (4) 2.4 Inteactng of output The fnal estmaton of state vecto fom all the models state s Estmated matx of covaance s deved as Xˆ( ) = Xˆ ( ) μ ( ) (5) = whee b= [ Xˆ ( ) ˆ X ( )]. T P( ) = μ ( )( P ( ) + bb ) (6) = 3 PARTICLE SWARM OPTIMIZATION (PSO) PSO algothm poposed by Kennedy and Ebehat [8] has been wdely used n many felds. It s an evolutonay algothm accodng to socal nteacton between ndependent patcles. In PSO method, evey potental soluton fo optmzaton poblem s supposed as a pont called patcle n the space. The swam composed by N patcles moves though the poblem space wth the movng velocty of each patcle. The poston and velocty of the th patcle s epesented as x = (x, x 2,, x N ) and v = (v, v 2,, v N ), espectvely, whee N s the dmenson of the space. The th patcle tacs ts pesonal best poston (pbest) as a vecto p = (p, p 2,, p N ); the global best poston (gbest) among all the patcles s epesented as p g = (p g, p g2,, p gn ).

4 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) 33 Usually the optmzaton poblem can be fomulated as follows: mn f(x), subect to g(x) 0 (7) whee X=(x, x 2,, x m ). The steps of PSO method ae outlned as follows:. Geneatng the ognal patcle poston and velocty. 2. Exceedng bounday contol. 3. Computng the ftness functon f(x) fo each patcle. 4. Updatng the pbest : pbest + ( + + x ) ( f f x < f pbest ) = pbest othewse (8) 5. Updatng the gbest : gbest + ( + + pbest ) ( f f x < f pbest ) = gbest othewse (9) 6. Updatng the poston and velocty: v + = w v + c ( pbest x ) + (20) d d d d c2 2 ( gbestd xd ) x = x + v (2) + + d d d whee =,2, n, d =,2 m, n and m ae the numbe of patcles and dmensons n the space, w epesents the neta weght facto whch s between 0.4 and 0.9, c and c 2 ae acceleaton constants usually selected as 2, and 2 ae unfomly dstbuted andom numbes n (0, ). 7. Retun to step (2) and go on the teaton. 4 DWELLING TIME ALLOCATION ALGORITHM BASED ON PSO 4. Desgn fo covaance matx W of measuement nose The covaance matx W of measuement nose s contolled by the emtted enegy. As we now, ada equaton at tme s as follows: R PGGls = (22) L 2 4 av T R tb 3 (4 p ) KTRSNR whee t B s the sngle dwellng tme of the beam fom the nomal decton at tme, P av s the aveage adated powe, G R s the eceve gan, s s the ada coss secton of the taget, K s the Boltzmann constant, T R and L ae, espectvely, effectve nose tempeatue and ada system loss, R s the detecton ange, G T s the tansmt gan, S NR epesents the sgnal-to-nose ato of the system at tme. Suppose when the taget whose ange s R 0, the ada has to emt the powe P av0, and the ada equaton becomes

5 34 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) R P G G ls = L (23) 2 4 av0 T R 0 0 tb0 3 (4 p ) KTRSNR 0 Combnng (22) wth (23), the emtted sgnal-to-nose ato at tme can be wtten as S tps R = (24) 4 B av NR0 0 NR 4 tb0pav0 R whee the emtted powe s supposed to be a constant paamete n ths pape. The sngle pulse sgnal s adated by the ada, and the covaance of the measuement nose can be denoted as 2 ctp 0 8SNR = 2 3c W (25) wt c p S NR whee T p s the pulse wdth, c s the wave velocty, and w c s the cae fequency. We can see that dffeent t B can lead to dffeent W. Howeve, dung the tacng pocess, R s unnown befoe ada detecton. Theefoe, R n (24) s eplaced by R pe, whch s pedcted by R and v. R pe s pesented as R = R + v T pe R and v ae the taget s ange and velocty, whch ae estmated by the IMM tacng algothm at tme, and T s the tacng nteval. 4.2 Computaton of pedcted tacng covaance matx The pedcton of covaance fo model at tme can be epesented as (26) P ( ) ( ) 0 ( )( ( )) T + = f + P f + + Q (27) Then, the vaance matx S ( + ) and flteng gan K ( + ) can be wtten, espectvely, S ( ) ( )( ) T + = HP + H + W ( + ) (28) K P H S ( ) ( )( ) T + = + ( ( + )) (29) The covaance estmaton fo evey model can be epesented as P I- K H P (30) pe ( + ) = ( + ) ( + ) At last, the pedcted covaance matx s gven as whee m () s model pobablty at tme. pe pe P ( ) μ ( )( P ( )) (3) + = =

6 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) Dwellng tme allocaton algothm based on PSO The desed tacng covaance matx P des should be set fo the m adas n the netwo fst. Then, the dwellng tme of evey ada s selected as the patcles n the PSO, and then the mnmum and maxmum anges, veloctes ae desgned accodng to the adas pefomance. Intal locatons and veloctes of all patcles ae geneated andomly n whole seach space. Then, the ftness functon s desgned as f = mn(tace(p pe ( + ) - tace(p des ))) (32) Dung the PSO optmzaton, evey ada n the netwo wll select the dwellng tme T dw m, whch leads to the mnmum ftness functon. Then, a dwellng tme set can be gven as 2 m {,..., } T = T T T (33) dw dw dw dw To save most adaton tme and get the best LPI ablty of the ada netwo, the algothm wll choose the ada whch wll adate the mnmum dwellng tme n the netwo fo tacng at tme. 5 SIMULATION RESULTS In ths secton, Monte Calo smulatons ae pefomed to analyze the pefomance of the poposed dwellng tme schedulng algothm based on the PSO and pedcted covaance (PSO-PC). The IMM flte hee compses constant velocty (CV) model and coodnated tun (CT) ate model [7]. 5. Taectoy desgn Fgue shows the taget taectoy n 00s. Thee ae thee adas, whch ae labeled A, B and C n the ada netwo. The postons of the adas ae (0.80), (250.0) and ( 70,400), espectvely. 5.2 Compason of tacng pefomance The poposed dwellng tme desgn method (PSO-PC) of thee adas s ealzed n the smulaton, whch s also compaed wth the pefomance of evey sngle ada usng the schedulng stategy of dwellng tme n [6]. The oot mean squae eo (RMSE) of tme and the aveage ootmean-squae eo (ARMSE) of the whole tacng pocess can be fomulated as (34) and (35), espectvely: M c m 2 RMSE ( ) = ( x ˆ x ) (34) M c m = N ARMSE = t RMSE ( ) (35) N t = whee M c s the numbe of the Monte Calo smulaton, x s the tue state of the system, ˆx m s the estmated vecto at the mth smulaton, and N t s the total tacng tme n evey smulaton. In the smulaton, M c =00 and N t =00. Fgue 2 shows the ange RMSE of the poposed method dung the tacng. Fgue 3(a) and (b) shows the RMSE of the poposed method n X and Y decton, espectvely. Table shows the ARMSE of the ange, X decton, and Y decton. Compaed wth evey ada, we can see that the poposed method of PSO-PC pesents almost the same excellent tacng accuacy.

7 36 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) Fgue : Taectoy of the taget. Fgue 2: Compason of tacng pefomance.

8 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) 37 (a) (b) Fgue 3: Compason of tacng pefomance: (a) tacng pefomance of X decton and (b) tacng pefomance of Y decton. Table : Compason of ARMSE. Method R-ARMSE (m) X-ARMSE (m) Y-ARMSE (m) PSO-PC Rada A Rada B Rada C Compason of dwellng tme As dwellng tme of PSO-PC, Rada A, Rada B and Rada C s shown n Fg. 4, we can see that the poposed method not only pesents excellent tacng accuacy but also educes moe adated tme. As Fg. 5 shows the adaton label of the adas, we can see the adas wo n tun n ode to obtan excellent tacng and LPI pefomance. 6 CONCLUSIONS In ths pape, we have pesented a new stategy of dwellng tme allocaton n the ada netwo based on the PSO method and pedcted covaance theoy. Accodng to the optmzaton esults of evey ada, the ada wth the mnmum dwellng tme n the netwo wll be selected to tac the

9 38 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) Fgue 4: Compason of dwellng tme. Fgue 5: Radaton label of the adas.

10 Z. Zhang et al., Int. J. of Desgn & Natue and Ecodynamcs. Vol. 0, No. 4 (205) 39 taget. The smulaton esults show that the poposed method can save much moe dwellng tme wth excellent tacng accuacy fo tacng sngle taget n the netwo. As fo the futue wo, ths algothm can be modfed to tac moe tagets n complex ada netwo. ACKNOWLEDGEMENTS Ths wo was suppoted by the Natonal Natual Scence Funds Fund (64079), Colleges of Jangsu Povnce Natual Scence Fund (4KJB50009), the Scence and Technology on Electonc Infomaton Contol Laboatoy Poect, Scentfc Reseach Stat-up Fundng fom Jangsu Unvesty of Scence and Technology, Fundamental Reseach Funds fo the Cental Unvestes (NJ204000), and a Poect Funded by the Poty Academc Pogam Development of Jangsu Hghe Educaton Insttutons. REFERENCES [] Kshnamuthy, V., Emsson management fo low pobablty ntecept sensos n netwo centc wafae. IEEE Tansactons on Aeospace and Electoncs Systems, 4(), pp. 33 5, [2] Kuo, T.-W., Chao, Y.-S., Kuo, C.-F. & Chang, C., Real-tme dwell schedulng of componentoented phased aay adas. IEEE Tansactons on Computes, 54(), pp , [3] M, H.S. & Gutoun, A., Vaable dwell tme tas schedulng fo multfuncton ada. IEEE Tansactons on Automaton Scence and Engneeng, (2), pp , [4] Glass, J.D., Bla, W.D. & Ba-Shalom, Y., Optmzng ada sgnal to nose ato fo tacng manoeuvng tagets th Intenatonal Confeence on Infomaton Fuson (FUSION), Salamanca, 7 0 July, 204, pp. 7. [5] Jang, D.-S., Cho, H.-L. & Roh, J.-E., A tme-wndow-based tas schedulng appoach fo multfuncton phased aay adas. 20 th Intenatonal Confeence on Contol, Automaton and Systems (ICCAS), Gyeongg-do, Octobe, 20, pp [6] Seveson, T.A. & Paley, D.A., Dstbuted multtaget seach and tac assgnment wth consensus-based coodnaton. IEEE Sensos Jounal, 5(2), pp , [7] Zhang, Z., Zhou, J., Wang, F., Lu, W. & Yang, H., Multple-taget tacng wth adaptve samplng ntevals fo phased-aay ada. Jounal of Systems Engneeng and Electoncs, 22(5), pp , 20. [8] Kennedy, J. & Ebehat, R., Patcle swam optmzaton. Poceedngs of IEEE Intenatonal Confeence on Neual Netwos, Apl, 995, pp