Journal of Compuer Scence 9 (2): 695-709, 203 ISSN: 549-3636 203 do:0.3844/jcssp.203.695.709 Publshed Onlne 9 (2) 203 (hp://www.hescpub.com/jcs.oc) NEW TRACK-TO-TRACK CORRELATION ALGORITHMS BASED ON BITHRESHOLD IN A DISTRIBUTED MULTISENSOR INFORMATION FUSION SYSTEM Lu Yu, Wang Hapeng, He You, Dong Ka and 2 Xao Chuwan Research Insue of Informaon Fuson, 2 Tranng cenre of New Equpmen, Naval Aeronaucal and Asronaucal Unversy, Yana, 26400, Chna Receved 203-08-5, Revsed 203-0-9; Acceped 203-0-29 ABSTRACT Track-o-Track correlaon (or assocaon) s an ongong area of neres n he feld of dsrbued mulsensory nformaon fuson. In order o perform accuraely denfyng racks wh common orgn and ge fas convergence, hs sudy presens ndependen and dependen B-hreshold Track Correlaon Algorhms (called BTCAs), whch are descrbed n deal and he rack correlaon mass and mulvalency processng mehods are dscussed as well. Then, Based on BTCAs, wo modfed Bhreshold Track Correlaon Algorhms wh average Tes Sasc (called BTCA-TSs) are proposed. Fnally, smulaons are desgned o compare he correlaon performance of hese algorhms wh ha of Snger s and Bar-Shalom s algorhms. The smulaon resuls show ha he performance of hese algorhms proposed n hs sudy s much beer han ha of he classcal mehods under he envronmens of dense arges, nerferng, nose and rack cross and so on. Keywords: Daa Fuson, Track Correlaon, Radar Nework, Fuzzy Se. INTRODUCTION Usng daa from mulsensor sysem, he mularge rackng echnology has been largely appled o mlary affars and publc affars. In some applcaons, he daa s colleced by many sensors dsrbued over a large area. In vew of he secury, vably and communcaon bandwdh of such a mulsensor sysem, s unrelable o process hese daa wh cenralzed mehod. However, he dsrbued srucure of processng mehod s apprecable. Track-o-rackassocao n problem (You e al., 996; Snger and Kanyuck, 97; Bar-Shalom and Formann, 988; Gul, 994; Kosoka, 983; You e al., 989; Bowman, 979; Chang and Youens, 982; Bar-Shalom and Chen, 2004; Kaplan e al., 2008; Tan and Bar- al., 20; Osbome e al., 20; Wang e al., 202; La Scala and Farna, 2002; Bar-Shalom, 2008) s a crux of dsrbued mulsensor sysem. I s a problem of how o decde wheher wo racks comng from dfferen sensor sysems represen he same arge. The ssue of racko-rack assocaon was frs consdered n presened by Snger and Kanyuach (97), assumng racks wh ndependen esmaon errors (Snger s algorhm). Then, Bar-Shalom exended o he case of correlaed errors n (Bar-Shalom and Formann, 988) (Bar-Shalom s algorhm) and Kosaka presened he Neares Neghbor (NN algorhm) n (Gul, 994). A K-Neares Neghbor algorhm was gven n (Kosoka, 983) and Bowman proposed a Maxmum lkelhood algorhm n (You e al., 989). Chang and Youens (982) ransformed rack-o- Shalom, 20; Bar-Shalom and Campo, 986; Mor e rack assocaon no Muldmensonal assgnmen Correspondng Auhor: Lu Yu, Research Insue of Informaon Fuson, Naval Aeronaucal and Asronaucal Unversy, Yana, 26400, Chna 695
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 problem and ge resolved wh Hunger/Munker mehod (Bowman, 979). In hese algorhms above, Snger s algorhm, Bar- Shalom s algorhm and NN algorhm are usually appled o he acual sysem. However, hese algorhms wll lead o false correlaon or mssng correlaon when under he envronmens of dense arges, nerferng, nose, rack cross and so on. To resolve hese problems of Snger s algorhm and Bar- Shalom s algorhm and n vew of hsory nformaon of racks, several b-hreshold rack correlaon algorhms based on he double hreshold deecon mehod are proposed n hs sudy. Besdes, effecve rack correlaon mass managemen and mulvalency processng mehods are dscussed as well o ge hgher correlaon precson and faser convergence... Sysem Descrpon The dynamcs of arge can be modeled n he dscree form as follows Equaon (): X(k + ) = F(k)X(k) + G(k)V(k) k =, 2..., () Where: X(k) R n = The sae vecor a me k V(k) R n = A sequence of zero-mean, whe Gaussan process nose wh covarance marx Q(k) and F(k) R n,n = The ranson marx of he sysem G(k ) R n,h = The nose dsrbuon marx The nal sae vecor s assumed normally dsrbued wh mean µ and covarance P(0). Therefore, one knows ha Equaon (2): E[V(k)] = 0, E[V(k)V(k)] = Q(k) δ (2) The measuremen of node a me k s gven by Equaon (3): ( ) = ( ) ( ) + ( ) (3) Z k H k X k W k where, W (k) s a sequence of zero-mean, whe, Gaussan measuremen nose vecor wh covarance R (k), H (k) R m,n s he measuremen vecor of he h node a 2 me k and I =, 2,,,M. Ths sudy only dscusses he suaon of M = 2. Assumng ha he measuremen nose sequences are ndependen Equaon (4): E[W (k)] = 0,E[W (k)w (k)']r (k) δ (4) Each node processes s observaons locally o produce he sae esmaon and predcon of a arge by kl kl usng Kalman fler. Assume ha he racks of arges had been naled by usng some mularge rackng algorhms and he sae esmaon of arges ganed n each node would be communcaed o a cenral processor, where rack fuson akes places. The sae esmaon of he h arge from he h sensor can be wren as follows Equaon (5): X (k + K + ) = X (k + K) + K (k + ) [Z (k + ) H (k + )X (k + k)] One-sep predcon of he sae s Equaon (6): X (k + k) = F(k)X (k k) (5) (6) and he one-sep predcon covarance s Equaon (7): P (k + k) = F(k)P (k k)f'(k) + G(K)F(k)G '(K) (7) he fler gan s Equaon (8): K (k + ) = P (k + k)h (k + )[H (k + )P ' (k + k)h (k + ) + R (k + )] ' and he updae sae covarance s Equaon (9): P (k + k + ) = [I K (k + )H (k + )P (k + k)] =,2,...,M, =,2,...,n.2. BI-Threshold Track Correlaon Algorhms (8) (9).2.. Independen and Dependen B-hreshold Track Correlaon Algorhm There s a double hreshold deecon sgnal processng mehod n he auomac radar deecon heory (La Scala and Farna, 2002). Based on he double hreshold deecon mehod, ndependen and dependen bhreshold rack correlaon algorhms are proposed here. Defne he ses of rack number naled by node and node 2 Equaon (0): U = {,2,...,n }' U 2 = {,2,...,n 2} (0) Le X (l) denoes he sae of arge esmaed by node. Assume ha for he same me one has an esmae X 2 j (l) of arge j from node 2. Denoe ɵ j(l) as he esmaon of ɵ j(l) and Equaon ( and 2): 696
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 ˆ (l) = X (l) X (l) 2 j j (l) = X (l) X (l) ( U, j U ) 2 j j 2 () (2) where, X and X j are he correspondng rue saes. One wans o es for he same arge hypohess H : X (l) and X 2 j (l) are he esmaons of he same arge Vs. H : X (l) and X 2 j (l) are he esmaons of dfferen arges. Then, he problem of rack correlaon becomes he hypohessesng problem. The Independen B-hreshold Track Correlaon Algorhm (IBTCA) can be descrbed as follows. Usng he es varable of Snger s algorhm Equaon (3 and 4): ξ (l) = (l)'[p (l) + P (l)] (l)l =,2,...,R 2 j j j j m j(l) = m j(l ) + m j(0) = 0, f ξ j(l) < δ 0 (3) (4) where, P (l) s he esmaon error covarance of node correspondng o arge and m (l) denoes he correlaon mass ha rack from node correlaed wh rack j from node 2 ll me l. The frs hreshold s se as follow Equaon (5): P{ ζ j(l) > δ H 0} = α (5) where, α s, say, 0.05. Then he es of H 0 vs. H s as follow Equaon (6): accep H f m (R) < L (6) j However, H 0 may no be acceped f m j (l) L, l = L, L+,,R for ha here may be more han one rack wll be correlaed wh rack. Ths problem s reaed n he followng par. In he Dependen B-hreshold Track Correlaon Algorhm (DBTCA), he es varable of Bar- shalom s algorhm s used Equaon (7): 2 2 ψ j(l) = j (l)'[p (l) + P j (l) P j (l) 2 ' (7) P (l)] (l) l =,2...R j 2 where, P j (l) denoes he cross-covarance Equaon (8): P (l) = [I K (l)h (l)][ Φ(l )P (l) Φ '(l ) 2 2 j j + G(l )Q (l )G '(l )][I K (l)h (l)] 2 2 j (8) whch s a lnear recurson wh nal condon P (0) = 0. Under he Gaussan dsrbued assumpons, 2 j ζ j (l) and ψ j (l) s ch-square dsrbued wh x n degrees of freedom. The x n here denoes he dmenson of sae esmaon vecor..3. Track Mass Desgnng Two knds of rack mass are desgned here. One of hem s rack correlaon mass and he oher one s rack separaon mass. Smlar o he assocaon mass (La Scala and Farna, 2002; Bar-Shalom, 2008), he rack correlaon mass m (l) denoes he mes of rack from node correlaed wh rack j from node 2 ll me l and he separaon mass of rack and j s defned as follow Equaon (9): D j(l) = D j(l ) + D j(0) = 0, ζj(l) δor ψj(l) δ From (8) one can see ha f Equaon (20): (9) D j(l ) > R L(WhereR and L havebeen se) (20) The correlaon es would no be performed beween rack and j a me l. Snce m j (l = R)<L (rack and j are uncorrelaed) mus be n exsence f D j >R-L a me l. Smlarly, he correlaon beween rack and j wll be nearly confrmed f Equaon (2): m j(l ) L (2) The correlaon es beween rack and j would be cease a me l f only one rack (j) can sasfy (20), hen rack and j would be regarded as he correlaed rack and performed no correlaon es any more. However, f here are more han one rack (j) can suffce (20), he correlaon es should be performed las l = R o gve a precse correlaon mass for he mulvalency processng laer. On he oher hand, he rack I wh no oher rack correlaed ll l=r wll be performed es n he nex cycle..4. Mulvalency Processng Mehod There are wo suaons where mulvalency processng mehod appled, one of hem s l = R and he oher s l<r. In case one, here are more han one rack (j) suffce for m j (l = R) L hus wll be correlaed wh rack. In hs case, rack j* whch maxmze he rack correlaon mass m j (l) wll be correlaed wh rack Equaon (22): 697
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 { } j* = arg max m (l = R) j j, j,..., j (22) j 2 q where, {j,j 2,..,j q }s he se of rack (j) correlaed wh rack. When here are more han one rack can maxmze rack correlaon mass m j (l), he rack j wll be acceped f Equaon (23 and 24): R ζ (R) = mn ζ (l)j* j, j,...j (IBTCA) (23) * * * { } j j* 2 q j* R l = R ψ (R) = mn ψ (l)j* j, j,...j (DBTCA) (24) * * * { } j j* 2 q j* R l = In case wo, he correlaon es wll be ceased f (9) s suffced. Oherwse, a emp sysem rack wll be se. Correspondng o a gven rack, he rack j* s acceped f j* argmax m j (l). If here are more han one rack (j*) acceped, he mulvalency processng mehod wll be appled. In hs case, he rack j wll be correlaed wh rack f **argmn D j (l). However, f here are more han one rack whch can be correlaed wh rack, he rack jp wll be acceped f Equaon (25): l ɶ j = arg mn x j (q) j { j, j,..., j } (25) P 2 r j* l q= Where Equaon (26): ɶ x j (q) = X (q) X j (q) (26) and { j, j 2,..., jr } s he se of rack (j*) can sasfy**argmn D j (l). Once j s correlaed wh rack, he correlaon es would no be performed o rack or j a me l. Snce he daa of rack ransformed seram by each sensor, se of L/R should be dynamc, such as /, 2/2, 2/3, 3/4, 3/5, 4/5, 4/6, 5/7, 6/8 and so on. Also one can see ha Snger s and Bar-Shalom s algorhm s a specfc presenaon of ndependen and dependen b-hreshold rack correlaon algorhm when L/R = /..5. Esmaon o Sans Correlaon Probably Le P (A) denoe he probably of sascal dsance from he same arge acceped by he frs hreshold. Accordng o he rule of x 2 es, P (A) = α (α s se n (5)). Assumng ha he cumulave R esmaon error swaches are sascal ndependen, P (A = Y) s bnomal dsrbued Equaon (27): P (A R L ) ( ) ( ) A R A A L = + = α α = α α (27) Then, he sans probably can be esmaed as follow Equaon (28): R A A R A ɵ Ps = P (A y) = C Rα ( α) (28) A= R L+ where, L s he second hreshold. From (28) one can calculae he sans probably n he case of L/R = 3/4 and L/R = 6/8: P ɵ s (3/ 4) 0.002256 P ɵ s (6/8) = 0.00002. Therefore, (28) can be used o se he value of L/R..6. Modfed B-Threshold Algorhms Based On Average Tes Sasc Bar-Shalom and Campo (986), a new sae sasc for correlaon hypohess s defned as follows Equaon (29): λ (k) = j = λ + ɵ k ɵ j(l)'c (l) ɵ j(l) l= j(k ) j(k)'c j (k) j(k) ɵ (29) 2 where, C (k) = P (l) + P (l) and λ j (0) = 0. Under he j j j Gaussan dsrbued assumpons, he ndvdual erms Equaon (30): ε (K) = ɵ ɵ (30) j j(k)'c j (k) j(k) Known as he normalzed esmaon error squared, are each ch-square dsrbued wh x n degrees of freedom, where x denoes he dmenson of sae esmaon vecor. I should be noced ha he sum of ch-square varables (λ j (k)) as an approxmaely chsquare dsrbuon wh x kn degrees of freedom (and hus approxmaely mean x kn and varance 2 x kn) (Bar-Shalom, 2008). Nex, a modfed funcon based on average es sasc for ndependen b-hreshold correlaon (IBCTA-ATS) s defned as follows Equaon (3): λj(k) ϕ j(k) = k = (l) P (l) + P (l) (l), ϕ (0) = 0 k 2 ˆ ˆ j j j j k l = (3) Approxmaely, ϕ j (k) s a ch-square dsrbued random varable wh x n degrees of freedom, whch can 698
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 be used for correlaon hypohess es. Then he es of H 0 vs. H s as follows Equaon (32): accep H0 f ϕj(k) δ(k), U, j U2 (32) The hreshold s se such ha Equaon (33): { j 0} P ϕ (k) > δ (k) H = α (33) where, α s he sgnfcance level wh α = 0.05. In IBCTA-ATS, rack mass and mulvalency processng mehod s as showed before. In vew of he dependence beween he esmaon errors from he wo rack fles arses from he common process nose,a dependen sb-hreshold correlaon algorhm based on Average Tes Sasc (DBCTA-ATS) s presened here. All seps of hypohess es for rack correlaon are as descrbed n IBCTA-ATS wh he followng modfcaons. Wh heknown cross-covarance P (l), es sasc n (3) s modfed o Equaon (34): 2 j arges are random and he nal posons of hese arges are normally dsrbued n a regon llusraed n Fg.. The nal velocy and azmuh of hese arges are unformly dsrbued n 4~200 m sec and 0~2 π, respecvely. Fgure, r, r 2 denoe he observaon ' ' radus, r,r denoe he radus of undeecable area and 2 ' o',o'' are he coordnaon orgn of nodes. Where r = ' ' ' 0, r 2 =20, r = 2, r 2 = 2.5, a = b = 25, c = 235, d = 30, x = 380, y = 270 km. The sae vecor n () s X = (x,x,y,y ), he ranson marx and nose dsrbuon marx s Equaon (35): T 0 0 T / 2 0 0 0 0 0 F(k) G(k) = 0 0 T 0 T / 2 0 0 0 0 (35) where, T s he sample nerval and T = 4s. The measuremen vecor n (2) s Z =(x,y), he measuremen marx s Equaon (36): γ j(k) = k (34) k 2 2 2' ɵ j(l)'[p (l) P j (l) P j (l) P j (l)] ɵ j(l) l= + We all known ha he opmal es would requre usng he enre daabase hrough me k and hs s no easy o realze. However, he hsory nformaon of rack has been used n he four algorhms proposed n hs sudy and he compuaon and memory requremens of hese new algorhms wll no grow obvously snce each es sasc (as showed n (3), (7), (3) and (32)) has a recursve srucure..7. Smulaon One has run smulaons o compare he correlave performance of four b-hreshold rack correlaon algorhms here wh he Snger s and Bar-Shalom s algorhm..8. Smulaon Model and Parameer Sengs There are wo nodes consdered n he smulaons and a 2-D radar s se n each node. A Mone Carlo smulaon wh 50-runs was carred ou for wo envronmens. In case, here are 60 arges and here are 20 arges ha composed of a los maneuverng, cross and spl arges n case 2. The maneuvers of hese 0 0 0 H = 0 0 0 And Equaon (37): q (k) Q(k) = q 22(k) 2 q (k) = 5 0 x(k) ɺ 2 q 22(k) = 5 0 y(k) ɺ Fg.. The observaon area of sensors (36) (37) 699
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 The nose process sandard devaons of rang and azmuh measuremens from each sensor are assumed o be 70m and 0.07rad, 80m and 0.07rad, respecvely. The measuremen nose covarance marx s Equaon (38 and 39): 2 σx (k) σxy (k) R(k) = 2 σyx (k) σy(k) 2 2 2 2 2 2 σ x (k) = σp cos θ (k) + p (k) σθ sn θ(k) 2 2 2 2 2 2 σ y (k) = σ P sn θ (k) + p (k) σ θ cos θ (k) 2 2 2 2 2 σ xy (k) = [ σ P p (k) σ θ]sn θ (k) cos θ (k) (38) (39) 2 2 where, σ xy (k) = σ yx (k) and σ σ denoe he nose process p, θ sandard devaons of rang and azmuh measuremens and ρ(k) θ(k) denoe he rang and azmuh measuremens. Assumng ha all of he measuremens have been assocaed o he rack correcly, he nal seng of fler s gven as follows Equaon (40 and 4): x() ɵ = z () ɵ x() ɺ = [z () z (0)] / T y() ɵ = z 2() y() ɵ ɺ = [z 2() z 2(0)] / T P() = 2 2 σ x () σx () / T σ xy () σxy () / T 2 2 2 2 σ x () / T 2 σx () / T σxy () / T 2 σxy () / T 2 2 σ yx () σ yx () / T σ y () σ y () / T 2 2 2 2 σ yx () / T 2 σ yx () / T σ y () / T 2 σy () / T (40) (4).9. Sysem Flow Char of B-hreshold Algorhm The Sysem Flow Char of he Dependen Bhreshold Algorhm s gven n Fg. 2..0. Resuls and Analyss Wh -run smulaon, Table and 2 show Ec and Ee of Snger s, Bar-Shalom s and b-hreshold rack correlaon algorhms n case and case2, respecvely. Fgure 3-5 show he correc correlaon rao n case and case 2, respecvely. Fgure 4-6 show he error correlaon rao n case and case 2, respecvely. From hese smulaon resuls one can see ha correlave performance of Bar-Shalom s algorhm s a lle beer han ha of Snger s algorhm. Also one can see ha correlave performance of he four b-hreshold rack correlaon algorhms proposed n hs sudy s much beer han ha of Snger s and Bar-Shalom s algorhm, especally n he case 2 where here exss a heavy arge densy and a lo of maneuverng arges, where he mprovemen rao of Ec reaches abou 30 o 45% respecvely. In addon, he correlaon performances of ndependen b-hreshold algorhms are a ler beer han ha of dependen b-hreshold algorhm. However, he L/R ruler mus be se before he execuon of hese b-hreshold algorhms. Wh gradual growh of arges n smulaon, Fgure 7-4 show he correlaon resul of dfferen algorhms proposed n hs sudy wh 3/4 rules and 6/8 rulers respecvely. One can see ha he correlaon performance of b-hreshold algorhms wh 6/8 rules s a ler beer han ha of bhreshold algorhms wh 3/4 rules from hese smulaon resuls. Table. Ec and Ee of each algorhm n case (L/R = 6/8) Ec Ee -------------------------------------------------------------------------------- ------------------------------------------------------------------ Bar- Bar- Sngre s Sngre s IBTAC- DBTCA- Sngre s Sngre s IBTCA- DBTCA- N = 60 L algorhm algorhm IBTCA DBTCA ATS ATS algorhm algorhm IBTCA DBTCA ATS ATS Nl 0.6667 0.7000 0.6667 0.7000 0.8950 0.8950 0.2667 0.833 0.2667 0.833 0.03 0.03 60 2 0.6780 0.7458 0.8305 0.8475 0.920 0.9237 0.272 0.864 0.695 0.525 0.0753 0.0727 59 3 0.6780 0.7458 0.8644 0.8644 0.9430 0.9240 0.272 0.864 0.356 0.356 0.0533 0.0723 59 4 0.6780 0.7458 0.8983 0.8656 0.9523 0.9260 0.272 0.2034 0.07 0.334 0.0440 0.0703 59 5 0.6780 0.7458 0.9322 0.884 0.963 0.9327 0.272 0.2034 0.0678 0.86 0.0350 0.0637 59 6 0.6667 0.7368 0.9298 0.8896 0.9707 0.9463 0.2807 0.205 0.0702 0.04 0.0257 0.0500 57 7 0.6545 0.7273 0.9455 0.8909 0.9770 0.9570 0.2909 0.282 0.0545 0.09 0.093 0.0393 55 8 0.645 0.770 0.9434 0.8868 0.9770 0.9570 0.309 0.2264 0.0566 0.32 0.093 0.0393 53 9 0.645 0.770 0.9434 0.9057 0.9770 0.9570 0.309 0.2264 0.0566 0.0943 0.093 0.0393 53 0 0.6257 0.7059 0.942 0.926 0.9770 0.9570 0.337 0.2353 0.0588 0.0784 0.093 0.0393 5 0.6257 0.7059 0.942 0.926 0.9770 0.9570 0.337 0.2353 0.0588 0.0784 0.093 0.0393 5 2 0.6257 0.7059 0.942 0.926 0.9770 0.9570 0.337 0.2353 0.0588 0.0784 0.093 0.0393 5 700
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 2. The sysem flow char of dependen b-hreshold rack correlaon algorhm (Noce: Ec, Ee and Es denoe he correc, error and sans correlae rao) 70
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 3. Correc correlaon rao versus me (case) Fg. 4. Error correlaon rao versus me (case) 702
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 5. Correc correlaon raoversus me (case2) Fg. 6. Error correlaon rao versus me (case2) 703
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 7. Correc correlaon rao versus me (N = 30) Fg. 8. Error correlaon rao versus me (N = 30) 704
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 9. Correc correlaon rao versus me (N = 90) Fg. 0. Error correlaon rao versus me (N = 90) 705
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg.. Correc correlaon rao versus me (N = 50) Fg. 2. Error correlaon rao versus me (N = 50) 706
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Fg. 3. Correc correlaon rao versus me (N = 20) Fg. 4. Error correlaon rao versus me (N = 20) 707
Lu Yu e al. / Journal of Compuer Scence 9 (2): 695-709, 203 Table 2. Ec and Ee of each algorhm n case 2(L/R = 6/8) Ec Ee ------------------------------------------------------------------------- --------------------------------------------------------------------- Bar- Bar- Sngre s Sngre s IBTAC- DBTCA- Sngre s Sngre s IBTCA- DBTCA- L algorhm algorhm IBTCA DBTCA ATS ATS algorhm algorhm IBTCA DBTCA ATS ATS N = 20 0.5083 0.5083 0.5083 0.5083 0.82 0.82 0.4000 0.3833 0.4000 0.3833 0.870 0.870 20 2 0.5083 0.5250 0.767 0.747 0.8720 0.8762 0.4083 0.4083 0.2833 0.2583 0.262 0.220 20 3 0.5083 0.5250 0.799 0.7667 0.9098 0.8827 0.4083 0.467 0.2083 0.2333 0.0883 0.55 20 4 0.5083 0.5250 0.8000 0.7833 0.935 0.8843 0.467 0.4333 0.2000 0.267 0.0667 0.38 20 5 0.5042 0.520 0.8487 0.839 0.9463 0.8905 0.4202 0.4370 0.53 0.68 0.058 0.077 9 6 0.492 0.5000 0.8684 0.8596 0.9590 0.953 0.4386 0.456 0.36 0.404 0.0392 0.0828 4 7 0.4867 0.4956 0.876 0.8584 0.9648 0.985 0.4425 0.4602 0.239 0.46 0.0333 0.0797 3 8 0.482 0.49 0.8929 0.8750 0.9645 0.977 0.4464 0.4732 0.07 0.250 0.0337 0.0805 2 9 0.477 0.4862 0.9083 0.876 0.9645 0.977 0.4587 0.477 0.097 0.284 0.0337 0.0805 09 0 0.4762 0.4857 0.9048 0.8857 0.9645 0.977 0.4667 0.4857 0.0952 0.43 0.0337 0.0805 05 0.472 0.4808 0.9038 0.8750 0.9645 0.977 0.472 0.5000 0.0962 0.250 0.0337 0.0805 04 2 0.4660 0.4757 0.9029 0.8738 0.9645 0.977 0.4757 0.5049 0.097 0.262 0.0337 0.0805 03 Noce: Nl denoes he number of arge n he common survellance 2. CONCLUSION Four b-hreshold rack correlaon algorhms are proposed and compared wh he Snger s and Bar- Shalom s algorhm n hs sudy. Accordng o he smulaon resuls, he dfference beween correlave performances of hese algorhms s no so obvous when here are a few arges n survellance and he dfference beween correlave performances of hese algorhms wll ncrease wh he envronmens geng more complex. Therefore, he bhreshold algorhms presen a beer general correlave performance n dense mularge envronmens, more cross, spl and maneuverng rack suaons. To Snger s and Bar- Shalom s algorhm, he correlave performance of Bar-Shalom s algorhm s a lle beer han ha of Snger s algorhm. To he b-hreshold algorhms, he correlave performance of ndependen algorhm s beer han ha of dependen algorhm and he bhreshold algorhms wh 6/8 6 rules has a beer correlave performance han he b-hreshold algorhms wh 3/4 rules. Though he smulaons s performed n he case of correlang he daa beween congenerc sensors, hese Four b-hreshold rack correlave algorhms here can also resolve he problem of correlang racks beween heerogeneous sensors. 3. ACKNOWLEDGMENT Ths sudy was fnancally suppored by Naonal Naural Scence Foundaon of Chna under gran number 603200 and Shandong Provncal Naural Scence Foundaon of Chna under gran number ZR20FQ002. 4. REFERENCES Bar-Shalom, Y. and H. Chen, 2004. Mulsensor racko-rack assocaon for racks wh dependen errors. Proceedngs of he 43rd IEEE Conference on Decson and Conrol, Dec. 4-7, IEEE Xplore Press, pp: 2674-2679. DOI: 0.09/CDC.2004.428864 Bar-Shalom, Y. and L. Campo, 986. The effec of he common process nose on he wo-sensor fusedrack covarance. IEEE Trans. AES, 22: 803-805. DOI: 0.09/TAES.986.3085 Bar-Shalom, Y. and T.E. Formann, 988. Trackng and Daa Assocaon. s Edn., Academc Press, New York, ISBN-0: 020797607, pp: 353. Bar-Shalom, Y., 2008. On he sequenal rack correlaon algorhm n a mulsensor daa fuson sysem. IEEE Trans. Aerospace Elecr. Sys., 44: 396-396. DOI: 0.09/TAES.2008.45706 Bowman, C.L., 979. Maxmum lkelhood rack correlaon for mulsensor negraon. Proceedngs of he 8h IEEE Conference on Decson and Conrol ncludng he Symposum on Adapve Processes, Dec. 2-4, IEEE Xplore Press, pp: 374-376. DOI: 0.09/CDC.979.270200 Chang, C. and L.C. Youens, 982. Measuremen correlaon for mulple sensor rackng n a dense arge envronmen. IEEE Trans. Auomac Conrol, 27: 250-252. DOI: 0.09/TAC.982.0307 Gul, E., 994. On he rack smlary es n rack splng algorhm. IEEE Trans. Aerospace Elecr. Sys., 30: 604-606. DOI: 0.09/7.272282 Kaplan, L.M., Y. Bar-Shalom and W. Blar, 2008. Assgnmen coss for mulple sensor rack-o-rack assocaon. IEEE Trans. Aerospace Elecr. Sys., 44: 655-677. DOI: 0.09/TAES.2008.456023 708
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