Research Article Centralized Fuzzy Data Association Algorithm of Three-sensor Multi-target Tracking System

Size: px

Start display at page:

Download "Research Article Centralized Fuzzy Data Association Algorithm of Three-sensor Multi-target Tracking System"

Brian Chambers
5 years ago
Views:

1 Reearch Joural of Appled Scece, Egeerg ad echology 7(6): 55-6, 4 DOI:.96/rjae.7.89 ISSN: ; e-issn: Maxwell Scefc Publcao Corp. Submed: Aprl, Acceped: May 8, Publhed: February 5, 4 Reearch Arcle Ceralzed Fuzzy Daa Aocao Algorhm of hree-eor Mul-arge racg Syem Zhaofeg Su, Zhezhe Yua ad L Zhou School of Iformao ad Elecrcal Egeerg, Ludog Uvery, Yaa 645, Cha School of Egeerg, Ocea Uvery of Cha, Qgdao 66, Cha Abrac: For mprovg he effec of mul-arge racg dee arge ad cluer cearo, a ceralzed fuzzy opmal agme algorhm () of hree-eor mul-arge yem propoed. Ad o he bae of h, a geeralzed probablc daa aocao algorhm (GPDA) baed o algorhm preeed. he fuo algorhm ge effecve -uple of meaureme e by ug compoe of everal afacory oluo of he fuzzy opmal agme problem ad he ue geeralzed probablc daa aocao algorhm o calculae he updae ae of arge. Smulao reul how ha, he apec of mularge racg accuracy, algorhm uperor o he opmal agme () algorhm baed o ae emae ad GPDA algorhm beer ha algorhm. Bu coderg he me pe, algorhm ped a mmum of me ad GPDA algorhm exacly o he corary. herefore, compared wh algorhm, he wo algorhm preeed he udy each ha advaage ad hould be choe accordg o he eed of he acual applcao whe ue. Keyword: Ceralzed, fuzzy, geeralzed probablc daa aocao, mul-arge racg, he opmal agme INRODUCION Wh he rapd developme of cece ad echology, moorg yem ha bee a progre from gle-eor yem o mul-eor yem. Mul-eor mul-arge racg yem a moorg yem ug homogeeou or heerogeeou eor o decrbe he evromeal codo. Daa aocao problem a ey echque for mul-arge racg. Now he ypcal mul-eor mul-arge racg daa aocao algorhm clude Jo Probablc Daa Aocao (JPDA) algorhm, geeralzed probablc daa aocao (GPDA) algorhm, mulple hypohe racg (MH) algorhm, he opmal agme algorhm, ec (He e al., ; Ha e al., ). Each commo mul-arge racg algorhm ha uque performace characerc ad applcao evrome. Boh Jo probablc daa aocao algorhm ad geeralzed probably daa aocao algorhm are more applcable o dee arge ad cluer cearo (Pa e al., 5, 9). I geeral deeco cearo, each of hem ealy caue rac excuro or polymerzao due o whole eghborhood propere of probably calculao. Whle he opmal agme algorhm baed o cera opmzao rule more applcable o daa aocao problem uder geeral deeco evrome. I dee arge ad cluer evrome, oe-o-oe feable rule requred by he opmal agme algorhm ealy lead o more accurae aocao, reulg decreag accuracy of mularge racg (Popp e al., ; Zhag e al., 7). o play he advaage of probablc daa aocao ad he opmal agme algorhm ad avod her dadvaage, Zhou ad Zhag () propoe a geeralzed probablc daa aocao algorhm baed o he opmal agme algorhm. he reul of he ude how ha geeralzed probablc daa aocao algorhm baed o he opmal agme algorhm o oly ca avod defcecy of error accumulao ad lo of formao reuled by equeal proceg of meaureme of mul-eor geeralzed probablc daa aocao algorhm, bu alo ca effecvely avod he hgh wrog aocao rae o racg accuracy of he opmal agme algorhm by ug oe-o-oe feable rule uder dee arge ad cluer evrome. Sude have how ha, fuzzy e heory ca beer deal wh daa aocao problem dee arge ad cluer cearo (Xu ad Che, ). o furher effecvely mprove he a-jammg capably of he opmal agme algorhm of daa aocao uder Correpodg Auhor: Zhaofeg Su, School of Iformao ad Elecrcal Egeerg, Ludog Uvery, Yaa 645, Cha h wor lceed uder a Creave Commo Arbuo 4. Ieraoal Lcee (URL: hp://creavecommo.org/lcee/by/4./). 55

2 Re. J. Appl. Sc. Eg. echol., 7(6): 55-6, 4 dee arge ad cluer cearo, h udy frly propoe a fuzzy opmal agme algorhm for mul-eor mul-arge racg. O h ba, fue he algorhm above ad geeralzed probablc daa aocao algorhm ad ge a geeralzed probablc daa aocao algorhm baed o he fuzzy opmal agme algorhm. Smulao reul how ha, compared wh he opmal agme algorhm baed o ae emae, he fuzzy opmal agme algorhm o oly ha beer mul-arge racg accuracy, bu alo ha le me pe. Whle compared wh he fuzzy opmal agme algorhm, he geeralzed probablc daa aocao algorhm baed o he fuzzy opmal agme algorhm furher mprove mul-arge racg ad locao accuracy dee arge ad cluer cearo SYSEM DESCRIPIONS Le u uppoe ha he ae equao of dcreeme yem a follow: where, X ( + ) φ( ) X ( ) + G( ) V ( ) (), φ ( ) R he ae-rao marx a, me ; G( ) R repree a proce oe drbuo marx; X ( ) R a ae vecor of he arge a me ; V ( ) R a equece of zeromea, whe Gaua proce oe wh covarace marx Q () a me, proce oe of dffere me are depede,.e.: E[ V ( )] () E[ V ( ) V ] Q( ) δ l () he meaureme equao of dcree-me yem : Z ( ) H ( ) X ( ) + W ( ) (4) m where, Z ( ) R meaureme vecor a me ; m H () he meaureme marx; W ( ) R a zero-mea, whe Gaua meaureme oe equece wh covarace R () ad meaureme oe of dffere me are depede,.e.: E[ W ( )] (5) ' E[ W ( ) W ] R( ) δ (6) l V ( ) E W ( ) ~ X ( ) Q ( ) δ l ' ' [ V ( l ) W ( l ) X ~ ( ) ] R ( ) δ where, X ~ ( ) X() Xˆ ( ) l P ( ) HE FUZZY OPIMAL ASSIGNMEN ALGORIHM Fuzzy facor e ad memberhp fuco: Le u uppoe ha he fuzzy facor e U { u, u, L, u, L, u}, where u deoe he h fuzzy facor. he fuzzy facor e uually clude Eucldea dace bewee poo, veloce ad accelerao of he wo arge x ad y dreco ad Eucldea dace bewee headg ad headg chage rae of he wo arge. Becaue ha hee facor have dffere effec o aocao judgme, oly hoe facor ha play a mpora role aocao judgme ca be eleced praccal applcao. h wll o oly eure he accurae racg o he arge wh dffere moveme, bu alo ca avod he algorhm oo complex, o a o ge he goal of decreag he compuaoal burde of he formao fuo yem. Iuvely, he Eucldea dace bewee poo of arge hould be he mo mpora, he he Eucldea dace bewee headg ad dreco coe agle of arge. All hee facor coue he ma body of fuzzy aocao judgme, whle he Eucldea dace bewee accelerao ad chagg rae of headg or dreco coe agle ca be ued a he auxlary judgme, he wegh ca be ae a a very mall value or zero. Le u uppoe ha he wegh agme vecor of he fuzzy facor e U A { a, a, L, a }, where a he correpodg wegh of he h facor u. I geeral, a, where he eleco of (7) a eed o be decded by he mporace or mpac of he yh facor. Uually, a a al a ad he wegh of he fal fuzzy facor are very mall or zero. Accordg o he characerc of fuzzy facor po-rac aocao yem, ormal drbuo memberhp fuco adoped h udy. he al ae decrbed a X () whch Deermao of he fuzzy facor: I h udy, oe elec fuzzy facor bewee meaureme po Z follow a Gau drbuo, wh mea ˆX ( ) ad (l) [x (l), y (l), (l), (l)] ad predced meaureme covarace P ( ) ad: (l l-) a follow: 56

3 Re. J. Appl. Sc. Eg. echol., 7(6): 55-6, 4 u ˆ + ( ˆ ˆ ( l) [(ˆ x x ( l l )) y y ( l l )) ] ( ) [ ˆ ( ) + ˆ ( )] [ ˆ ( ) + ˆ u l x& l y& l l y& l y& ( l l )] u( l) θ,, L, m ; j,, L,. (8) where m he umber of meaureme cofrmao rego a pree me: θ a [ y& / x& ] (9) a ˆ ( ) / ˆ [ y& l l x& ( l l )] Suppoe ha he bac probably agme fuco for meaureme from dffere eor o arge (,, L ) are m, m ad m, repecvely, focal eleme are Ap, Bq ad Cr, repecvely, he he coe meaure of he meaureme of he fr eor, he h h meaureme of he ecod eor ad he h meaureme of he hrd eor ca be decrbed a: c m ( A ) m ( B ) m p q ApIBqICr φ ( C ) r (6) x & [ x xˆ ( l )] / () ˆ ( ) ˆ x& l l x& ( l l ) () where amplg erval. he fuzzy opmal agme algorhm: Le u uppoe ha he memberhp fuco decrbg he mlary bewee he po ad rac baed o he fac : h µ τ σ L () ( u ) exp( ( u / )),,,,. L a, by ug he weghed average mehod, oe ca ge he egraed mlary degree bewee meaureme po Z ( l ) ad rac a: For he fuzzy wegh e A { a, a,, } f a µ,,, L, M,,, L,. () he he fuzzy aocao marx bewee meaureme po Z ( l ) ad rac a me l ca be expreed a: f f L f f f f F L L L L L fm f ( ) ( ) m l L f m l (4) By ormalzg each row of marx (4), oe ca ge he bac probably agme marx of meaureme o dffere arge a:, M ( m ),, L, m ;,, L, (5) where m he bac probably agme fuco for meaureme o arge. 57 where, Ar, B, C U. U he defcao frame of arge. he ) he aocao co C ( c marx of meaureme daa of hree eor ad he daa aocao problem of hree-eor mul-arge yem ca be raformed o a -D agme problem a follow: mc ubjec o: ; ; ;,, L,,, L,,, L, (7a) (7b) where, are dcaor varable. If a -uple of meaureme orgae from a real arge, hould be ; oherwe,. GENERALIZED PROBABILISIC DAA ASSOCIAION ALGORIHM BASED ON FUZZY OPIMAL ASSIGNMEN Coderg ha he fuzzy opmal agme algorhm a globally opmal agme algorhm baed o oe-o-oe feable rule, dee arge ad cluer evrome, wll loe a lo of formao o mpleme po-rac aocao by oly ug compoe of he opmal oluo of (7a-7b) a effecve -uple of meaureme. Ad he geeralzed probablc daa aocao algorhm of equeal proceg of meaureme from mul-eor a cacade algorhm. I he equeal proce, wll loe ome orgal formao ad ca ealy lead o error accumulao, reulg mul-arge racg preco declg. o olve he problem, h eco

4 propoe a geeralzed probablc daa aocao algorhm baed o he fuzzy opmal agme. I eay o ee ha each compoe of oluo of (7a-7b) happe o correpod o a effecve -uple of meaureme. All compoe he eleced good oluo co of he effecve -uple of meaureme e. herefore, oe ca oba a equvale meaureme by emag he poo of he correpodg arge for each effecve -uple of meaureme. Ad by calculag he aocao probably bewee he equvale meaureme ad arge rac, oe ca ae advaage of GPDA algorhm o rac mul-arge. I h way, oe ge he geeralzed probablc daa aocao algorhm baed o he fuzzy opmal agme. he followg he dealed decrpo of he fuo algorhm. For each vald -uple of meaureme, oe ca emae he poo x, y ) of he correpodg ( arge (,, L, ) by ug he followg formula: where, xˆ yˆ, x σ y x y x σ y Re. J. Appl. Sc. Eg. echol., 7(6): 55-6, 4 x σ σ (8) y σ σ are he locao varace x, y dreco, repecvely. x x + u, y y + v are he locao compoe of arge meaured by eor wo coordae axe, repecvely. ae he poo emae of correpodg arge of he h -uple of meaureme a he compreheve meaureme z,,, m, he oe ca calculae he aocao probably bewee he h -uple of meaureme ad arge rac. Furher, he updae ae of arge ca be calculaed by ug GPDA algorhm. he ae ad covarace updae formula are a follow: Xˆ ( ) Xˆ ( ) + K ( ) m β ( ) v ( ) (9) where, ˆ ˆ X ( ) F ( ) X ( ) he ae predco of arge a me, K () fler ga of arge a me, ˆ v ( ) z ( ) Z ( ) meaureme of redual: where, P ( ) β ( ) P ( ) ~ + ( β ( )) P ( ) + P ( ) c () 58 c P ( ) [ I K ( ) H ( )] P ( ) () ~ P ( ) W ( ) P ( ) W ( ) () v P ( ) m [ m v β ( ) v ( ) v β ( ) v ( )][ ( ) m β ( ) v ( )] SIMULAION ANALYSES () I order o verfy he valdy of he propoed algorhm, algorhm, algorhm ad GPDA algorhm are compared dffere mulao codo. I he mulao, aumed ha hree eor rac egh arge ad each arge move a a varable peed a plae. he al velocy are repecvely v x 4 /, v y / ; agle meaureme error ad ragg meaureme error of he hree eor are repecvely he ame; deeco probably Pd. 95 ; gae probably Pg ; he al value of he wegh vecor ae a a. 7, a. ad a. ; radar amplg me ; cluer coeffce λ. he mulao ep are 5 ad mulao umber 5. he mulao reul are a follow: Whe arge-o-arge erval τ m, comparo of roo-mea-quare error (RMSE) of algorhm, algorhm ad GPDA algorhm are a follow: Whe arge-o-arge erval τ 5m, comparo of RMSE of algorhm, algorhm ad GPDA algorhm are a follow able how he average me pe of dffere algorhm whe he arge-o-arge erval 5 m, he ragg meaureme error m ad he agle error.rad. Smulao ep are 5 ad mulao umber 5. I ca be ee from Fg. ha whe arge-o-arge erval o very mall, algorhm beer ha algorhm, bu he opmzao of magude o bg. Ad oe ca ee from Fg. o 4, wh he deerorao of meaureme evrome, he magude of algorhm beg uperor o algorhm correpodgly creae. he reul how ha, compared wh algorhm, algorhm more uable for dee arge ad cluer evrome. I alo ca be ee from Fg. o 4, comparo wh algorhm, GPDA ha more accurae arge racg effec ad beer racg

5 Re. J. Appl. Sc. Eg. echol., 7(6): 55-6, 4 able : Comparo of me pe of dffere algorhm CMS- Algorhm FOAGPDA me () Fg. : RMSE of hree algorhm uder codo of e m, e.rad r me Sep θ GPDA GPDA 5 5 Fg. 4: RMSE of hree algorhm uder codo of e r m, e θ.rad feable rule dee arge ad cluer cearo, bu alo her he advaage of a-jammg performace of GPDA algorhm. herefore, varou mulao codo, he fuo algorhm how beer performace of mul-arge racg. able how ha algorhm ped le me ha he correpodg reul of CMS -OA algorhm, whle GPDA ped lghly more me ha he correpodg reul of CMS -OA algorhm. CONCLUSION GPDA 5 5 me Sep 5 5 me Sep Fg. : RMSE of hree algorhm uder codo of e r m, e θ.rad 5 4 GPDA 5 5 me Sep Fg. : RMSE of hree algorhm uder codo of e r m, e θ.rad ably. I maly becaue ha GPDA o oly effecvely avod formao lo ad error accumulao caued by equeal proceg meaureme from dffere eor CMS-GPDA algorhm ad avod he deerorag daa aocao qualy by ug algorhm uder oe-o-oe 59 I order o beer olve mul-eor mul-arge racg problem, a fuzzy opmal agme algorhm of daa aocao of hree eor yem propoed. he algorhm fr ue fuzzy compreheve mlary o coruc po-rac correlao marx ad he ue combao rule of D-S evdece heory o coruc meaureme daa aocao marx of hree eor baed o fuzzy compreheve mlary. Smulao reul how ha he fuzzy opmal agme algorhm uperor o he opmal agme algorhm baed o ae emae. o furher ehace he a-jammg performace of he fuzzy opmal agme algorhm, h udy pu forward a fuo algorhm whch ue compoe of everal good oluo of he fuzzy opmal agme algorhm a effecve -uple of meaureme ad he ae advaage of geeralzed probablc daa aocao algorhm o rac mul-arge. Compared wh he fuzzy opmal agme algorhm, he geeralzed probablc daa aocao algorhm baed o he fuzzy opmal agme algorhm furher mprove he accuracy of mul-arge racg dee arge ad cluer evrome, bu he me pe alo creae accordgly. How o furher opmze he performace of he fuo algorhm a problem whch eed o furher udy he fuure.

6 Re. J. Appl. Sc. Eg. echol., 7(6): 55-6, 4 REFERENCES Ha, C.Z., H.Y. Zhu ad Z.S. Dua,. Mul-ource Iformao Fuo. ghua Uvery Pre, Bejg. He, Y., G.H. Wag, D.J. Lu ad Y.N. Peg,. Muleor Iformao Fuo wh Applcao. Publhg Houe of Elecroc Idury, Bejg. Pa, Q., X.N. Ye ad H.C. Zhag, 5. Geeralzed probably daa aocao algorhm. Aca Elecro. Sca, (): Pa, Q., Y. Lag, F. Yag ad Y.M. Cheg, 9. Moder arge racg ad Iformao Fuo. Naoal Defee Idury Pre, Bejg. Popp, R., K. Papa ad Y. Bar-Shalom,. M-be S-D agme algorhm wh applcao o mularge acg. IEEE. Aero. Elec. Sy., 7(): -9. Xu, Y.Y. ad X.H. Che,. Fuzzy e heory he mul-eor formao fuo. Compu. Appl. Sofw., 8(): -4. Zhag, J.W., Y. He ad W. Xog, 7. Muleor mulpled hypohe algorhm baed o daa compreg echc. J. Bejg Uv., Aeroau. Aroau., (): Zhou, L. ad W.H. Zhag,. Geeral probablc daa aocao algorhm baed o he opmal agme. J. Compu. Iform. Sy., 8(7):

Lecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination

Lecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination Lecure 3 Topc : Drbuo, hypohe eg, ad ample ze deermao The Sude - drbuo Coder a repeaed drawg of ample of ze from a ormal drbuo of mea. For each ample, compue,,, ad aoher ac,, where: The ac he devao of