Study on Multi-Target Tracking Based on Particle Filter Algorithm

Transcription

1 Research Journal of Aled Scences, Engneerng and Technology 5(2): , 213 ISSN: ; E-ISSN: axell Scenfc Organzaon, 213 Submed: ay 4, 212 Acceed: June 8, 212 Publshed: January 11, 213 Sudy on ul-targe Tracng Based on Parcle Fler Algorhm 1,2 Junyng eng, 1 Jaomn Lu, 1 Yongzheng L and 1 Juan Wang 1 College of Informaon Scence and Engneerng, Yanshan Unversy, Qnhuangdao 664, Chna 2 Dearmen of Comuer Scences, Shjazhuang Unversy, Shjazhuang 5, Chna Absrac: Parcle fler s a robably esmaon mehod based on Bayesan frameor and has unque advanage o descrbe he arge racng non-lnear and non-gaussan. In hs sudy, frsly, analyses he arcle degeneracy and samle movershmen n arcle fler mul-arge racng algorhm and secondly, ales arov Chan one Carlo (CC) mehod o mrove re-samlng rocess and enhance erformance of arcle fler algorhm. Keyords: Imoran samlng, CC, mul-arge racng, arcle fler, sequenal INTRODUCTION In recen years, many sngle-arge vdeo sequence racng sysem are successfully develoed one afer anoher, bu he mul-arge racng sysem s sll a challengng rojec, esecally he racng of mulle arges of smlar aearance and n comlex moon. A resen, he classc algorhms ha dely aled are: Neares Neghbor Fler (NNF), Jon Probably Daa Assocaon Fler (JPDAF) and ulle Hyohess Tracng (HT), ec., NNF algorhm s roosed by Snger and needs less comuaon and no reles on cluer dsrbuon model, good for easy rojec mlemenaon (Tae e al., 25). Hoever, only uses he measuremen n sascal sense ha closes o he redced oson of raced arge as a canddae measuremen and n realy, he measuremen closes o he cener of redced locaon s no necessarly he correc objecve measuremen1. JPDA algorhm s roosed by Bar-Shalom, ec., hch s regarded as one of mos effecve algorhms for soluon of mul-arge daa assocaon under nensve measuremen and s racng success rae s relavely hgh under all crcumsances. Wh JPDAF algorhm, he search of assocaed soluon s acually a seeng of combnaon ssue and he comuaon amoun of searchng rocess s n exonenal groh rend as quany of arges and measuremen gron, so s dffcul for such algorhm o be used dely n raccal rojec (ourad and Jors, 22). Red roosed HT algorhm of mul-arge racng based on All Neghbor omal fler roosed by Snger and conce of confrmaon marx roosed by Bar- Shalom. Such algorhm ll aan a beer resul n racng under hgh cluer densy envronmen and be able o solve he roblems of arge aear and dsaear n racng erod (Alexandre and Rahael, 24). Hoever, such algorhm ll have comuaon amoun rse radly as arge number and observed quany ncreased, so s alcaon s lmed n raccal rojec. Wh arcle flers ung no alcaon, he roblems exsed n classcal algorhms above sad have been mroved. Parcle Flerng (PF) echnque s a Omal Regresson Bayesan flerng algorhm based on CC smulaon, hch s no lmed by lnear error and hgh Gaussan nose hyohess and s alcable for non-lnear non- Gaussan model (Nummaro e al., 23). The basc dea s o ae a seres of eghed arcles from curren sysem sae dsrbuon o esmae and udae he nex sysem sae. Arnaud and Nando (21) have a research of he sequenal mone carlo mehods n racce. Franços e al. (211) roose a drec, redcon- and smoohng-based alman and arcle fler algorhms. Ths sudy nroduces he arcle fler such raccal esmaon roblem-solvng mehod no he feld of vson racng, consrucng he racng frameor based on arcle fler and combnng h characerscs of arges a all levels, o manufacure racers of good erformance ha have mulmodal racng feaures and be able o mrove robusness. In secfc mlemenaon, re-samlng n CC mehod ll be aled o solve arcle degeneracy and samle movershmen n arcle flerng vsual mul-arge racng algorhm. CC mehod can effeely enhance he erformance of arcle fler algorhm and reduce he comuaonal comlexy. Corresondng Auhor: Junyng eng, College of Informaon Scence and Engneerng, Yanshan Unversy, Qnhuangdao 664, Chna 427

2 Res. J. Al. Sc. Eng. Technol., 5(2): , 213 ul-arge racng echnque and bayesan mehod: To solve dynamc sae sysem usng Bayesan mehod, eole hoe o buld sae oseror robably densy funcon based on all he nformaon ha could be obaned (ncludng all measured value). Snce embodes all avalable nformaon, hs funcon can be consdered s he comlee soluon of hs esmaon roblem. In rncle, he omal esmaon of he sae can be go from robably densy funcon, hen ge a measured value, can also ge a esmae. Therefore, Bayesan recursve fler s a very good choce. When a ne measured value comes, e deal h n order and don' have o save all of he daa. So, he fler consss of o ses, Predcon and fx: Predcon sage s o redc he robably densy funcon a curren me by sysem model. Fx sage s o udae he robably densy funcon of he sae afer geng he measured value a curren momen. Assume he sae sace model of dynamc sysem s: 1 x f x, v (1) z h x, u (2) In hch, x ndcaes he sae of sysem a me and z ndcaes he measuremen vecor a me, as nx nv nx nx nu nz shon n Fg. 1. f : R R R and h : R R R, resecvely ndcaes Saus ransfer funcon and measuremen funcon, v, u resecvely ndcaes he rocess nose and measuremen nose. Bayesan fler s a recursve mehod base on robably densy. From he analyses of he frameor, he ove Saus of objec can be modelng use he arov rocedure. Ge formula as bello: x x x x 1: 1 1 In hch, x1 : 1 x1, x2, x 1 can see, x x can change no (3) x. From formula 3, x x 1: 1 1 by recursve mehod. Tha s, he value of curren rocess sae deends on he value of las sae and all he oher revous value. Then, he dynamc model of he sae can be descrbed by he formula belo: x f x 1, 1 (4) In hs formula, x ndcaes he rocess sae a me, f s he funcon ang of las sae x -1 o curren sae x, -1 s he rocess nose. Accordng Fg. 1: Dynamc sae sace model he srucure n Fg. 1, We can acheve he measuremen model by combne he sysem sae and he measure value of racng sysem: z h x, v (5) z ndcaes he rocess sae a me, h s he funcon ang of sysem sae x o measuremen sae z, v s he measuremen nose. In he rocess of fler, he man urose s hrough he rmve sae value x a me and he measured value se z 1: o ge xˆ, he esmae value of sae. Can use he follong formula o descrbe hs rocess: x z c z x x z 1: 1: 1 x z1 : 1 x x 1 x 1 z 1 dx 1 (6) (7) In hch, normalzaon can coeffcen c can be defned as: z z1: 1 x z1: z x dx 1 / (8) c 1 x z : x z1 : 1 s ror robably, x z lelhood degrees, x x 1 1 ndcaes he oseror robably, s he s he ranson robably. Lelhood degrees and ranson robably can be deduced by formula 6 and 7. Then, he oseror robably can be go hrough he recursve formula 7, 8 and 9 of Bayesan fler algorhm. For mul-arge racng sysem, assume he arge number s, s one of hem. Assume all arges movemen s obey he frs order aro chan and he movemen of hese arges s ndeenden. Then realzng mul-arge racng by esmae on vecor 1,,. A me, he formula of sysem sae can be gve as bello: 428

3 F, V 1 Res. J. Al. Sc. Eng. Technol., 5(2): , 213 1,, (9) Parcle fler mul-arge racng echnque: Parcle fler heory: Parcle fler s a robably esmaon mehod based on Bayesan frameor and s very suable o descrbe he arge racng uncerany. Parcle fler aroach rovdes a flexble frameor and many radonal vson racng mehods can mae a grea robusness enhancemen hrough slgh model modfcaon and embedmen no he arcle fler frame or alone. oreover, arcle fler aroach has unque advanage n handlng nonlnear non- Gaussan mul-modal cases (nguang e al., 21). The essence s o realze Bayesan fler n non-aramerc one Carlo smulaon mehod. Parcle fler aroach self s able o exress a number of assumons n arcle ses, so can be used o solve mul-arge racng roblem. Due o daa assocaon s only consdered n a gven erod of me, he comlex of daa assocaon s hus reduced. Usng hybrd boosra fler o solve he daa assocaon roblem, n hch each arcle nvolves sngle arge sae nformaon and exresses one arge sae hyohess; usng Gaussan mxer model o exress oseror dsrbuon of all arges under he gven observaon condons and each model of oseror dsrbuon corresonds o a arge (lsen e al., 22). The core dea of arcle fler algorhm s o use eghng of a seres of random samles and oseror robably densy requred by exresson, o ge he esmaed sae value. When he samle number s very large, such robably esmaon ll be equal o oseror robably densy. Assume Ns ndcae he arcle number, hen, 1,..., means a suor on se and s corresondng egh s, 1,..., N and normalzed egh s 1 1, hen s s N, 1 ndcaes he random arcle se descrbng oseror densy. Thereuon, oseror robably densy a he me can use dscree egh sum ha s aroxmae o: : 1 (1) 1 In hch, he egh can be samled and seleced from moran densy funcon q 1 : n sequenal moran samlng mehod. If he samle can be obaned from moran densy q 1 :, hen he egh of he h arcle 429 can be defned as: q 1: 1: (11) If he moran densy funcon can be decomosed as follos: q q q 1 : 1, 1: 1 1: 1 Then he oseror robably densy can be exressed as: 1: 1 1: 1: 1 1, 1: 1 1 1: 1 1: : 1 1: : 1 (12) And udaed formula for eghs s obaned herefore: : 1 q 1, 1: q 1 1: 1 1 q, 1 1: Weghs can be normalzed as: 1 (13) ~ (14) If q q, 1 1: 1, s acheved, namely he moran densy funcon only deends on 1 and, hen only sorage samle bu no 1 and he as observaon 1: 1 s needed, herefore comuaon sorage can be grealy reduced. A hs me he egh s revsed as: 1 1 q, 1 (15) Thus, he oseror robably densy a he me K can use dscree egh sum ha aroxmae o:

4 1: 1 Res. J. Al. Sc. Eng. Technol., 5(2): , 213 ~ (16) For mul-arge racng sysem, N (quany) arcles are nvolved n nal arcle se: S 1 n s, (17) N n1,..., N n s, In hch each elemen from 1,..., s obaned from ndeenden samlng. The arcle se a he me -1 s assumed as n n N n S 1 s 1, 1n1,..., N, n hch n Each n arcle s a vecor of dmenson n 1 x and s, reresens he h elemen n s n 1 and n x reresens he sae vecor dmenson of he h arge. Each eraon n arcle fler algorhm s dvded no o ses: redcon and egh udang. Predcon means samlng from roosed densy funcon F and roosed densy funcon s conssen h he arge moon model; egh udang s o mae he egh a he me -1 mulled by he observaon lelhood: n,1 n, F s 1, v ~ n s n, F s 1, v n, (18) For he lelhood calculaon of he nh arcle, he observed value ~ s n, n 1,..., N can be exressed as: m 1 m n j n z,..., z ~ s z ~ s m j1 q V l 1 z ; ~ s j n, q j1 (19) j j j In hch, n, l z s z K ~ s n, ; ~, q,..., observed value from he h arge and quany of arge a he me.,, 1 means he robably of he j h means he Re-samlng: The basc roblem o be solved n sequenal morance samlng algorhm s arcle degeneracy, afer a fe or mulle recurson, he eghs of mos arcles become very small and only a fe arcles have a relavely large eghs. Re-samlng echnque s used heren o solve arcle degeneracy, namely removng he arcles of 43 small egh and reroducng hose of large eghs. Dealed rocess s as follos. Afer sysemac observaon, he frs se s o recalculae and confrm he egh ranges of he arcles. The realsc arcles ll be graned relavely large eghs and hose devang from realy ll be gven relavely small ones. The second se s re-samlng rocess, n hch he arcles of large eghs ll derve much more offsrng arcles and hose of small eghs ll corresondngly derve less ones, moreover, he eghs of offsrng arcles ll be re-se. The hrd se s sysem sae ranson rocess, n hch he sae of each arcle a he me ll be redced hrough addng a random amoun of arcles. The forh se s sysem observaon rocess a me, smlar o he frs se, he fnal reresenaon of arge sae ll be obaned hrough eghng of a numbers of arcles. These ne arcles roagaed no he calculae of nex frame, Then he dynamc model change he oson of arcles and he observaon model change he egh of arcles, deermne he arge oson. Re-samlng cyclng consanly, hs rocess s shon n Fg. 2. Parcle fler re-samlng nhbs he egh degeneracy, bu also nroduces oher roblems. A frs, he arcles are no longer ndeenden, reducng he ooruny of arallel comung because of connuous re-defnon of ne arcle se; second, he arcles of relavely large eghs ll be chosen for many me, eaenng he arcle dversy and he samle arcles conan many dulcae ons, hen he sysem nose s small, hey sad ll be obvous and afer several eraon, all arcles ll converge o a on and hs s non as arcle deleon. Parcle deleon resuled from re-samlng rocess maes he number of arcles exressng PDF sae oo small and herefore nadequae, hle unlmed ncrease of arcle number s no realsc. CC mehod: arov Chan one Carlo (CC) mehod s nroduced o generae samles from arge dsrbuon hrough consrucng arov chan, hch has a good convergence effec (Tae e al., 21). In each rocess of eraon of sequenal moran samlng, he arcles can move o dfferen laces by combnng h CC, so ha arcle deleon s avoded and furhermore, arov chan can ush he arcles o he laces closer o PDF sae and mae he samle dsrbuon more reasonable. There are many CC mehods u no alcaon and erools Hasng mehod s adoed heren.

5 Res. J. Al. Sc. Eng. Technol., 5(2): , 213 curren arge emlae. Hoever, due o mage shadng, lgh change, deformaon or accumulaon of machng error, he dynamc emlae ll easly lead o arge racng drf and even los. Dynamc emlae can be exressed as a forgeng rocess as follos: udaed 1 fxed ne (2) Fg. 2: The man rocess of re-samlng Secfc re-samlng rocess s as follos: Accordng o he samles unformly dsrbued n he range (, 1), hresholds u-u (, 1) are obaned. Samlng as er dsrbuon robably x () ( ) ( ) ( ) ( x x 1),.e., x ~ ( x x 1). () Acce x ( ) ( y x ), f u mn[ 1, ~ ] ( ) ; oherse, ( y x ) () dro x ( ) ( ), mae ~ x x. Temlae udang: Selecon of arge emlae s an moran ar of vsual racng algorhm and a good arge emlae shall be dsncve and unque o ensure he racng accuracy and effecveness. In moon rocess, he arges ll be changed due o effecs of s moon, lgh and ersecve and only aroraely and reasonably udang of arge emlae can overcome o some exen he macon of such changes on racng effec. Reasonable udae sraegy shall be able o ada o slo changes of arge characerscs, bu also rad changes. Temlae s generally dvded no saonary emlae and dynamc emlae. Saonary emlae s ofen aled because of samle and relable. Hoever, characerscs of movng arge ll be changed over me, hen he change of movng arge sae leads o corresondng change of s characersc, requres he algorhm o ae arorae sraegy o resonse and obvously he saonary emlae canno sasfy such requremen. Dynamc emlae s a resoluon resondng o he requremens above sad. The smles udae rule for dynamc emlae s udae frame by frame, hch abandons all revous emlae nformaon and ados he bes mached sub-regon mage of revous me as 431 In hch, ndcaes reenon of saonary emlae ha can aes emrcal value. Coeffcen Bhaacharyya ndcang arge smlary s adoed heren as a arameer, comared h emrcal value, s more n lne h udae requremen. fxed ndcaes dynamc emlae and generally s arge eghed color hsogram n nal oson. udaed ndcaes ne emlae and generally s arge eghed color hsogram n esmaed oson. By usng he dynamc emlae udae rule above sad, he arge eghed color hsogram model conans he arge color nformaon of nal me and curren me, bu also maes real-me adjusmen of udae rae accordng o arge smlary n esmaed oson, hch can effecvely nhb racng errors from accumulang and racng arge from drfng. CONCLUSION Targe racng s usually non-lnear and non- Gaussan and he arges usually do volunary movemen, so her movemen canno be accuraely descrbed n mahemacal equaons. The sudy nroduces he arcle fler such raccal esmaon roblem-solvng mehod no he feld of vson racng, consrucng he racng frameor based on arcle fler and combnng h characerscs of arges a all levels, o manufacure racers of good erformance ha have mulmodal racng feaures and be able o mrove robusness. In secfc mlemenaon, re-samlng n CC mehod ll be aled o solve arcle degeneracy and samle movershmen n arcle flerng vsual mularge racng algorhm. CC mehod can effeely enhance he erformance of arcle fler algorhm and reduce he comuaonal comlexy. ACKNOWLEDGENT Ths research as suored by he Naural Scence Foundaon of Hebe Provnce under Gran No. F The auhors ould le o han he anonymous reveers for her valuable remars and commens.

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