Improving Data Association Based on Finding Optimum Innovation Applied to Nearest Neighbor for Multi-Target Tracking in Dense Clutter Environment

Transcription

1 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): Improving Daa Associaion Based on Finding Opimum Innovaion Applied o Neares Neighbor for Muli-Targe Tracking in Dense Cluer Environmen E.M.Saad, El.Bardawiny, H.I.ALI 3 and N.M.Shawky 4 Elecronics and Communicaion Engineering Deparmen, Helwan Universiy, Cairo, Egyp. Radar.Deparmen,.M.T.C.College. Cairo, Egyp 3 Elecronics and Communicaion Engineering Deparmen, Helwan Universiy Cairo, Egyp 4 Elecronics and Communicaion Engineering Deparmen, Helwan Universiy Cairo, Egyp Absrac In his paper, a new mehod, named opimum innovaion daa associaion (OI-DA), is proposed o give he neares neighbor daa associaion he abiliy o rack maneuvering muli- arge in dense cluer environmen. Using he measuremens of wo successive scan and depending on he basic principle of moving arge indicaor (MTI) filer, he proposed algorihm avoids measuremens in he gae sie of prediced arge posiion ha are no originaed from he arge and deecs he candidae measuremen wih he lowes probabiliy of error. The finding of opimum innovaion corresponding o he candidae valid measuremen increases he daa associaion performance compared o neares neighbor (NN) filer. Simulaion resuls show he effeciveness and beer performance when compared o convenional algorihms as NNKF and JPDAF. Keywords: Daa Associaion, Muli-Targe Tracking (MTT), Moving Targe Indicaor (MTI) Filer, Neares Neighbor Kaman Filer (NNKF), Join Probabilisic Daa Associaion Algorihm (JPDA).. Inroducion Muliple-arge racking (MTT) is an essenial componen of surveillance sysems. Real-world sensors; e.g., radar, sonar, and infrared (IR) sensors ofen repor more han one measuremen ha may be from a given arge. These may be eiher measuremens of he desired arge or Cluer measuremens. Cluer refers o deecions or reurns from nearby objecs, clouds, elecromagneic inerference, acousic anomalies, false alarms, ec. A general formulaion of he problem assumes an unknown and varying number of arges ha are coninuously moving in a given region. The saes of hese arges and he noisy measuremens ha are sampled by he sensor a regular ime inervals (scan periods) are provided o he racking sysem. When racking a arge in cluer, i is possible o have more han one measuremen a any ime since a measuremen may have originaed from eiher he arge, cluer, or some oher source. I is impossible o associae he arge wih a measuremen perfecly. The performance of a racking filer, however, relies heavily on he use of he correc measuremen. In addiion o he deecion probabiliy is no perfec and he arges may go undeeced a some sampling inervals. A primary ask of he MTT sysem is daa associaion ha is responsible for deciding on each scan which of he received muliple measuremens ha lie in he specified gae sie of he prediced arge posiion should updae wih he exising racking arge. The secondary goal is esimaion of he number of arges and heir posiion (saes) based on he measuremens originaing from he arges of ineres. In general, daa associaion beween measuremens and arges is needed, bu his is difficul o realie because of measuremen error, false alarms, and missed arges. Due o he daa associaion resul is crucial for overall racking process; a gaing process is used o reduce he number of candidae Corresponding auhor negmshawky@gmail.com

2 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): measuremens o be considered. In daa associaion process, he gaing echnique [] in racking a maneuvering arge in cluer is essenial o make he subsequen algorihm efficien bu i suffers from problems since he gae sie iself deermines he number of valid included measuremens. Anoher problem in case of racking muliple arges, daa associaion becomes more difficul because one measuremen can be validaed by muliple racks in addiion o a rack validaing muliple measuremens as in he single arge case. To solve hese problems, he imporan of an alernaive approaches known as neares neighbor daa associaion (NNDA) [-5], probabilisic daa associaion (PDA) [6,7], join probabilisic daa associaion (JPDA) [7,], and muliple hypohesis Tracking (MHT) [], ec. has been used o rack muliple arges by evaluaing he measuremen o rack associaion probabiliies wih differen mehods o find he sae esimae [-]. NNDA ha depends only on choosing he neares valid measuremen o he prediced arge posiion, has been used in real work widely because of is low calculaion cos, bu i readily miss-racks in dense cluered environmen. PDA, JPDA and MHT need prior knowledge and some of hem have large calculaion amoun [3-6]. We propose here an exended algorihm applied o convenional NNDA o be able o rack he muli-arge in dense cluer environmen. This proposed algorihm is more accurae o choose he rue measuremen originaed from he arge wih lower probabiliy of error and less sensiiviy o false alarm arges in he gae region sie han NNDA algorihm. Depending on he basic principle of moving arge indicaor (MTI) filer used in radar signal processing [6-] which ge rid from he fixed arges and he arges ha moving wih lower velociy and heir moving disance lower han specified cerain hreshold value, he proposed algorihm reduces he number of candidae measuremens in he gae by MTI filering mehod ha compares he moving disance measure for each measuremen in he curren gae a he updae sep o all previous measuremen in he same gae a he prediced sep and hen avoids any measuremen in he curren gae moves a disance less han he hreshold value due o comparison. Thus, decreasing he number of candidae measuremens in he curren gae lead o decreasing he probabiliy of error in daa associaion process. The main key o deec he moving or fixed false arge is he innovaion parameer ha measure he moving disance beween he curren measuremen and he prediced arge posiion. By calculaing his parameer for all measuremen in he curren gae compared wih he scanned previous measuremen in he same gae, he opimum innovaion of he candidae measuremen is obained. This is called opimum innovaion daa associaion (OI-DA) mehod which is combined wih NNDA algorihm o apply he proposed algorihm in muli racking arges in presence of various cluer densiies. Simulaion resuls showed beer performance when compared o he wo convenional NNKF, JPDA algorihm.. Background. Kalman Filer Theory Based on Kalman filer esimaion [], we lis he filer model. The dynamic sae and measuremen model of arge can be represened as follows x k k x k w A ( k ),,..., T () k k v H k x k,... T () Where x ( k ) is he n x arge sae vecor. This sae can include he posiion and velociy of he arge in space x ( x, y, x, y ), The iniial arge sae, x () for =,,..., T, is assumed o be Gaussian Wih mean m and known covariance marix p. Where he unobserved signal (hidden saes) x ( k) : k N, x ( k) X be modeled as a Markov process of ransiion probabiliy p x k x k and iniial disribuion p x N ( x ; m, p ). k is he m x measuremen vecor, A ( k ) denoes sae ransiion marix, H k denoes measuremen marix, w ( k ) and v k are muually independen whie Gaussian noise wih ero mean, and wih covariance marix Q(k-) and R(k), respecively. The innovaion mean (residual error) of measuremen i k is given by V k i k ˆ k i ( ) (3) where ˆ k H k m k (4) and he prediced sae mean and covariance is defined as m k A k m k and p k A k p k A k Q (5) Then, we can updae sae by

3 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): m ( k) m ( k) K ( k) V op ( k) (6) where V op is he seleced innovaion mean from V i (k ) corresponding o he choosing measuremen as a resul of daa associaion process, K (k) denoes gain marix calculaed by sae error covariance p (k) and innovaion covariance S (K), heir recursive equaions can be represened as follows p ( k) p ( k) K ( k) S ( K) K ( k) (7) S ( K) H ( k) p ( k) H ( k) R( K) () ( ) ( ) ( ) ( K) K k p k H K S () When muliple arge racking begins, we ge for each arge measuremens wihin correlaion gae (gae sie) as candidae measuremens when i k saisfies condiion i k H k m k S k i k H k m k (). where denoes correlaion gae. If here is only one measuremen, his can be used for rack updae direcly; oherwise if here is more han one measuremen, we need o calculae he equivalen measuremen.. Neares Neighbor Kalman Filer The NNKF is heoreically he mos simple single-scan recursive racking algorihm. The NNKF consiss of a discree-ime Kalman filer (KF) ogeher wih a measuremen selecion rule. The NNKF akes he KF s sae esimae xˆ(k- k-) and is error covariance P(k- k-) a ime k- and linearly predics hem o ime k. The predicion is hen used o deermine a validaion gae in he measuremen space based on he measuremen predicion ˆ k k and is covariance S(k). When more han one measuremen i k fall inside he gae, he closes one o he predicion is used o updae he filer. The meric used is he chi-squared disance: D i V i S k V i i k ˆ k S k i k ˆ k.. () The updae correcs he sae predicion by a ime-varying gain muliplying he difference beween he predicion and he acual measuremen. The error covariance is also updaed (see [] for furher deails). This filer is only mean-square opimal when here are no false alarms and a single arge is presen..3 -D Assignmen Algorihm When muliple arges are presen, he neares neighbor rule can be modified o ake arge mulipliciy ino accoun. Suppose here are T racks and M validaed measuremens beween hem. The single-scan measuremen-o-rack associaion problem may be posed as a -D assignmen problem [3] in which he assignmen cos beween measuremens i and rack is aken as he negaive logarihm of: g S i ( k) exp V i S k V i () The resuling assignmen problem may be solved by he algorihms based on shores augmening pahs [4]. The algorihm yields associaions ha enable racks o be updaed wih heir assigned measuremen. Tracks no receiving a measuremen are prediced bu no updaed. 3. Opimum Innovaion Daa Associaion The NNKF suffers from racking in dense cluer environmen and is performance is degraded wih many loss-racks accordingly, a new subopimal algorihm opimum innovaion daa associaion (OI-DA) is inroduced o increase he racking performance and o be able o rack maneuvering arges in heavy cluer. The main idea based on deecing or disinguishing beween he cluer measuremens in he gae of he prediced arge and he measuremen originaed from he moving arge using wo successive scan. The measuremens a ime k- ha lie in he gae of he prediced arge posiion (predic o ime k) is processed by he following mehod wih he measuremens a ime k ha lie in he same gae o obain he opimum innovaion corresponding o disance meric beween rue arge measuremen and he prediced arge

4 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online):

5 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): vy 4 y ( ) 5 k ( k ) 5 ( k ) ˆ 4 ( k ) 4 ( k ) 3 ( k ) ( k ) ( ) k ( k ) 3 ( k ) vx 4 x Fig. The curren and previous arges posiion of x,y coordinae in a gae posiion. To obain he opimum innovaion we have hree models ha are processed individually, where he NN algorihm is used as one of hem. In his secion as shown in Fig, we inroduce a new algorihm. In he predicion sep, Le Z k k, k,... w k be a se of n poins in he -D Euclidean space a ime k- where w n is he number of poins a ime scan and le ˆ k be a prediced posiion of he h racked arge a ime k. according o disance meric measure and gae sie, le Z k k,.. i k,.. m k i be a se of he candidae poins deeced in he h G of prediced posiion ˆ k whose elemens are a subse from he se Z k where i = o mi ( number of gae k deeced poins in gae G k a ime k-) and Z k be a se of all valid poins k i ha saisfy he disance measure condiion i k ˆ k S k i k ˆ k for each arge where is hreshold value ha deermines he gae sie and l = o w n, i = o mi, i. e for each arge, i is iniialied by and is increased by i = i + afer each valid poin is deeced up o las mi deeced poins. In he updaing sep, le Z k k, k,... k w be c a se of poins in he -D Euclidean space a ime k where w c is he number of poins a ime scan. The candidae poins deeced in he same gae G k as h G k of he prediced posiion ˆ k be a subse k k,.. k k from he se Z k Z j,.. mj where j = o mj (number of deeced poins in h gae a Z k be a se of all valid poins k ime k) and j ha saisfy he disance measure condiion j k ˆ k S k j k ˆ k for each arge where l = o w c, j= o mj for j=j+ afer each valid poin is deeced. To disinguish beween he deeced measuremens in G k ha originaed from he arge or originaed from cluer (false arge), he neares of each measuremen of x and y componen in G k o is corresponding measuremen in G k is calculaed and o observe he disance measure beween each measuremen in G k and is neares value. Then we consider ha he measuremen in G k is originaed from cluer in case is neares measure no exceed a hreshold value which represen fixed or false moving arge (cluer). This is based on calculaion of he innovaion mean for all deeced poins i ( k ), j(k) of x and y componen as follow; vxi( k ) xi( k ) HZx ˆ ( k) (3) vy i ( k ) y i ( k ) HZy ˆ ( k) ; i,,... mi vxj ( k) xj ( k) HZx ˆ ( k) (4) vy j ( k) y j ( k) HZy ˆ ( k) ; j,,..., mj Each poin j in G k has neares poin i in G k by calculaing he minimum absolue difference value ( vx j, vy j ) and is index ( vxi j, vyi j ) beween he calculaed innovaion means for all poin i a each poin j as follow; vx j min ( vx j ( k) vxi( k ) ) i,,.. mi vy j min ( vy j ( k) vy i ( k ) ) i,,.. mi vxi j arg min ( vx j ( k) vxi( k ) ) i,,.. mi vyi j arg min ( vy j ( k) vy i ( k ) ) i,,.. mi (5) (6)

6 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): Depending on he cluer poin has very small change compared o he change in arge poin of x and y componen a wo successive scan in each gae is cener is he predicion arge posiion. For simpliciy, if we assume as shown in Fig.(), he gae includes measuremens {,,3,4,5}a ime k and ime k- in x,y coordinae, i is clear ha (k),(k),3(k),5(k) are measuremens originaed from cluer while 4(k) is a measuremen originaed from he arge, we found ha he considering of cluer poin has high probabiliy when index vxi j is he same as or (equal o) vyi j while he considering of arge poin has high probabiliy when index vxi j is differen or (no equal o) vyi j, according o he above consideraion we deec how many poins mi represen a cluer poin (i.e he corresponding measuremens j are no valid and are avoided from daa associaion process) and how many poin mv represen a arge poin (i.e corresponding measuremens j are valid and one of hem has he opimum index ha is found by daa associaion process).the daa associaion process ake in consideraion he opimum innovaion mean ( vx op, vy op ) direcly in case ha he number of deeced poins mv is one, which is he normal case when he arge exis and he remaining poins represen a cluer(invalid poins) vxop vx j ( k) (7) vy op vy j ( k) Anoher case ha daa associaion process ake in consideraion he opimum innovaion mean ( vx op, vy op ) direcly when exising arge wih no cluer wihou enering in calculaion model of innovaion mean process. i.e. he calculaed number of deeced poin mj is one in G k. vxop vx j ( k), where j= () vy op vy j ( k) Two special cases may be occurring according o he scenario in he following applicaion assignmen:- The firs case, gae conain more han one moving arge and mv> as a resul of daa associaion process. The opimum innovaion mean ( vx op, vy op ) is calculaed by NNDA as follow; j arg ( ) ( ) min vx j k vy j k j omv () vxop vx j ( k) () vy op vy j ( k) Where j is he index of seleced measuremen from mv valid poin ha has he minimum disance from he prediced arge posiion. The second case, all measuremens in he gae are calculaed o be invalid as resul of daa associaion process i.e mv=, mi = mj. in his case we have wo consideraion:- - The arge may be exis and moves small disance when decreasing is velociy due o maneuvering and akes invalid consideraion as he remaining false arge in he gae bu he change in disance is sill higher han he hreshold value ha deec he arge as cluer i.e vx j, vy j. The opimum innovaion mean ( vx op, vy op ) is calculaed by selecing he measuremen ha has he maximum change in disance under condiion vx j, vy j as follow, j arg max vx j vy j () j omi vxop vx j ( k) () vy op vy j ( k) - The arge no deeced in he gae (missed) and all measuremens are considered o be false arge. In his case, he updaed arge is assigned o he prediced arge posiion and no innovaion mean value is required i.e vxop. (3) vy op w Finally, we obain he opimum innovaion mean ha is relaed o he rue seleced arge wih decreasing he probabiliy of error and is used in updaing arge o he correc posiion. Reducing he number of valid poins in h he gae by deecing he false measuremen o be invalid (i.e no include in he daa associaion process), his increase he probabiliy for choosing he rue measuremen originaed from he arge and improve he daa associaion process. 4. Implemenaion of Opimum Innovaion Daa Associaion (OI-DA) using he kalman filer. We propose an algorihm which depends on he hisory of observaion for one scan and uses innovaion mean calculaion wih a fixed hreshold o obain he opimum innovaion mean ha is relaed o he associaion pairing beween he choosing measuremen and rack (prediced arge) and is used in updae sae esimaion of he arge.

7 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): In convenional daa associaion approaches wih a fixed hreshold, all observaions lying inside he reconsruced gae are considered in associaion. The gae may has a large number of observaions due o heavy cluer, his leading o; increasing in associaion process since he probabiliy of error o associae arge-originaed measuremens may be increased. In our proposed algorihm deecing moving arge indicaor (MTI) filer is used o provide he possibiliy o decrease he number of observaions in he gae by dividing he sae of observaions ino valid represen moving arges and invalid represen he fixed or false arges ha only he valid are considered in associaion. The proposed OI-DA using Kalman filer is represened in algorihm. Algorihm OI-DA using Kalman filer. for = o T do. Do predicion sep, x k k ~ p x k Z : k N x k ; m k, p k where m k A k m k p k A k p k A k Q 3. Calculae opimum innovaion mean V op (k) by OI- DA algorihm described in algorihm 4. Do updae sep m ( k) m ( k) K ( k) V op ( k) p ( k) p ( k) K ( k) S ( K) K ( k) S ( K) H ( k) p ( k) H ( k) R( K) ( ) ( ) ( ) ( K) K k p k H K S 5. end for Algorihm Calculae V op (k) by OI-DA. Find validaed region for measuremens a ime k-:, i mi k k Z i,... By acceping only hose measuremens ha lie inside he gae : Z k Z : i k H k m k S k i k H k m k :. Find validaed region for measuremens a ime k: k k, j mj Z j,... By acceping only hose measuremens ha lie inside he gae Z k Z : j k H k m k S k j k H k m k where s k H k P k H k R 3. Calculae innovaion mean for all measuremen lie inside he gae a ime k-and k respecively vxi( k ) xi( k ) HZx ˆ ( k) vy i ( k ) y i ( k ) HZy ˆ ( k) ; i,,... mi vxj ( k) xj ( k) HZx ˆ ( k) vy j ( k) y j ( k) HZy ˆ ( k) ; j,,..., mj 4. if mj > calculae he index and change of he neares measuremen i in he gae a ime k- o each measuremen j in he gae a ime k for x and y componen. vx j min ( vx j ( k) vxi( k ) ) i,,.. mi vy j min ( vy j ( k) vy i ( k ) ) i,,.. mi vxi j arg min ( vx j ( k) vxi( k ) ) i,,.. mi vyi j arg min ( vy j ( k) vy i ( k ) ) i,,.. mi 5. Calculae invalid mi measuremen (false arge) in case vxi j vyi j and mv measuremen (rue moving arge) in case vxi j vyi j - Calculae direcly he opimum innovaion. vop ( vxop, vy op ) in case (mv =, j = index(mv)) or ( mj =, j = ) vxop vx j ( k) vy op vy j ( k) - Choose NN of mv valid measuremen o be he.. opimum innovaion vop ( vxop, vy op ) in case (mv >, j = index(mv)). j arg ( ) ( ) min vx j k vy j k j omv vxop vx j ( k) vy op vy j ( k) - Choose he measuremen o be he opimum innovaion vop ( vxop, vy op ) ha has he maximum change in disance under condiion

8 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): vx j, vy j in case mv =, mi = mj, j=index(mi) as follow, j arg max vx j vy j j omi vxop vx j ( k) vy op vy j ( k) - Oherwise he above condiion, he opimum will be se as vxop vy op 6- end 5. Simulaion Resuls Simulaion resuls have been carried ou o monior he performance of he proposed OI-DA algorihm compared o he convenional NNKF and JPDA filer. To highligh he performance of he proposed algorihm, we used a synheic daase o rack hree maneuvering arges which are coninues from he firs frame o he las frame in varying cluer densiy. The iniial mean m ( x, y, x, y ) for he iniial disribuion p x is se o m = [7.7,.6,, ], m = [3.3,.,, ], m 3 = [4.4,.7,, ], and covariance p = diag ([4, 4,, ]), =,,3. The row and column sies of he volume s s (V= W H ). We iniiae he oher parameers as:,v=x, he sampling ime = 4 sec, 4 3 sec, p D =., in addiion, we also se he marices of (),() as A, H, Q G G T, 4 R, 4 G Given a fixed hreshold ( 4 ), we showed ha a high signal o noise raio wih low cluer densiy ( =.5 m ), he hree algorihms appear o perform as expeced. Fig. 3(a),(b),(c) shows he esimaed arge racks using he NNKF, JPDAF and he OI-DA filers respecively a low cluer densiy. The figures show ha he hree filers were effecively able o rack he arges a high SNR. A low signal o noise raios he corruped arge rack in a uniform cluer wih high varying cluer densiy ( =. m for medium cluer and =. m for dense cluer ) is shown in Fig.4, where he NNKF and JPDA filers were no be able o rack he arges. Fig. 5,6 show he esimaed arge racks using he NNKF, he JPDAF, and he proposed OI-DA filers a he wo differen SNR as menioned above where In his figures, he colored solid line represens he underlying ruh arges of he rajecory (each arge wih differen color) while he colored + symbol represens rajecory of he racked arges. The figures shows ha only he OI-DA as shown in Fig. 5,6 (c) is able o rack he arges a wo differen heavy cluer densiy. The explanaion of his behavior is due o he fac ha, a low SNR he argeoriginaed measuremen may fall ouside he validaion gae when choosing he wrong valid measuremens during daa associaion process and as a resul, he esimaed arge saes will be cluer- originaed. The OI-DA has he advanage o increase he probabiliy of choosing he correc candidae measuremen. We also compared error roo mean square value (RMSE) for he differen hree approaches each wih hree arges a our hree cases in differen cluer as shown in Fig. 7. Our proposed algorihm has lower error, RMSE values han JPDAF over frame numbers and approximaely he same as NNKF. 6. Conclusions From he resuls obained in he simulaions for muliarge racking, i can be seen ha a low cluer densiy (high SNR), all he racking algorihm (NNKF, JPDAF and OI-DA) are able o rack he arges. However, a

9 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): heavy varying cluer densiy (low SNR), NNKF and JPDA algorihm fail o rack he arges, where he proposed OI-DA algorihm has he capabiliy o mainain he racked arges. From he valid based measuremen regions, The OI-DA algorihm disinguishes beween he fixed or false arges o be considered as invalid arges and he moving rue arges o be valid during daa associaion process. The OI-DA algorihm overcome he NNKF problem of loss racking he arges in dense cluer environmen and has he advanage of low compuaional cos over JPDAF. By using his new approach, we can obain smaller validaed measuremen regions wih improving he performance of daa associaion Process which have been shown o give arges he abiliy o coninue racking in dense cluer. True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by OIDA algorihm Tracked arge pah no by OIDA algorihm Tracked arge pah no 3 by OIDA algorihm (c) Fig. 3. X- and Y- rajecory show he sae of successful racking o maneuvering muli-arges (3 arge wih + symbol for racked arge posiion and solid line for rue arge pah) move in low cluer using 3 approaches algorihm (a) NNKF (b) JPDAF (c) OI-DA. True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by NNKF algorihm Tracked arge pah no by NNKF algorihm 4 Tracked arge pah no 3 by NNKF algorihm 4 6 (a) (a) (c) (b) (d) True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by JPDA algorihm Tracked arge pah no by JPDA algorihm 4 Tracked arge pah no 3 by JPDA algorihm 4 6 (b) (e) Fig. 4. The sae of racking 3 arges move in differen cluer densiy using 3 approaches algorihm NNKF as in (a),(b), JPDAF as in (c),(d) and OI-DA as in (e),(f). Images (a),(c),(e ) show racking in medium cluer and images (b),(d),(f ) show racking in dense cluer (f)

10 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by NNKF algorihm Tracked arge pah no by NNKF algorihm Tracked arge pah no 3 by NNKF algorihm (a) True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by NNKF algorihm Tracked arge pah no by NNKF algorihm Tracked arge pah no 3 by NNKF algorihm (a) True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by JPDA algorihm Tracked arge pah no by JPDA algorihm Tracked arge pah no 3 by JPDA algorihm (b) True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by OIDA algorihm Tracked arge pah no by OIDA algorihm Tracked arge pah no 3 by OIDA algorihm (c) Fig. 5 X- and Y- rajecory show he sae of racking 3 arges in medium cluer (+ symbol refer o racked arge posiion and solid line o rue arge pah) using 3 approaches algorihm (a) NNKF and (b) JPDAF loss rack while (c) OI-DA mainains racks True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by JPDA algorihm Tracked arge pah no by JPDA algorihm Tracked arge pah no 3 by JPDA algorihm (b) True pah for arge 3 True pah for arge True pah for arge 3 Tracked arge pah no by OIDA algorihm Tracked arge pah no by OIDA algorihm Tracked arge pah no 3 by OIDA algorihm (c) Fig. 6 X- and Y- rajecory show he sae of racking 3 arges in dense cluer (+ symbol and solid line refer o racked arge posiion and rue arge pah respecively) using 3 approaches algorihm (a) NNKF and (b) JPDAF loss rack while (c) OI-DA mainains racks

11 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): OIDA for arge OI-DA for arge OIDA for arge 3 NNKF for arge NNKF for arge NNKF for arge 3 JPDA for arge JPDA for arge JPDA for arge OI-DA for arge OI-DA for arge OI-DA for arge 3 NNKF for arge NNKF for arge NNKF for arge 3 JPDA for arge JPDA for arge JPDA for arge 3 RMS ERROR.3. RMS ERROR FRAME NUMBER FRAME NUMBER (a) (c).5.4 OIDA for arge OI-DA for arge OIDA for arge 3 NNKF for arge NNKF for arge NNKF for arge 3 JPDA for arge JPDA for arge JPDA for arge 3 Fig. 7 The roo mean square error[rmse] for each arge (3 arges) separaely over frame number (each frame ake 4 sec / one scan) for he 3 approaches algorihm as (a) wih low cluer,(b) wih medium cluer and (c) wih dense cluer. From (b), (c) he RMSE is mainained minimum for he proposed OI-DA and less sensiiviy o dense cluer. RMS ERROR FRAME NUM BER (b) References [] X. Wang, S. Challa, and R. Evans, Gaing echniques for maneuvering arge racking in cluer, IEEE Transacions on Aerospace and Elecronic Sysems, Vol.3, No.3, July, PP [] R. A. Singer, R. G. Sea, K. B. Housewrigh, Derivaion and evaluaion of improved racking filers for use in dense muliarge environmens, IEEE Trans on Informaion Theory, Vol., No. 4, 74, PP [3] Bar-Shalom Y., Li X. R., Mulliarge Mulisensor Tracking: Principles and Techniques., Sorrs, CT: YBS Publishing, 5. [4] VPS Naidu,G Girija, J R Raol Daa associaion and fusing algorihms for racking in presence of measuremen loss IE(I) journal-as Vol.6, May 5, PP7-. [5] Hui Chen, Chen Li Daa associaion approach for wo dimensional racking base on bearing-only measuremens in cluer environmen, Journal of Sofware Vol. 5, No. 3,, PP [6] Y. Bar-Shalom, E. Tse, Tracking in a cluered environmen wih probabilisic daa associaion, Auomaica, Vol., 75, PP [7] Yaakov Bar-Shalom,Fred Daum, and Jim Huang. The Probabilisic Daa Associaion Filer, IEEE Conrol Sysems Magaine Vol., No. 6, PP. -, December. [] K. C. Chang, Y. Bar-Shalom, Join probabilisic daa associaion for muli-arge racking wih possibly unresolved measuremens and maneuvers, IEEE Trans on Auomaic Conrol, Vol., 4, PP [] D. B. Reid, An algorihm for acking muliple arges, IEEE Trans on Auomaic Conrol, Vol. 4, No. 6, 7, PP.43-54,

12 IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue 3, No., May ISSN (Online): [] G. W. Pulford Taxonomy of muliple arge racking mehods IEE Proc.-Radar Sonar Navig., Vol. 5, No.5, 5, PP.-34 [] E.M.Saad, El.Bardawiny, H.I.ALI and N.M.Shawky New Daa Associaion Technique for Targe Tracking in Dense Cluer Environmen using Filered Gae Srucure Signal processing: An Inernaional Journal (SPIJ) Vol. 4, Issue 6,, PP [] E.M.Saad, El.Bardawiny, H.I.ALI and N.M.Shawky Filered Gae Srucure Applied o Join Probabilisic Daa Associaion Algorihm for Muli-Targe Tracking in Dense Cluer Environmen, IJCSI Inernaional Journal of Compuer Science Issues, Vol., Issue,, PP.6-7 [3] Blackman, Samuel, Rober Popoli, Design and Analysis of Modern Tracking Sysems, Boson: Arech House,. [4] Y. Bar-Shalom, X. R. Li, T. Kirubarajan, Esimaion wih applicaions o racking and navigaion, New York: John Wiley & Sons,. [5] H. Zhou, Z. Jin, D. Wang, Maneuver arges racking, Beijing: Defense Indusry Press,. [6] Y. He, J. J. Xiu, J. Zhang, X. Guan, Radar daa processing and applicaion, Beijing: Elecronic Indusry Press, 6. [7] M. I. Skolnik. Radar handbook, McGraw-Hill, Inc [] Simon Haykin, Classificaion of radar cluer in an air raffic conrol environmen proceedings of he IEEE, Vol. 7, No 6,, PP [] Gokhan Soysal and Mura Efe Performance comparison of racking algorihms for a ground based radar Commun.Fac.Sci. Univ.Ank. series A-A3, Vol. 5() (7) PP -6 [] Simon Haykin. Radar signal processing, IEEE ASSP Magaine, April 5. [] Grewal, M.S. and Andrews, A.p, Kalman filering, heory and pracice using MATLAB, Wiley inerscience,. [] Y. Bar-Shalom and T. E. Formann, Tracking and Daa Associaion, Academic Press,. [3] S. Blackman, Muliple Targe Tracking wih Radar Applicaions, Arech House, MA, 6. [4] R. Jonker, A. Volgenan, A Shores Augmening Pah Algorihm for Dense and Sparse Linear Assignmen Problems, Compuing, v. 3, 7,