Box-Particle Labeled Multi-Bernoulli Filter for Multiple Extended Target Tracking

Transcription

1 RADIOENGINEERING, VOL. 5, NO. 3, SEPTEBER Bo-Patcle Labeled ult-benoull Flte fo ultle Etended Taget Tacng ao LI, Zang LIN, We AN, Yyu ZHOU ollege of Electonc Scence and Engneeng, Natonal Unvesty of Defense Technology, No. 09, Deya Road, hangsha, P. R. hna anusct eceved anuay, 06 Abstact. Ths ae focuses on eal-tme tacng of multle etended tagets n clutte based on labeled mult- Benoull flte. To addess ths oblem, a novel aoach s oosed wthn the ecently esented bo-atcle famewo. Unle the tadtonal ont-atcle aoach, the measuements of etended tagets ae modeled as nteval measuements n ths wo, and the coesondng lelhood functon s gven based on nteval analyss. Then, labeled mult-benoull ecuson fo etended tagets s mlemented by bo atcles, efeed to as BP-LB flte. Futhemoe, BP--LB flte s oosed to bette accommodate the uncetanty of taget dynamcs by ntegatng the BP-LB flte wth nteactng multle models (I) algothm. Smulatons demonstate that the oosed aoach can sgnfcantly educe the numbe of atcles and well tac multle etended tagets wth less untme. Keywods Bo atcle, labeled mult-benoull, mult-taget tacng, etended taget, nteactng multle models.. Intoducton Standad tacng algothms assume that one taget geneates at most one ont measuement. Howeve, n many actcal stuatons ths assumton s not aoate [], []. Due to the nceasng esoluton of ada and otcal sensos, one taget may oduce multle ont measuements. Such taget s efeed to as etended taget. Etended taget tacng s a evalent tas. Recently, the andom-fnte-set (RFS) based mult-taget tacng algothms have attacted etensve attenton [3]. Based on RFS famewo, the obablty hyothess densty (PHD), adnalzed PHD (PHD) and mult-taget mult-benoull (ebe) fltes have been oosed [4 6]. Howeve, these fltes only ovde unlabeled estmates at each tme, and addtonal ost-ocessng s needed to fom taget tacs. To ovecome the ssue, the labeled RFS s ntoduced n [7] by augmentng the state of each taget wth a tac label. Subsequently, the Genealzed Labeled ult-benoull (GLB) and the δ-glb RFS wee oosed as the secfc subclasses of labeled RFS [8]. As an accuate and comutatonally effcent aomaton of the δ-glb flte, the labeled ult-benoull (LB) flte has been oosed n [9]. Both Gaussan tues (G) and sequental onte alo (S) technques have been mlemented fo these RFS based fltes [6], [0]. The tadtonal S s caed out by ont atcles (PP). The G mlementaton s constaned to lnea Gaussan scenaos, and the S mlementaton can be aled to some nonlnea non-gaussan scenaos. Howeve, n many actcal alcatons, the tagets usually ehbt stong maneuve, and the combnaton of nteactng multle models (I) algothm and RFS based flte s adoted to coe wth such adly maneuveng tagets []. In the I algothm, multle sngle-model fltes ae needed. onsequently, the tadtonal S mlementaton s comutatonally eensve, esecally when the numbe of tagets s lage o the I algothm s adoted. Ths motvates us to seach fo comutatonally cheae altenatves. Fo nteval measuements, the bo-atcle (BP) aoach has a otental to sgnfcantly educe comutatonal cost []. Thus, we focus on tacng multle etended tagets by bo-atcle aoach n ths wo. In tacng alcatons, the measuements may be affected by thee souces of uncetanty: stochastc, data assocaton and settheoetc uncetanty [3], [4]. The uncetanty ognatng fom andom nose s efeed to as statstcal uncetanty. The data assocaton uncetanty s the uncetanty as to whch measuements ae coesondng to the taget. Tadtonal tacng algothms, such as PHD flte and LB flte, have been desgned based on both stochastc and assocaton uncetanty. Howeve, they gnoe the effect bought by set-theoetc uncetanty. Because of unnown bases and othe easons, nteval measuements, athe than tadtonal ont measuements, can be usually obtaned. The bo-atcle aoach based on the nteval analyss famewo can well accommodate above tle uncetanty. In the Bayesan esectve, bo atcles can be nteeted as suots of unfom obablty densty functons (PDF). DOI: 0.364/e SIGNALS

2 58. LI, Z. LIN, W. AN, ET AL., BOX-PARTILE LABELED ULTI-BERNOULLI FILTER FOR ULTIPLE EXTENDED TARGET In fact, the nteval measuements ae common fo etended tagets. An etended taget can geneate seveal ont measuements based on Posson model, and they andomly dstbute aound the cente of taget etent []. onsequently, the unambguous oston coodnates of taget cente cannot be etacted. On the contay, the nteval measuements o ambguous taget egons ae avalable. In ths ae, we aly bo-atcle aoach to mlement the LB ecuson fo etended tagets. Fstly, the nteval measuement model of etended taget s modeled, and the lelhood functon wthn nteval analyss famewo s gven. Secondly, the bo-atcle mlementaton of LB flte fo lnea etended tagets (BP-LB flte) s deved. Then, to bette accommodate maneuveng etended tagets, the BP-LB flte and nteactng multle models (I) algothm ae combned, and BP--LB flte s oosed. Smulatons demonstate that the oosed aoach can each smla accuacy wth consdeably less comutatonal costs n comason wth ont-atcle aoach. The emande of the ae s oganzed as follows: Secton evews the theoes of Posson model of etended taget, LB flte and nteval analyss. Secton 3 ooses the BP-LB flte and BP--LB flte. The esults and analyss of the eements ae manly esented n Secton 4. Secton 5 daws conclusons.. Bacgound Ths secton ovdes a bef evew of Posson model of etended taget, LB flte and nteval analyss. oe detals can be found n [], [9], [].. Posson odel of Etended Taget In the mult-taget tacng scenao, the tacng s often efomed on ont measuements afte theshold segmentaton. The taget measuement set of etended taget s usually modeled by Posson model. The cadnalty dstbuton s [] n n e () n! whee s the mean numbe of ont measuements. The ont measuements ognatng fom the etended taget can be andomly dawn fom Gauss satal dstbuton aound taget cente.. LB Flte A mult-benoull RFS X can be seen as a unon of some ndeendent Benoull RFSs,.e. X,. Hee, and eesent the estence obablty and satal dstbuton of sngle taget, esectvely. In LB flte, a label s aended to sngle-taget state to enable the estmaton of a taget tac. Labeled sngle-taget state and mult-taget state ae denoted by and X, esectvely. The ecuson of LB flte s caed out on as follows [9]. ) Pedcton: Assume that the aamete set of osteo mult-taget densty at tme s gven by π,. The state sace and label sace. The edcted mult- ae eesented by and taget LB RFS aamete set s gven as + +P, +P, B B π,,. () The fst tem n () eesents suvvng tagets and the second one denotes bth tagets. s the label sace of bth tagets. The estence obabltes and satal dstbutons of suvvng tagets ae calculated as +P, P +P, S,,, P, (3) f, (4) P S,, (5) whee the suvval obablty of the tac s eesented by S (, ), and f, denotes the sngle-taget aov tanston densty. The aamete set of bth tagets s gven by bth model [9]. ) Udate: The label sace afte edcton ncludes two ats: suvvng tagets and bth tagets, so. The edcted LB aamete set s ewtten as a unfom LB aamete set as followng π,. (6) The LB flte s an aomaton of the δ-glb flte, and ts measuement udate s stll caed out n the aoach of δ-glb. To facltate the δ-glb udate, the edcted LB RFS s conveted nto an equvalent δ-glb fom,.e. X X X, (7) X L L, (8), (9) whee eesents the oecton fom the labeled state sace to the label sace, and X X. Befoe udate, measuement set attonng s needed fo etended taget tacng, whch attons ont measuement set nto multle subsets. A well-nown atton- X

3 RADIOENGINEERING, VOL. 5, NO. 3, SEPTEBER ng method s the dstance atton. It s caed out based on the fundamental nsght that measuements fom the same etended taget ae satally close to each othe [5]. In atcle alcatons, the dstance theshold can be set based on o nowledge, and then the most lely ones among all of the ossble attons ae adoted n measuement udate. Aftewads, the udated estence obabltes and satal dstbutons can be comuted by: I, ZI I, I I,, (0) I,, ZI I () whee I eesents the sace of mangs fom tac label to measuement, and : I 0,,, Z. Y X s nclude ndcato functon [9]..3 Inteval Analyss easuements wth bounded eos can be convenently modeled as nteval measuements. To facltate the ocessng of nteval measuements, the tool of nteval analyss has been develoed []. A eal nteval s defned as a closed and connected subset,.e.,. The and eesent esectvely the lowe bound and ue bound. Fo the case wth mult-dmensonal states, the nteval s egaded as a bo. Bo s defned as a atesan oduct of multle ntevals,.e. d, whee d s the numbe of dmensons. Afte a nonlnea oagaton, the esult of the oagaton may not be a bo. To coe wth ths ssue, ncluson functons ae necessay. Let f be a functon fom n m n m to. An nteval functon f fom to s sad to be an ncluson functon fo f, f f f, functon s usually adoted [], [6]. n. In the contet of tacng, natual ncluson The contacton s anothe motant concet fo boatcle aoach, whch s used n the calculaton of lelhood functon as gven n Sec. 3.. A onstant Satsfacton Poblem (SP) can be denoted by g =0,. () In shot, equaton () means fndng the smallest bo to elace ognal unde the constant. The onstant Poagaton (P) has bette sutablty n comason wth othe methods. Thus, the P method has been wdely used n many tacng alcatons [4], [6]. 3. Bo-Patcle Imlementatons 3. Inteval easuement odel and Lelhood Functon Fo a two-dmensonal case, the sngle-taget state can be descbed by nteval state vecto as,, y, y, and (3) whee y ae the oston ntevals of the taget cente, and y ae the coesondng velocty ntevals. Fo an etended taget, some ont measuements aound taget cente can be obtaned afte theshold segmentaton,.e. Z, y. Hee, the tem ee- sents the numbe of ont measuements ognatng fom the etended taget, and and y ae the oston coodnates of the th ont measuement. As ntoduced n Sec.., the s subect to Posson dstbuton. Obvously, the ecse cente of taget etent cannot be dectly obtaned. Howeve, the nteval at whch the taget cente z z, z z and locates s avalable,.e.. The z y ae nteval measuements of taget cente n -decton and y-decton, esectvely. In ths wo, they ae comuted by z, y, (4) z y y y, y (5) whee and y ae the estmated oston coodnates of taget cente, and y descbe the sze of nteval. They ae comuted by: y mean, (6) mean y, (7) ma, (8) ma y y y. (9) Fo convenence, the above ocessng, fom ont measuement set to one nteval measuement, s denoted z I Z. by The measuement lelhood functon g (z) s equed by Bayes-le fltes. Ths s also tue fo bo-at- T

4 530. LI, Z. LIN, W. AN, ET AL., BOX-PARTILE LABELED ULTI-BERNOULLI FILTER FOR ULTIPLE EXTENDED TARGET cle flte. In the contet of ths ae, the measuement lelhood fo nteval measuement z s gven as z, z hp g (0) whee the functon hp, z etuns a contacted veson of. In ths wo, the dectly measued comonents ae contacted based on nteval measuements,.e. z, y y z y. The unmeasued comonents, and y, ae contacted based on o nowledge. = y y whee denotes the volume of nteval. 3. BP-LB Flte In ths subsecton, the bo-atcle mlement of LB flte s deved n detal, whch s efeed to as BP-LB flte n ths ae. In classcal LB flte, the satal dstbuton () s aomated usng a set of weghted ont atcles as () whee denotes the Dac delta functon concentated at, s the numbe of ont atcles, and eesents the weght of the th ont atcle. In bo atcle aoach, bo atcles ae nteeted as suots of unfom PDF, then equaton () s ewtten as: U () whee U eesents the unfom PDF ove the bo. The detals about BP-LB ecuson ae esented as followng. ) Pedcton: Suose that the osteo mult-taget densty at s an LB RFS wth aamete set π,, s aomated by a set of weghted bo atcles,,,, U,,.e. (3) whee s the numbe of bo atcles of tac at tme. The edcted LB densty conssts of suvvng etended tagets and bth etended tagets n (). In the BP-LB flte, the aamete set of suvvng etended tagets can be calculated by whee,, P S,, P, P U,, P =, (4), (5),, +, P f, (6),,,, P S S =. (7) The suvval obablty S s assumed to be state ndeendent. The outut of f s a bo contanng f. The aamete set of bth etended tagets ae gven by bth model n Sec. 4.. ) Udate: Afte edcton, the unfom mult-taget densty π, s gven, and each s aomated by a set of bo atcles, U,,,,,.e.. (8) Then, the equvalent δ-glb fom s obtaned by (7 to 9). Based on dstance atton as ntoduced n Sec.., the ont measuement set s dvded nto dsonted subsets, N n n.e. Z Z, sub. Z sub, eesents the nth subset and t n n conssts of some ont measuements,.e. Z n,m n,m, y n m sub,. The dstance theshold Th a used n dstance atton s secfed a o. Then, subsets ae conveted nto nteval measuements usng the method n- N n toduced n Sec. 3.,.e. Z z whee z n n I Z, sub. The udate usng the nteval measuement set s gven by I, I, I I, I ZI I I n,, Z, (9) Z. (30) The weghts and the satal dstbutons ae calculated by I, I Z Z I, (3)

5 RADIOENGINEERING, VOL. 5, NO. 3, SEPTEBER Z,, U, (3),,, h P, z, (33) Z,,, Z Z ;, (34),, Z ;, (35), Dg z, ;,f 0 (36) qd, f 0 whee g z s the nteval measuement lelhood and has been gven as (0). denotes the clutte densty, and the clutte s modeled as Posson model [9]. D eesents the detecton obablty, t s state ndeendent, and q. D D 3) Resamlng: Smla to the tadtonal ont-atcle aoach, the esamlng ste s necessay fo the boatcle aoach to event degeneacy of bo atcles. Howeve, nstead of elcatng bo atcles wth lage osteo weghts, we atton them nto multle sub boes. These sub boes ae equally weghted. onsequently, the esoluton n the egons of state sace can be efned, and taget state ntevals can be contacted. In ths wo, we andomly c a dmenson to be dvded fo the selected bo-atcle []. In addton, the unng, megng and state etacton ae smla to those n [4]. Punng of hyotheszed tacs means that the tacs wth estence obabltes below the theshold Th del wll be deleted. Two tacs wthn a dstance theshold Th me wll be meged. A taget s declaed esent only f the estence obablty s geate than theshold Th Ta. Fnally, the mult-taget state can be etacted by whee atcle.,, md (37) md eesents fndng the cente of the bo 3.3 BP--LB Flte To bette accommodate maneuveng etended tagets, BP--LB flte s oosed by ntegatng the BP- LB flte wth I algothm. To deve the BP--LB flte, s ntoduced to denote sngle moton model. The state of sngle etended taget s consequently eesented by,. The moton model of the taget s usually egaded as a aov chan wth tanston obablty mat H h st [7]. Fo eamle, hst t s denotes the obablty that a taget swtches fom model s to model t, whee st, and h t st. The tem s the numbe of moton models. In essence, the BP--LB flte conssts of a fnte numbe of sngle-model BP-LB fltes coesondng to dffeent moton models. In addton to those stes n BP- LB flte, mng ste s addtonally equed [8]. The othe stes ae smla to BP-LB flte, and the mng ste of BP--LB flte s gven as follows. Assume that at tme the mult-taget osteo densty s π,,, and each s aomated by a set of augmented bo atcles,,,,,.e., U,,. (38), Then, the med LB aamete set can be eessed by: π,,. (39) Snce the model tanston s only decded by model tanston obablty and s ndeendent of the state tanston,, t can be comuted by, s s s t,, t s,, t s s st h Theefoe,, s. τ t, s aomated by (40),,, h,,,, t t. (4) It can be found that much moe atcles ae needed and the numbe of atcles afte mng fo tac s nceased to. Thus, comutatonally cheae mlementaton s motant fo maneuveng taget tacng. Subsequently, the edcton and udate ae caed out based on augmented bo atcles. Note that the augmented sngle-taget state tanston densty s f,, h f.

6 53. LI, Z. LIN, W. AN, ET AL., BOX-PARTILE LABELED ULTI-BERNOULLI FILTER FOR ULTIPLE EXTENDED TARGET 4. Numecal Studes 4. Smulaton Setu The smulaton esults ae dvded nto two ats: Fstly, multle lnea etended tagets ae taced by the oosed BP-LB flte and the tadtonal ont-atcle LB flte (PP-LB flte) [], [9]. Secondly, the BP- -LB flte s comaed wth the sngle-model BP- LB flte (BP-V-LB flte) and mult-model PP-LB flte (PP--LB flte) n the scenao contanng multle adly maneuveng etended tagets. onsde a D suvellance egon n the atesan coodnates, secfed by the lowe-left cone (, ) and ue-ght cone (5, 5). Each sequence has 30 fames and eod s T = s. Thee ae thee etended tagets n each sequence, and they ae embedded nto each sequence as Posson model. The aveage numbe of taget ont measuements s 8. The aveage numbe of clutte measuements s 0 n each fame. In the fst eement, thee tagets all move at a constant velocty (V) model n the suvellance egon. Howeve, the tagets may move at a constant velocty model o a coodnated tun (T) model n the second eement. Smla to classcal LB flte, the bth ocess s modeled as a mult Benoull RFS [9],.e. π,, 0.06, U. 3 B B B B B B Tang the Taget as an eamle, and the ntal taget state vecto s 385, 399,[ B 5,5],[55,69],[ 5,5]. (4) The velocty vecto s contacted based on o dstbuton. In ths wo, t follows a unfom PDF,.e. 5, 5 5,5 y 5, 5 5,5. and The state tanston functons of V model and T model ae descbed by (43) and (44) [8]. The tun ate of T model n the second eement s set to Ω = 0.8 ad. f T f V T T sn T cos 0 0 cost 0 snt cost snt 0 0 snt 0 cost T (43) (44) The statstcal efomance of the algothm s evaluated usng the Otmal Sub-Patten Assgnment (OSPA) metc [9], because t ontly catues dffeences n cadnalty and ndvdual elements between two fnte sets n a mathematcally consstent yet ntutvely meanngful way. Then, fo, c 0, X,, m and Y y,, yn, f m n, d If m > n, c c X, Y mn n n c m c d, y. (45) c c nm d X, Y d Y, X. If m = n =0, d X, Y 0. We use the aametes c = 50 and = n ths wo. Some aametes used n LB ecuson ae lsted n Tab.. Tha Vaable S D Th me Th del ThTa Value Tab.. Paametes of LB ecuson. 4. Tacng ultle Lnea Etended Tagets In ths eement, thee ae thee etended tagets n ths scenao, and they all move at a V model. The tycal ont measuements ognatng fom the Taget ae gven n Fg.. The tue taget tacs ae shown n Fg.. Taget, Taget and Taget 3 ae bon at s, 0 s and 0 s, esectvely. The tacng esults obtaned fom PP-LB flte and the oosed BP-LB flte fo a sngle un s also gven n Fg.. It can be seen that two fltes can successfully tac thee lnea etended tagets. To ovde a efomance comason n sense of statstcal evaluaton, the aveage cadnalty and aveage OPSA dstance ove 50 onte alo uns ae shown n Fg. 3 and Fg. 4, esectvely (a) Fame (c) Fame (b) Fame (d) Fame5 Fg.. The ont measuements of Taget at dffeent fames n the fst eement.

7 RADIOENGINEERING, VOL. 5, NO. 3, SEPTEBER Taget Taget Taget3 tue tacs PP-LB BP-LB Fo RFS based algothms, the cadnalty means the numbe of estmated tagets. The OSPA dstance s a oe metc, whch enalzes both the cadnalty eo and the eo n the state sace. As shown n Fg. 3, both PP-LB flte and BP-LB flte can accuately estmate cadnalty. Howeve, the oosed BP-LB flte can acheve moe accuate state estmaton. The OSPA ea aeas at about 0 s, because of bth tagets. As shown n Tab., 40 bo atcles ae enough fo each tac n the oosed BP-LB flte. Howeve, PP-LB flte eques 000 ont atcles. The numbe of atcles needed fo BP-LB flte s much smalle than that of PP-LB flte. As a esult, the aveage untme of BP-LB flte s much less than that of PP-LB flte. It oves the oosed BP- LB flte can emaably deceases the untme fo multle lnea etended tagets Fg.. The tue tacs and tacng esults n the fst eement. adnalty 4 3 eal numbe PP-LB BP-LB Tme Fg. 3. adnalty statstcs fo PP-LB and BP-LB fltes n the fst eement. OSPA 6 4 PP-LB BP-LB Tme Fg. 4. Aveage OSPA dstances fo PP-LB and BP-LB fltes n the fst eement. Flte Paamete PP-LB BP-LB Suvvng atcle numbe Newbon atcle numbe 000 Runtme (sec) Tab.. Aveage untme and the numbe of atcles fo PP-LB and BP-LB fltes n the fst eement. 4.3 Tacng ultle aneuveng Etended Tagets In ths eement, tue taget tacs ae shown n Fg. 5. Thee ae two hghly maneuveng etended tagets and one lnea etended taget n ths scenao. Fo eamle, Taget s bon at s and des at 30 s. It fstly moves at V model fom s to 9 s, then eecutes T model fom the 0 s to s, and fnally moves at V model fom 3 s to end. The motons of the tagets ae summazed n Tab. 3. Let denote the V model and denote the T model. The ntal moton models ae set to V. The model tanston mat s set to H (46) The tacng esults obtaned fom PP--LB, BP-V-LB and BP--LB fltes fo a sngle un ae also shown n Fg. 5. When the moton model swtch occus, the sngle-model flte fals to catue the tagets. Howeve, the PP--LB flte and BP--LB flte can well accommodate taget maneuve. The aveage cadnalty and the aveage OPSA dstance ove 50 onte alo uns ae dected n Fg. 6 and 7. BP-V-LB flte yelds lage cadnalty eo at 0 s to 0 s and 6 s-30 s due to taget maneuve. Futhemoe, thee ae hgh eas n OSPA metc whee the estmated cadnalty s ncoect. It oves that sngle-model flte s not enough to tac adly maneuveng etended tagets. Taget Bon tme De tme Taget s 30 s Taget 0 s 30 s V moton s-9 s, 3 s-30 s s-5 s, 9 s-30 s Taget 3 0 s 30 s s-30 s T moton 0 s- s 6 s-8 s Tab. 3. The moton of etended tagets n the second eement.

8 534. LI, Z. LIN, W. AN, ET AL., BOX-PARTILE LABELED ULTI-BERNOULLI FILTER FOR ULTIPLE EXTENDED TARGET Taget tue tacs BP-V-LB PP--LB BP--LB Flte Paamete PP- -LB BP- V-LB BP- -LB Suvvng atcle numbe Newbon atcle umbe 000 Runtme(sec) Taget Tab. 4. Aveage untme and the numbe of atcles n the second eement s, and t s about ten tmes less than that of PP-- LB flte. It oves that BP--LB flte s moe comutatonally effcent than PP--LB flte. Theefoe, the oosed aoach s moe aoate fo ealtme tacng. 00 Taget Fg. 5. The tue tacs and tacng esults n the second eement. adnalty 4 3 eal numbe BP-V-LB PP--LB BP--LB 5. onclusons Ths ae esents a novel aoach to tac multle etended tagets wthn the bo-atcle famewo. BP- LB and BP--LB fltes ae oosed to tac lnea etended tagets and adly maneuveng etended tagets, esectvely. In ou aoach, the measuements of etended taget ae modeled as nteval measuements, and the ont samles ae elaced by egon samles n LB ecuson. omaed wth tadtonal ont-atcle aoach, the oosed aoach needs fewe atcles to guaantee a smla accuacy. onsequently, multle etended tagets can be taced usng less untme, whch s motant fo eal-tme alcatons Tme Fg. 6. adnalty statstcs fo BP-V-LB, PP--LB and BP--LB fltes n the second eement. OSPA BP-V-LB PP--LB BP--LB Tme Fg. 7. Aveage OSPA dstances fo BP-V-LB, PP-- LB and BP--LB fltes n the second eement. As ndcated by Fg. 7, both PP--LB flte and BP--LB flte efom comaably well. Howeve, much fewe atcles ae needed by the BP--LB flte. The aveage untmes of these thee fltes ae lsted n Tab. 4. The aveage untme of BP--LB flte s Refeences [] AI, F., FAN, H., FU, Q. Benoull flte fo etended taget n clutte usng Posson models. hnese ounal of Electoncs, 05, vol. 4, no., DOI: 0.049/ce [] GILHOL, K., GODSILL, S., ASKELL, S., et al. Posson models fo etended taget and gou tacng. In SPIE Poc alfona (USA), 005,. 5930R 5930R. DOI: 0.7/ [3] AHLER, R. P. S. Statstcal ultsouce ulttaget Infomaton Fuson. London (UK): Atech House, 007. [4] AHLER, R. P. S. ulttaget Bayes flteng va fst-ode multtaget moments. IEEE Tansactons on Aeosace and Electonc Systems, 003, vol. 39, no. 4, DOI: 0.09/TAES [5] AHLER, P. R. S. PHD fltes of hghe ode n taget numbe. IEEE Tansactons on Aeosace and Electonc Systems, 007, vol. 43, no. 4, DOI: 0.09/TAES [6] VO, B. T., VO, B. N., ANTONI, A. The cadnalty balanced mult-taget mult-benoull flte and ts mlementatons. IEEE Tansactons on Sgnal Pocessng, 009, vol. 57, no.,. 409 to 43. DOI: 0.09/TSP [7] VO, B. N., VO, B. T., PHUNG, D. Labeled andom fnte sets and the Bayes mult-taget tacng flte. IEEE Tansactons on Sgnal Pocessng, 04, vol. 6, no. 4, DOI: 0.09/TSP [8] VO, B. T., VO, B. N. Labeled andom fnte sets and mult-obect

9 RADIOENGINEERING, VOL. 5, NO. 3, SEPTEBER conugate os. IEEE Tansactons on Sgnal Pocessng, 03, vol. 6, no. 3, DOI: 0.09/TSP [9] REUTER, S., VO, B. T., VO, B. N., et al. The labeled mult- Benoull flte. IEEE Tansactons on Sgnal Pocessng, 04, vol. 6, no., DOI: 0.09/TSP [0] VO, B. N., A, W. K. The Gaussan mtue obablty hyothess densty flte. IEEE Tansactons on Sgnal Pocessng, 006, vol. 54, no., DOI: 0.09/TSP [] REUTER, S., SHEEL, A., DIETAYER, K. The multle model labeled mult-benoull flte. In 8 th Intenatonal onfeence on Infomaton Fuson. Washngton, D (USA), 05, [] GNING, A., RISTI, B., IHAYLOVA, L., et al. An ntoducton to bo atcle flteng. IEEE Sgnal Pocessng agazne, 03, vol. 30, no. 4, DOI: 0.09/SP [3] SHIKORA,., GNING, A., IHAYLOVA, L., et al. Boatcle obablty hyothess densty flteng. IEEE Tansactons on Aeosace and Electonc Systems, 04, vol. 50, no. 3, DOI: 0.09/TAES [4] SONG, L., ZHAO, X. Bo-atcle cadnalty balanced multtaget mult-benoull flte. Radoengneeng, 04, vol. 3, no., [5] GRANSTRÖ, K., LUNDQUIST,., ORGUNER, U. A Gaussan mtue PHD flte fo etended taget tacng. In 3 th onfeence on Infomaton Fuson. Ednbugh (UK), 00,. 8. DOI: 0.09/IIF [6] GNING, A., RISTI, B., IHAYLOVA, L. Benoull atcle/bo-atcle fltes fo detecton and tacng n the esence of tle measuement uncetanty. IEEE Tansactons on Sgnal Pocessng, 0, vol. 60, no. 5, DOI: 0.09/TSP [7] LONG, Y. L., XU, H., AN, W., et al. Tac-befoe-detect fo nfaed maneuveng dm mult-taget va -PHD. hnese ounal of Aeonautcs, 0, vol. 5, no., DOI: 0.06/S () [8] LI, X. R., ILKOV, V. P. Suvey of maneuveng taget tacngat V: multle-model methods. IEEE Tansactons on Aeosace and Electonc Systems, 005, vol. 4, no. 4, DOI: 0.09/TAES [9] SHUHAHER, D., VO, B. T., VO, B. N. A consstent metc fo efomance evaluaton of mult-obect fltes. IEEE Tansactons on Sgnal Pocessng, 008, vol. 56, no. 8, DOI: 0.09/TSP About the Authos... ao LI was bon n 988. He eceved hs.sc. n Electonc Scence and Technology fom Natonal Unvesty of Defense Technology n 0. He s cuently wong towad the Ph.D. degee and nteested n sgnal ocessng, small taget detecton and tacng. Zang LIN was bon n 98. He eceved hs Ph.D. degees n ommuncaton and Infomaton System fom Natonal Unvesty of Defense Technology n 0. Hs eseach nteests nclude sgnal ocessng and nfomaton fuson. We AN s bon n969. She s cuently a Pofesso n Natonal Unvesty of Defense Technology. He eseach s focused on sace nfomaton acquston and ocessng. Yyu ZHOU was bon n 948. He s cuently a Pofesso n Natonal Unvesty of Defense Technology. Hs eseach s focused on ada sgnal ocessng, assve locaton technology.