Multi-Sensor Distributed Fusion Based on Integrated Probabilistic Data Association

Transcription

1 Mult-Seor trbuted Fuo Baed o Itegrated Probabltc ata Aocato Eu-Hyu Lee 3rd evelopmet vo Agecy for efee evelopmet aejeo Republc of Korea Emal: jobdavd@addrer aro Mušc ae Lyul Sog ept of Electroc Iformato Sytem Egeerg Hayag Uverty A-a Republc of Korea Emal: daromuc@gmalcom tog@hayagacr Abtract h paper preet two mult-eor fuo algorthm for gle target tracg cluttered evromet We etablh a trac qualty meaure for fuo trac cetralzed fuo ad trac-to-trac fuo he fuo algorthm are derved by etedg the tegrated probabltc data aocato IPA) techque to multeor ytem We propoe a cetralzed fuo algorthm called the Mult-Seor IPA MS-IPA) he Mult-Seor trbuted trac-to-trac Fuo IPA MSF-IPA) flter algorthm alo propoed for dtrbuted eor ytem Both algorthm recurvely update the probablty of target etece whch may be ued for fale trac dcrmato Keyword Mult-Seor trbuted rac Fuo Itegrated Probabltc ata Aocato IPA) rac Etece Cetralzed Fuo I INROUCION h paper preet two gle target tracg algorthm that determe the target etece probablte of fuo trac cluttered evromet Oe a cetralzed fuo ad the other a trac-to-trac fuo A majorty of algorthm for gle-eor target tracg clutter are baed o the all-eghbor probabltc data aocato PA) [-4 9] Sgle eor target tracg algorthm are beg eteded to fd the etmato oluto for multple eor ytem he PA eteded to mult-eor PA MSPA) [-] where the parallel or the equetal [3] updatg cheme are ued For tracg a maeuverg target the preece of clutter wth multple eor the PA combed wth the teractve multple model IMM) [6] flter called equetal mult-eor IMM/PA S- IMM/MSPA) that uggeted [7] where the equetal flterg of [3] appled for fug the formato of multple eor h algorthm later adapted to a parallel updatg cheme ad deoted a IMM/MSPA [8] hee approache to gle target tracg have a commo aumpto that every trac true e follow a target I other word the probablty of target etece PE) o that PE ot ued a a trac qualty meaure for fale trac dcrmato he uage of PE a a trac qualty meaure propoed the tegrated probabltc data aocato IPA) [3 4] whch combed wth the IMM flter IMMIPA) [9] for maeuverg target tracg For mult-target tracg clutter the eteo to mult-target tracg Jot PA JPA)[6] ad tegrated PA JIPA) wth trac etece probablty [5] are propoed o allevate computatoal load of the mult-target data aocato algorthm lear mult-target IPA LM-IPA) [5] ad teratve JIPA JIPA) [9] are propoed baed o gle eor hee algorthm may be appled a equetal form to hadle each eor meauremet eparately for cetralzed fuo or they may be appled to each eor to geerate trac for dtrbuted trac-to-tac fuo For trac fuo multple eor ytem trac formato from each eor ad aocato betwee the trac are eeded Varou trac fuo algorthm uch a cove fuo Bar-Shalom-Campo rule traclet fuo ad trac aocato metrc [-] have bee developed for dtrbuted tracg tuato hee approache are baed o the aumpto that aocato betwee trac are perfect ad there o fale trac o that trac qualty meaure ot eeded It may ot be poble to atfy the aumpto real applcato I th paper the cofrmed trac regardle of fale ad true ature of the trac geerated by each eor are tramtted to a fuo ceter wth trac formato cludg the PE he goal of the paper to develop mult-eor IPA MS-IPA) for cetralzed fuo ytem ad mult-eor trbuted trac-to-trac Fuo IPA MSF-IPA) for dtrbuted fuo ytem he paper orgazed a follow Secto II preet the problem formulato he MS-IPA algorthm decrbed Secto III Secto IV preet the MSF-IPA algorthm followed by a mulato eample Secto V followed by cocludg remar VI II PROBLEM SAEMEN We aume that the target dyamc are modeled

2 Cartea coordate by F + ν R + ) where the target tate vector at tme F the trato matr ad ν a zero-mea whte Gaua oe equece wth ow varace Q Smlar to other target tracg algorthm the pot target aumpto ued Each target may create zero or oe target meauremet per eor per ca accordg to probablty of detecto P he target meauremet for the -th eor deoted a y H + w ) where w a ample of zero-mea whte Gaua oe equece wth covarace R Clutter meauremet are radom ad follow a Poo dtrbuto [] A Poo proce characterzed by the clutter meauremet dety eote by z the et of m meauremet receved by the -th eor at a curret ca Let z deote the -th preet meauremet of y z z If the target meauremet y By deotg the meauremet et of eor collected up to the ca tme a Z { } z Z 3) the the cumulatve et of all meauremet from N eor collected up to tme gve by Z Z Z Z N { } { } N z z z Z 4) he evet that the target et at tme deoted by χ he the probablty that the target et at tme P χ ) ad the probablty that the target doe ot et P χ ) P χ) 5) he objectve to recurvely calculate the poteror probablty dety fucto pdf) from p χ Z ) p χ Z ) P χ Z ) 6) where the tate etmate ad t error covarace uder the codto of target etece for the mult-eor ytem are obtaed from p χ Z ) d 7) III MULI-SENSOR IPA MS-IPA) We preet the MS-IPA algorthm for the ytem wth two eor by modfyg the etg gle eor baed IPA SS-IPA) [3] h approach correpod to a cetralzed fuo cheme whch all meauremet are ued multaeouly he MS-IPA equato ca be ealy adapted to the cae of N eor ce the form of the reult aalogou to the SS-IPA A State Etmate ad Error Covarace Matr he tate etmate for the two-eor ytem p Z Z ) d m m m m p χ χ χ Z ) d 9) where χ the hypothe that the -th meauremet of the eor the target meauremet f t mea there o eor target detecto) ad all other are clutter meauremet the tate etmate for each meauremet et from both eor a [8] ad the data aocato probablty repreetg the weght for each meauremet et defed a P χ χ χ ) Z ) he updated tate etmate ad t error covarace P are obtaed by the Kalma flter algorthm wth the predcted tate etmate ad t error covarace P uch a + K z H ) ) P I K H ) P z atfe z z ) for ) for z z ) for ) for ) where the taced meauremet z 3) ad where the meauremet matr H deped o target detecto outcome uch a P ) ) p χ Z ) d 8) he PE P χ Z ) obtaed by a recurve formula

3 H H ) for ) for H H H ) for ) for 4) I the equato above the ubcrpt m mple a m matr he error covarace matr of 5) equal m m + ) ) P P 5) B he ata Aocato Probablte he data aocato probablte for the two-eor ytem at tme uder the codto of target etece are obtaed a PP G) PP G ) P p z )/ λ ) PPG PP G) P pz ) / λ PP pz z )/ λλ ) 6) where P the detecto probablty of the target for the eor P the gatg probablty λ G the clutter dety ad a ormalzg cotat gve by P P ) P P ) G G m P PPG ) p z ) / λ m P PG) P p z ) / λ m m P P p z z λλ )/ ) 7) We coder cae whe calculatg the meauremet lelhood I the gle meauremet cae p z ) N z ; ) H S 8) where the covarace wrtte a S H P H + R 9) I the two-meauremet cae p z z ) p z z Z ) z ) N ; H S z where H H H ) ad the covarace S wrtte a S H P H + R ) Note that R dag R R ) ue to the jot Gaua pdf for the jot meauremet cae the aocato probablty ot the product of aocato probablty calculated depedetly for each eor meauremet I [] a appromato that the data aocato probablty equal the product of each data aocato probablty of the eor ued C Probablty of rac Etece he update of the probablty of trac etece cot of two tep he propagato tep the ame a the SS-IPA propagato For the Marov Cha I [3] the a pror probablty of trac etece at tme calculated by P χ Z ) πp χ Z ) + π P χ Z ) ) where the compoet of the Marov Cha trato matr are π P χ χ ) π P χ χ ) 3) he ecod tep a update tep gve meauremet at tme he poteror probablty of trac etece at tme calculated by P χ Z ) P χ ) Z ) P χ Z ) 4) IV MULI-SENSOR ISRIUBE RACK-O-RACK FUSION IPA MSF-IPA) Here we eted the MS-IPA algorthm to Mult-Seor trbuted trac-to-trac Fuo IPA MSF-IPA) he MS-IPA procee meauremet et from two eor he MSF-IPA procee cofrmed local IPA trac receved from the dvdual eor he beeft of th approach are that t ca be appled for trac fuo applcato the dtrbuted eor ytem cluttered evromet ad ehace the fale trac dcrmato performace We coder the followg trac fuo tuato Each eor tramt cofrmed trac to a fuo ceter ad the MSF-IPA algorthm ued to fug the trac

4 Itally there are o trac the fuo ceter ad the tal trac are geerated from the cofrmed trac tramtted from each eor he cofrmed local trac clude both true ad fale trac Each SS-IPA tate ad update trac from meauremet of each eor ad t cofrm the trac reachg the cofrmato threhold of the PE or termate the trac wth low PE whch called fale trac dcrmato h cofgurato depcted Fg Fg MSF-IPA We aume that the two eor cover the detcal urvellace area ad tramt the local trac at the ame tat Let η η ad deote trac of eor ad eor ad the trac fuo trac ad{ η } { η } ad { } the et of trac of eor ) ad eor ) ad the fuo ceter repectvely he poteror probablty dety fucto of the tate for each tracη η ad the pror probablty dety fucto for trac aumg trac etece are η η η η η P χ Z ) N ; P ) 5) η η η η η P χ Z ) N ; P ) 6) χ ad P Z ) N ; P ) 7) he trac et of { η } ad { η } aume the role of meauremet et of trac he trac η ad η are obtaed wth the trac detecto probablte P ad P For trac fuo the lelhood of trac η wth repect to trac η η p E Z) η 8) p ) p Z) d where the ubcrpt deote the -th eor ad the lelhood fucto atfe η η η η p ) N ; H P ) 9) where H η the meauremet matr mappg from the tate pace of tracη to the pace of trac ad t the detcal matr due to the detcal coordate he lelhood fucto η η η p N ; S ) 3) where the trac ovato covarace obtaed mlar to 34) a η η η η S P + P P P ) 3) where the cro covarace betwee the trac defed a η η P E ) ) ) 3) I the MSF-IPA approach to the trac fuo the tate etmate ad error covarace matr are computed through fug the trac η ad η wth by the correlated Kama flter update equato ad trac aocato η η probablty he trac aocato probablty η η η η P χ χ χ Z ) P ) P ) η η η η P P ) p / λη η > η η η L P ) P p / λη η η > η η η η PP p / λη / p λη η > η > 33) η where χ a poble trac aocato evet that each of the trac et { η } follow the target χ mea that oe of the trac et { η } follow the target) P the trac detecto probablty λ the clutter dety η η η P χ Z )) the PE of η For the jot meauremet cae the lelhood fucto for η > ad η > codered a the product of two depedet lelhood fucto of each eor for mplcty ad eay mplemetato L equal L P ) P ) { η} η η + P P ) p / λη η > { η } η η + P ) P p / λη η > { η} { η} η η η η PP p λη p λη η> η> + / ) / ) 34) he PE for the fuo trac updated wth the equato L 35) L ) where { }) P χ Z the predcted PE of fuo trac a 6)

5 he tate etmate ad the error covarace matr are updated a follow he fuo ceter calculate there are trac tate ad t covarace etmate P at he tate etmate ad the error covarace etmate are predcted to Each trac fued wth oe trac η of trac et { η } by the correlated Kalma flter update for η > adη ) or η adη > ) by η η η + K ) 36) where the Kalma ga η η η equal K P P ) S ) wth K η defed 48) If η zero η S η For η > ad η > ) the trac fuo eecuted equetally other word the trac tate η ued to update to geerate η frt ad η ued to update η ) to geerate η η by η η) η η η η Kη + ) 37) where the Kalma ga K η defed by η η η η η η Kη P P ) Sη ) 38) ad S η η η S η P + η ) P η η η η η P P 39) where the cro covarace betwee trac η ad η defed by η η η η P E{ ) ) } 4) ) We ow that the trac tate equvalet to the η trac tate η ) ad the error covarace P η equvalet to the error covarace P η he fal fued tate etmate for the trac et wth the trac aocato probablte { η} { η} ) η η η η η η 4) he fal fued covarace matr equal { η} { η} η η η η ) η η ) η η ) P P + ) ) 4) η η ) ) where the error covarace matr P η η for the tate η η ) defed by P I K ) P I K ) η η) η η η η η η η η η η η η Kη P Kη I Kη P Kη η η η η Kη P ) I Kη ) P η for the tate + ) + ) ) + ad the error covarace matr 36) equal η η η P I K ) P I K ) η η η η η η + K P K + I K P K η η η + K P ) I K ) ) ) ) h fhe the MSF-IPA recuro cycle at V SIMULAION EXAMPLE 43) η of 44) Smulato compare the two-eor baed MS-IPA algorthm wth the gle-eor baed IPA ad MSF- IPA algorthm regard to trac cofrmato ad fale trac dcrmato performace wth varou probablte of target detecto a cluttered evromet he MS- IPA a optmal cetralzed fuo methodology whch both eor ad eor tramt all the meauremet to a fuo ceter ad trac are talzed ad updated by feable combato of the meauremet from the eor h cetralzed fuo approach may ot be practcal for may real mult-eor ytem due to the eceve commucato burde ad/or ytem terface requremet However t ca be ued a a performace boud Both eor cover a two-dmeoal urvellace rego m log ad 4m wde ad each eor oberve the whole rego wth the ca tme of ec he clutter meauremet follow a uform Poo dtrbuto wth the clutter meauremet dety 4 /ca/ m for both eor Oe target move uformly for 5 ecod other word 5 ca he target tart at locato [ m 5 m ] ad t tal velocty [5 m/ m/ ] he target dyamc model follow ) he tate cot of poto ad velocty coordate ad y ) wth the trato matr F ) F F ) F ) 45) where the amplg perod he proce oe zeromea whte Gaua oe equece wth ow varace 4 3 Q ) /4 / Q q Q ) 3 Q ) / 46) 4 where q 866 m / he taced meauremet matr

6 H [ ] H H H H 47) wth the eor meauremet matrce H ad H for the two eor ad repectvely he meauremet error covarace matr R R 5 R R R m R 5 48) he Marov Cha I target etece propagato model [ π π ] [98 ] 49) he mulato epermet cot of 3 Mote Carlo ru for hgh ad low detecto probablty P ) tuato For the hgh detecto probablty cae P 8 whle P 6 for the low detecto probablty cae he trac are tated ug oe-pot talzato [3] ad tal PE aged to each trac he trac are cofrmed f the PE eceed the cofrmato threhold ad are elmated f the PE fall below the termato threhold Each mulato epermet cot of 3 mulato ru 5 ca per each eor) he fale trac dcrmato reult are how Fg for P 8 ad Fg3 for P 6 Each graph how the umber of cofrmed true trac C) ad cofrmato rate of true trac at every gle ca Fg3 Cofrmed rue rac Rate P 6) he quattatve tattcal outcome at the 5 th ca are ummarzed a follow a) C to follow ther orgal target ad to mata more tha 5 ca b) C wth trac mateace perod le tha 5 ca he Cotal) ummato of a) ad b) he C Rate the percetage of Cotal) for 3 target he umber of cofrmed fale trac ca CFSca) the ummato of the etg perod for all cofrmed fale trac ca whch clude the trac whch urvve to the 5 th ca ad the trac termated before the 5 th ca he computato load evaluated by etmatg the average tme of each mulato for 3 Mote Carlo ru ad t average rug tme ecod through Matlab 7 programmg o a 5 GHz Itel PC rug wdow XP preeted the ABLE I ad II a how ABLE I Cofrmed rue rac Performace Comparo P8) tem SS-IPA MSF-IPA MS-IPA a) b) 7 Cotal) C Rate CFSca tmeec/ru) Fg Cofrmed rue rac Rate P 8) ABLE II Cofrmed rue rac Performace Comparo P6) tem SS-IPA MSF-IPA MS-IPA a) b) Cotal) C Rate CFSca tmeec/ru) he MSF-IPA algorthm delver gfcatly better

7 fale trac dcrmato performace compared to the SS- IPA algorthm I the dtrbuted ytem cluttered evromet the MSF-IPA algorthm ha trac cofrmato rate cloe to the cetralzed fuo cheme eve the cae of low target detecto probablty Ug addtoal eor lely to further mprove MSF-IPA performace VI CONCLUSIONS h paper preet the MS-IPA algorthm for cetralzed fuo ad the MSF-IPA algorthm for dtrbuted fuo for mult-eor gle tracg cluttered evromet he ey ue to develop algorthm for target etece probablty calculato for fuo trac for trac mateace We demotrate that the propoed approache are ueful low target detecto probablty evromet where they reveal fat ad hgh cofrmato rate uperor tha gle eor approache We alo how that MSF-IPA a vable oluto for mult eor fuo a t requre o eceve creae computatoal cot compared to gle eor approache ad much le tha MS-IPA Referece [] Y Bar-Shalom ad E Fortma racg ad ata Aocato New Yor: Academc Pre 988 [] Y Bar-Shalom ad E e racg a cluttered evromet wth probabltc data aocato Automatca vol pp Sep 975 [3] Mušc R Eva ad S Staovć Itegrated Probabltc ata Aocato IPA) IEEE ra Automatc Cotrol vol 39 o 6 pp 37-4 Ju 994 [4] Mušc Automatc tracg of maeuverg target clutter ug IPA Ph dertato Uverty of Newcatle New South Wale Autrala 99 [5] Mušc B La Scala ad R Eva Mult-target tracg clutter wthout meauremet agmet IEEE ra Aeropace ad Electroc Sytem vol 44 o 3 pp Jul 8 [6] H A P Blom ad Y Bar-Shalom he teractg multple model algorthm for ytem wth Marova wtchg coeffcet IEEE ra Automatc Cotrol vol 33 o 8 pp Aug 988 [7] A Houle ad Y Bar-Shalom Multeor tracg of a maeuverg target clutter IEEE ra Aeropace ad Electroc Sytem vol 5 o pp March 989 [8] S Jeog ad J K ugat Multeor tracg a maeuverg target clutter ug IMMPA flterg wth multaeou meauremet update IEEE ra Aeropace ad Electroc Sytem vol 4 o 3 pp -3 July 5 [9] Mušc ad S Suvorova racg Clutter ug IMM-IPA Baed Algorthm IEEE ra Aeropace ad Electroc Sytem vol 44 o pp -6 Ja 8 [] C W Fre ad L Y Pao Alteratve to Mote-Carlo Smulato Evaluato of wo Multeor Fuo Algorthm Automatca vol 34 pp 3- Ja 998 [] Oello N N ad G W Pulford Smultaeou Regtrato ad racg for Multple Radar wth Cluttered Meauremet Proceedg of the 8 th IEEE Worhop o Stattcal Sgal ad Array Proceg Jue 996 pp 6-63 [] G W Pulford ad R Eva Probabltc data aocato for ytem wth multple multaeou meauremet IEEE ra Aeropace ad Electroc Sytem vol 43 o 4 pp Oct 7 [3] Wller C B Chag ad K P u Kalma Flter Algorthm for a Multeor Sytem Proceedg of the IEEE Coferece o eco ad Cotrol pp ec 993 [4] B O Adero ad J B Moore Optmal Flterg Pretce Hall 979 [5] Mušc ad R Eva Jot Itegrated Probabltc ata Aocato: JIPA IEEE ra Aeropace ad Electroc Sytem vol 4 o 3 pp Jul 4 [6] E Fortma Y Bar-Shalom ad M Scheffe Soar tracg of multple target ug jot probabltc data aocato IEEE Joural of Oceac Egeerg vol 8 o 3 pp Jul 983 [7] Y Bar-Shalom O the trac-to-trac correlato problem IEEE ra Automatc Cotrol vol 6 o pp Apr 98 [8] Y Bar-Shalom ad L Campo he effect of the commo proce oe o the two-eor fued-trac-covarace IEEE ra Aeropace ad Electroc Sytem vol pp Nov 986 [9] L Sog HW Km ad Mušc Iteratve Jot Itegrated Probabltc ata Aocato Proceedg of 6 th Iteratoal Coferece o Iformato Fuo pp 74-7 Jul 3 [] A Charlh F Govaer ad W Koch rac-to-rac Fuo Scheme for a Radar Networ IE Iteratoal Coferece o Radar Sytem pp -6 Glagow UK 3 [] S Mor KC Chag ad CY Chog Comparo of rac Fuo Rule ad rac Aocato Metrc Proceedg of 5 th Iteratoal Coferece o Iformato Fuo pp [] CY Chog S Mor W Barer ad KC Chag Archtecture ad algorthm for trac aocato ad fuo IEEE ra Aeropace Electroc Sytem vol 38 o pp [3] Mušc ad L Sog rac talzato: Pror target velocty ad accelerato momet IEEE ra Aeropace ad Electroc Sytem vol 49 o pp Ja 3