I.J. Informaton echnoogy and Computer cence -9 ubshed Onne June n C http://.mecs-press.org/ Asynchronous Data Fuson Wth arae Fterng Frame a Department of Informaton ngneerng Zhenghou Coege of Anma usbandry ngneerng Zhenghou..Chna 5 -ma: nhu@6.com Junhu u tudes Affars Offce Zhenghou Coege of Anma usbandry ngneerng Zhenghou..Chna 5 -ma: nhu@6.com Abstract hs paper studes the desgn of data fuson agorthm for asynchronous system th nteger tmes sampng. Frsty the mutsensor asynchronous sampngs s mapped to the basc as accordngy a sampng sequence of snge sensor can be taen. econdy amng at the sensor th the densest sampng ponts the modfed parae fterng s gen. Afterards the sequenta fterng fuson method s ntroduced to dea th the case that there are mutpe mapped measurements at some sampng pont. Fnay a noe parae fterng fuson agorthm for asynchronous system th nteger tmes sampng s proposed. Besdes a udgment scheme to dstngush measurement number at eery sampng pont n the fuson perod s aso desgned. One smpe computer numerca aue smuaton s demonstrated to adate the effecteness of the udgment scheme and the proposed asynchronous fuson agorthm. Inde erms data fuson; asynchronous system; nteger tmes sampng; parae fterng; sequenta fterng I. IODUCIO In recent years mutsensor data fuson technoogy s pad great attenton n many mtary and c feds and s etensey apped. At present a ot of data fuson agorthms to dfferent appcaton bacgrounds and constrants are presented [-]. For the research of cassca data fuson the synchronous mutsensor system n hch eery sensor has common sampng rate and sampng tme s unform s none of man obects. But n the practca system these sensors n the mutsensor system hae often dfferent sampng rates and sampng ponts because of dfferent tas requrement and dfferent nds of sensors. As a resut t s nterestng to study asynchronous data fuson th dfferent sampng rates and has mportant theoretca sense and etense appcaton scene. Up to no some usefu data fuson agorthms for Identfy appcabe sponsor/s here. If no sponsors deete ths tet bo. sponsors asynchronous system under the centraed frame hae been presented [678]. he or n [] s to frsty dscrete the contnuous system secondy estabsh the reate measurement to current state by use of the reaton beteen the states of oca ponts and the fuson center and afterards use the centraed fuson to estmate the state of the target. But ths agorthm ony adapts the case that eery sensor ony has one measurement n the fuson perod and the more compe case cannot be deat th. An nterestng or s aso done n [6] by combng aeet th aman fter. It can treat th the nose-reducton effectey but the mutsensor case cannot be soed. In [7] the mutsensor mutscae fuson as consdered; neertheess the gen agorthm s compe. In addton the desgn of data fuson agorthm for mutrate sampng system ere researched n []. Bascay they both adopt the remodeng dea to the state of sampng ponts n the fuson perod. hereby these to agorthms are suboptma n the sensor of near mnmum mean square error. Amng at the aboe-mentoned probems ths paper taes a nd of mutsensor dynamc system th dfferent sampng rates and ntroduces the parae fterng and sequenta fterng to soe asynchronous data fuson th nteger tmes sampng. Accordngy a noe optma asynchronous data fuson agorthm s proposed and the runnng steps are sted n ths paper. Its man structure ncudes four aspects such as measurement mappng parae fterng udgment of measurement number and sequenta fterng. he rest of ths paper s organed as foos. In ecton II t descrbes the mutsensor system th nteger tmes sampng and probem formuaton. ecton III proposes a noe parae fterng fuson agorthm. Computer smuaton s done n ecton IV. Fnay e concude n ecton V. Copyrght C I.J. Informaton echnoogy and Computer cence -9
Asynchronous Data Fuson Wth arae Fterng Frame II. OB FOUAIO A. ystem Descrpton A nd of mutsensor system hch s composed of sensors s consdered. ery sensor obseres the target state th dfferent sampng rate and the measurement s here s the measurement matr. he correspondng state equaton of sensor s here the sampng perod of sensor s hch a s an nteger and ; here s aso an nteger. uppose that the sampng perod for hch the sampng perod s the bggest among them s the fuson perod then o there are measurements for sensor n a fuson perod then 5 It easy nos that the sampng perods for a of sensors hae the nteger tmes reaton from q. and q.. Fgure. shos the mutsensor system th. ; s th sampng tme of sensor n th fuson perod and 6 here ; and n crete tme arabe. n n r of sensor. rocess nose a Gaussan hte nose sequence and satsfes { } 8 s a ds s state ector s state transfer mat n here ;. p s the measurement of sensor p n to at s the measurement matr. easurement nose p s aso a Gaussan hte nose and ts statstca property s { } { } here ;. s a poste matr and there are correate beteen process nose and measurement noses namey { } here ;. he orgna state s a random ector and satsfes { } {[ ][ ] } s 9 B. robem Formuaton Fgure. he sampng of mutsensor system th hen the dynamc gen by q. and can be 7 In order to conenenty descrbe the proposed agorthm t s necessary to transform the aboementoned mutsensor dynamc system to a snge one. Based on the sampng tme of fuson center the sampng ponts of a of sensors can be mapped to ths reference as see Fgure.. e easy no: frsty there s one measurement at east at the sampng pont n a fuson perod after they are mapped. And the measurement number at eery sampng pont s dfferent bascay. econdy n a fuson perod there are a measurements from sensor at eery sampng pont. Copyrght C I.J. Informaton echnoogy and Computer cence -9
Asynchronous Data Fuson Wth arae Fterng Frame 5 Copyrght C I.J. Informaton echnoogy and Computer cence -9 5 Fgure. he mapped mutsensory dynamc sampng system hen the basc dea of parae fterng fuson agorthm th nteger tmes sampng s as foos: the sampng ponts of a of sensors are mapped to the reference as on the bass of sampng tme of fuson center. Afterards the tme as of sensor can be taen as bass and the parae fterng agorthm can be performed. specay hen the sampng pont has mutpe measurements the sequenta fterng fuson n [9] can be used. Fnay e can get the fuson estmate based on the goba nformaton for eery sampng pont n the fuson perod. In order to reae aboe-mentoned dea the foong probems must be soed: One s ho to perform the parae fterng agorthm based on sensor. he other s ho to dstngush hch sensor measurements eery sampng tme has n a fuson perod. et the fuson agorthm s estabshed n terms of song aboe-mentoned to probems. III. AA FIIG FUIO AGOI WI IG I AIG A. arae Fterng Fuson Agorthm By consderng ths subsecton presents the parae fterng fuson agorthm n the case that there s ony one measurement at eery sampng pont namey ony consder the measurement of sensor. From q.7 and q.8 state equaton and measurement equaton of sensor are as foos: 5 o one has the foong theorem. heorem Accordng to and 5 one can get the foong ne mutsensor system 6 7 here [ ] 8 9 and roof. he deratons of q. 6 to q. can be fnshed easy. In terms of e hae { } A.
6 Asynchronous Data Fuson Wth arae Fterng Frame Copyrght C I.J. Informaton echnoogy and Computer cence -9 o one has A. A. here A. and [ ] } ] [ ] [ A.5 hereby } A.6 he proof s fnshed. hen the parae fterng fuson agorthm based on the measurements of sensor s as foos []. One step state predct durng the fuson perod here 5 One step state predct beteen the fuson perods 6 7 By use of q. 6 q. can be rertten to 8 here 9 tate update at eery tme n the fuson perod A here I A Update for correspondng sate beteen fuson perods A
Asynchronous Data Fuson Wth arae Fterng Frame 7 here and 5 A I 6 7 8 A 9 A { o q. and q. can be rertten to } Because t noes many arabes n the aboegen agorthm n order to prode cear understandng Fgure. shos a arabes to compute and. Fgure. A arabes to compute the goba estmate at hs subsecton ges the parae fterng agorthm for hch eery sampng pont ony has one sensor measurement. oeer Fgure. shos that t s possbe that some sampng pont coud hae seera measurements namey s no onger snge measurement. In ths case the sequenta fterng fuson can be ntroduced to dea th t. As a resut t s the ey to dstngush ho many measurements eery sampng tme n the fuson perod has. hen the udgment scheme s gen by the net subsecton. B. easurment udgment scheme For the mutsensory dynamc system th the sampng of nteger tmes the a about the change of measurement number at eery sampng pont. hen the udgment scheme to measurement number at eery sampng pont n the fuson perod sees Fgure.. n ^ mod? o og c mod ^? o og c? o < n? o num n num og c num Fgure. he udgment scheme to measurement number at eery sampng pont n the fuson perod In ths fgure mod s moduo operaton and the output parameter num n represents the mapped measurement number at eery sampng pont n the fuson perod. Ceary aboe-mentoned scheme can ony udge the measurement number at eery sampng pont and cannot epan hch sensor they beong to. For the mutsensor system researched n ths paper the measurement at tme can be gen as foos f mod f mod here num. C. Agorthm ummary Accordng to the anayss n subsecton A and B e sum up the parae fterng fuson agorthm as foos: Copyrght C I.J. Informaton echnoogy and Computer cence -9
8 Asynchronous Data Fuson Wth arae Fterng Frame ap sampng ponts of a of sensors to the tme as of sensor and tae the tme of sensor as bass to perform fuson fterng. et up and sampng tmes.. erform 6 7 8 and sequentay. 5 Use and 5 to compute the estmate of sensor and correspondng coarance. 6 Accordng to and to compute the estmate and the estmate coarance. 7 Use the udgment scheme gen by Fgure. to dstngush the measurement number at ths tme. 8 If num ese go to. se contnue. 9Adopt the sequenta fterng fuson method n [9] to fuse other measurements num and assgn the taen estmate and error coarance to and respectey. If then and go to. se go to. Fnay compute. nd. IV. COU IUAIO hs secton uses computer smuaton to ony adate the effecteness of the proposed parae fterng fuson agorthm for the asynchronous sampng system. A of resuts are the mean of onte Caro smuatons. A. ampe For the system gen by q.7 and q.8 e tae 5. 98.. here 5. Orgna aue. hen the smuaton resuts are shon by Fgure.5 Fgure.6 and Fgure.7. he absoute error mean s gen by abe.i. Y--ensor number Y--stmate 5 5 6 7 8 9 5 6 X--ampng pont Fgure.5 utsensor measurements th 8 6 - - ea state arae fterng fuson -6 5 5 5 5 5 5 X--muaton pont Fgure 6 stmate resut of the proposed parae fterng fuson Y--stmate error.5.5 -.5 - stmate error -.5 5 5 5 5 5 5 X--muaton pont AB I. Agorthm Absoute error mean of stmate ABOU O A OF IA he parae fterng fuson agorthm.95 Fgure.7 stmate error of the ne agorthm From Fgure.5 to Fgure.7 and abe. e can get the foong concusons: Fgure.5 hch demonstrates the measurement dstrbuton of mutsensor dynamc system th shos that measurement number of eery sensor satsfes Copyrght C I.J. Informaton echnoogy and Computer cence -9
Asynchronous Data Fuson Wth arae Fterng Frame 9 q.6. It aso means that the udgment scheme s aso effecte. It shos that the proposed agorthm n ths paper can effectey dea th data fuson of nteger tmes sampng and achee outstandng tracng estmate effect. In a ord the proposed parae fterng fuson method can effectey adapt the mutsensor system th nteger tmes sampng and can reae good estmate resut. V. COCUIO hs paper studes the desgn of data fuson agorthm for asynchronous mutsensor system th nteger tmes sampng accordngy by ntroducng parae fterng technoogy a noe data fuson agorthm to dfferent sampng rate s proposed. he deraton process and smuaton resut are presented to adate ts effecteness. here are many open ssues for eampe to consder the communcaton deay and transmsson error n the parae fterng fuson. FC [] Chengn Wen Donghua Zhou uan an and ongca Zhang Dstrbuted Informaton Fuson Agorthm for nge ensor ynamc ystem On he Bass Of utscae Dynamc odes Acta Automatc nca of Chna o.7 no. pp.58~65. [] Je Wang Chonghao an and Xaorong Asynchronous utsesnro Data Fuson Journa Contro and Decson of Chna o.6 no.6 pp.877-88. [] Aouan A ce On asynchronous data fuson roc of the Annua outheastern ymposum on ystem heory. Athens pp.-6 99. [] Aouan A ce erformance anayss of an asynchronous trac fuson and archtecture roc of I. Orando 997 9-5. [5] amd. ashempour umt oy Aan J. aub Decentraed structures for parae aman fterng I ransactons on Automatc Contro o. no. pp. 88-9 988. [6] Chengn Wen utscae Data Fuson for ut ensor nge ode Dynamc ystems Acta ectronca nca o.9 no. pp.-5. [7] png Yan Bng Wang and Feng A e Agorthm of utscae Fuson stmaton Based on aman Fterng Journa of enan Unersty of Chna atura cence o. no. pp.6-9. [8] Baoshu Wang Fangshe he esearch On utpe argets racng Based On he Data Fuson echnque Jouna of Xdan Unersty of Chna o.5 no. pp.69-7 998. [9] Chengn Wen Bng uanbo Ge A Data Fuson Agorthm Based on Fterng tep by tep Acta ectronca nca of Chna o. no.8 pp. 6-67. [] uanbo Ge Guo an Wang anhao ang and Chengn Wen he esearch on Asynchronous Data Fuson Agorthm Based on ampng of atona umber mes Acta ectronca nca of Chna o. no. pp. 5-58 6 [].Y.Yan B..u and D..Zhou he modeng and estmaton of asynchronous mutrate mutsensor dynamc systems Aerospace cence and echnoogy no. pp.6-7 6. a femae and master as born n 979. he s a ecturer at department of Informaton ngneerng Zhenghou Coege of Anma usbandry ngneerng. er research nterests ncude target tracng and data fuson. Junhu u mae and master as born n 98. e s a ecturer at tudes Affars Offce Zhenghou Coege of Anma usbandry ngneerng. s nterests ncude sgna processng and nformaton fuson. Copyrght C I.J. Informaton echnoogy and Computer cence -9