Journal of Communcatons Vol. 0, No. 8, August 05 Manuvrng argt racng Usng Currnt Statstcal Modl Basd Adaptv UKF for Wrlss Snsor Ntwor Xaojun Png,, Kuntao Yang, and Chang Lu School of Optcal and Elctronc Informaton, Huazhong Unvrsty of Scnc and chnology, Wuhan, 430074, Chna Wuhan Scond Shp Dsgn Rsarch Insttut, Wuhan, 430064, Chna Emal: {ngarthurpng, mluchang}@hotmal.com; yanguntao@mal.hust.du.cn Abstract hs papr prsnts Currnt statstcal modl basd Adaptv Unscntd Kalman Fltr (CAUKF) for manuvrng targt tracng, whch s basd on Rcvd Sgnal Strngth Indcaton (RSSI). In ordr to ntroduc th Kalman fltr, th stat-spac modl, whch uss RSSI valus as th masurmnt quaton, nds to b obtand. hus a currnt statstcal modl for manuvrng targt basd on th path loss modl s prsntd. o avod th ngatv nflunc of currnt statstcal modl s lmtd acclraton, th functonal rlaton btwn th manuvrng status of targt and th stmaton of th nghborng poston nformaton s appld to carry out th adaptaton of th procss nos covaranc Q(). hn, a novl da of modfd Sag-Husa stmator s ntroducd to adapt th procss nos covaranc matrx Q(), whl th adaptv masurmnt nos covaranc matrx R() s mplmntd by a fuzzy nfrnc systm. h xprmntal rsults show that th fnal mprovd CAUKF s an algorthm wth fastr rspons and bttr tracng accuracy spcally n manuvrng targt tracng. Indx rms Manuvrng targt tracng, adaptv unscntd alman fltr, currnt statstcal modl, wrlss snsor ntwor, rcvd sgnal strngth ndcaton I. INRODUCION h dvlopmnt pac of targt tracng rsarch s hghly td up wth th advancmnt of Wrlss Snsor Ntwor (WSN) and wrlss tchnologs. As snsor nods n WSN bcom smallr and strongr, th ablty of nformaton procssng s much strongr and wrlss ntwor opraton managmnt s also mor ntllgnt. At prsnt, many targt tracng algorthms for wrlss systm hav bn proposd. Bcaus Rado Frquncy Idntfcaton (RFID) basd tracng tchnology s lowcost and oprabl, so t s usd wdly n practcal applcatons. h partcular ntrst s th ablty to trac targts carryng actv RFID tags, by xplotng mtrcs of thr prodc transmssons such as m of Arrval (OA), m Dffrnc of Arrval (DOA), Angl of Arrval (AOA), and Rcvd Sgnal Strngth Indcaton (RSSI) []. h tradtonal RSSI basd tracng mthod Manuscrpt rcvd May, 05; rvsd July 7, 05. hs wor was supportd by th Natonal Natural Scnc Foundaton of Chna undr Grant No. 67508. Corrspondng author mal: ngarthurpng@hotmal.com. do:0.70/jcm.0.8.579-588. that s calld trangulaton mthod always uss a st of rfrnc nods to locat an unnown nod, whch convrts th RSSI valus from ach rfrnc nod nto dstanc stmat [], [3]. h trangulaton mthod rls on th masurmnts from ach rfrnc nod, whch has th ntrscton ara. Howvr, th dstanc stmats do not always ntrsct du to nos ntrfrnc, mang t vrtually mpossbl to trangulat th poston of th unnown nod. Hnc a rcursv mthod capabl of mantanng a poston stmat must b usd to guarant stat stmats vn whn no RSSI masurmnts ar avalabl or thy ar hghly corruptd by nos. Stat-spac modl s a powrful tracng tchnqu that rls on a manuvrng modl for th stmat of th unnown nod poston and an obsrvaton modl that rlats th poston to obsrvd masurmnts btwn th rfrnc nods and th unnown nod [4]. If th modl s lnar, th classcal Kalman fltr [5] s optmal for th stat stmaton. Unfortunatly, ths s a rar occurrnc n practc bcaus masurmnt modl basd on path loss modl s nonlnar. A common approach to ovrcom ths problm s to lnarz th systm bfor usng th Kalman fltr, rsultng n th Extndd Kalman Fltr (EKF) [6]. EKF s th most wdly usd fltrng mthod for nonlnar dynamc systm. Howvr, ths mthod of lnarzaton may ntroduc larg rrors n a postror man and covaranc of th stat stmaton. In lght of th ntuton that to approxmat a probablty dstrbuton s asr than to approxmat an arbtrary nonlnar transformaton, a novl fltr calld Unscntd Kalman Fltr (UKF) [7] was prsntd. In partcular, th UKF matchs th man corrctly up to th scond ordr n aylor srs and prdcts th covaranc corrctly up to th thrd ordr, whl th EKF can only approxmat th man up to th frst ordr. Howvr, l classcal Kalman fltr, th tradtonal UKF formulaton assums complt a pror nowldg of th procss nos covaranc matrx Q() and th masurmnt nos covaranc matrx R(). In most practcal applcatons, ths matrcs ar ntally stmatd or, n fact, ar unnown. h problm hr s that th optmalty of th stmaton algorthm n th UKF sttng s closly connctd to th qualty of ths a pror nos matrcs. Calculaton of th matrcs Q() and R() for a partcular masurmnt systm s a straght-forward procss, but t 05 Journal of Communcatons 579
Journal of Communcatons Vol. 0, No. 8, August 05 s not guarantd that Q() and R() rman constant wth tm gong by n hghly non-statonary nos condtons, so t s mpratv to contnuously tun th UKF n vw of th changng nos condtons n ordr to gt good fltrng prformanc. In ths papr, a novl fuzzy adaptv UKF s ntroducd. Basd on th currnt statstcal modl [8], a dvlopd adaptv UKF algorthm s proposd, whch stmats th procss nos covaranc matrx Q() by a nw formula. hn an mprovd fuzzy adaptv UKF s appld to stmat th covaranc matrx R(). h xprmntal rsults show that th fnal mprovd adaptv UKF can rduc prdcton rror and sns th varaton of moton fastr. It s compard wth th convntonal Currnt statstcal modl basd UKF (CUKF) [9], th tradtonal Currnt statstcal modl basd Adaptv Unscntd Kalman Fltr (CAUKF) and th Adaptv UKF (AUKF) usng mthod n [0]. h rmandr of th papr s organzd as follows. In Scton II, an adaptv currnt statstcal modl basd UKF s ntroducd. In Scton III, an mprovd adaptv UKF s prsntd. Scton IV dscrbs smulaton rsults of th algorthms. Numrcal xprmnt rsults ar provdd n Scton V. Fnally, Scton VI provds th concluson for ths papr. II. CURREN SAISICAL MODEL BASED UKF Currnt statstcal modl s a nd of tm-corrlatd modl wth non-zro man. It s assumd that th acclraton of targt () t [9], [] s dfnd by a( t) aˆ ( t) a( t) () whr at ˆ( ) s zro-man Marov procss, at () s th man of acclraton, assumd to b constant n vry samplng prod. h currnt statstcal modl [9], [] basd on RSSI s dnotd as wth X ( ) ( ) X ( ) U( ) a W ( ) RSSI ( ) f ( X ( )) V ( ) ( ) 0 0 0 0 0 0 0 ( ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( ) 0 0 0 ( ) 0 0 0 0 ( ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ( ) 0 0 0 0 0 0 0 ( ) 0 0 0 0 0 0 0 0 ( ) 0 0 0 0 0 0 0 ( ) 0 U ( ) 0 0 0 0 0 0 ( ) 0 0 0 0 () (3) (4) 05 Journal of Communcatons 580
Journal of Communcatons Vol. 0, No. 8, August 05 whr X ( ) [ x x x y y y z z z ]. x, y and z ar th prdctd coordnats of th manuvrng targt n thr dmnsonal spac, th prdctd vlocts of th targt n thr dmnsonal coordnat systm ar rprsntd by x, y and z rspctvly, x, y and z ar th prdctd acclratons of th manuvrng targt, whl RSSI ( ) [ RSSI RSSI RSSI 3 RSSI 4 ] s th RSSI vctor, whch s mad up of th RSSI valus btwn th unnown nod and rfrnc nods. s acclraton corrlaton coffcnt. V ( ) s zro-man RSSI RSSI (m) 0 lg ( x x ) ( y y ) ( z z ),, 3, 4 Assum th nonlnar systm s gvn by () and (), th standard UKF [6] algorthm can b summarzd as follows. Gvn th stat vctor at tmstp, a st of sgma ponts ar gnratd and stord n columns of th N ( N ) sgma pont matrx χ, whr N s th dmnson of th stat vctor. h sgma ponts ar slctd to l on th prncpal componnt axs of th covaranc P( ), and nclud an xtra pont wht Gaussan nos, whos varanc s R( ). h procss nos W ( ) s a dscrt tm squnc of wht X ( ). h sgma ponts ar computd by nos, and E[W ( )W ( j )] 0,( j 0). Procss nos covaranc matrx s gvn by q Q( ) E[W ( )W ( )] a q q 3 q q q3 q3 q3 q33 χ0, X ( ), N (0) χ, X ( ) ( ( N ) P( )) N N, 3 3 4 5 3 4 q3 3 ( ) q 3 (4 3 ) q3 ( ) ( ) q33 q (9) χ, X ( ) ( ( N ) P( )),, (5) whr q (8) (), N whr s a scal paramtr that dtrmns how far th sgma ponts ar sprad from th man and s dfnd by (N ) N () (6) whr dtrmns th sprad of th sgma ponts around X ( ) and s usually st to a small postv s th modfd Raylgh dstrbuton varanc of valu (.g. 0-4 ), and s a scondary scal paramtr that approxmats th hghr-ordr trms and s usually st to thr 0 or 3 N. h prdcton stp or tm updat s prformd by propagatng th gnratd sgma ponts through th stat quaton. h propagatd sgma ponts ar thn combnd wth assocatd wghts to produc th prdctd stat and covaranc. h tm updat quatons ar th manuvrng acclraton as shown n (7), 4 [amax aˆ (t )], a 4 [-a ˆ max a (t )], a X ( ) ( ), U ( )a ( ) aˆ (t ) 0 N X ( ) W ( m) X ( ) (7) aˆ (t ) 0 (4) 0 N P( ) W ( c ) [ X ( ) X ( )] whr amax s th postv uppr lmt of th acclraton, 0 whl a max s th ngatv lowr lmt of th acclraton, aˆ(t ) s th currnt prdctd acclraton. In ths papr, stat-spac modl basd on RSSI s mprovd and xtndd to thr-dmnsonal spac. In two-dmnsonal spac, thr rfrnc nods ar rqurd at last to locat on unnown nod. Howvr, four nods ar ndd at last n thr-dmnsonal spac. Hnc four gvn nods A( x, y, z ), B( x, y, z ), C ( x3, y3, z3 ), D( x4, y4, z4 ) ar [ X ( ) X ( )] Q( ) (5) whr W ( m ) and W (c) ar th wghts dfnd by W0( m ) N W ( c ) W ( m ) chosn, th RSSI valus btwn th unnown movng, W0( c ) N, ( N ) ( ),,, N (6) whr s usd to ncorporat a pror nowldg of th dstrbuton of X and for a Gaussan dstrbuton, s optmal. nod and th four rfrnc nods ar masurd. h masurmnt quaton, whch s basd on path loss modl [], corrspondng to RSSI s gvn by 05 Journal of Communcatons (3) 58
Journal of Communcatons Vol. 0, No. 8, August 05 o comput th masurmnt updat, th sgma ponts ar transformd through th nonlnar masurmnt quaton to obtan th prdctd RSSI stmats usng RSSI ( ) f ( X ( )) N ( m) ( ) ( ) 0 (7) RSSI W RSSI (8) Wth th transformd stat vctor RSSI ( ) postror stat stmat s computd usng, a X ( ) X ( ) K( ) [ RSSI ( ) RSSI ( )] (9) whr K ( ) s th Kalman fltr gan and dfnd by N ( m) ZZ 0 K( ) PXZ P ZZ [ ( ) ( )] (0) P W [ RSSI ( ) RSSI ( )] () RSSI RSSI R N ( m) XZ 0 P W [ X ( ) X ( )] [ RSSI ( ) RSSI ( )] () wo sgnfcant covaranc matrcs, P ZZ and P XZ ar usd hr. Durng th tratv procss P ZZ wll b rducd so that th transformd sgma ponts mov towards th clustr man. Wth th ntroducton of th masurmnt data RSSI ( ), th clustr man wll thn mov furthr towards th tru man. As a rsult, P XZ wll b rducd. R s th masurmnt nos covaranc matrx. Fnally, a postror stmat of th rror covaranc s gvn by P( ) P( ) K( ) P K ( ) (3) a( ) x( ) y( ) z( ) s th prdcton of x( ) y( ) z( ) and rgardd as a (.., th man of acclratons) hr. hn (3) can b rwrttn as X ( ) ( ) U ( ) a ( ), '( ) ( )( ( N ) P( )),, N (4), '( ) ( )( ( N ) P( )) N,, N, N whr 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '( ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ZZ. Hnc th unscntd Kalman algorthm s fulflld. III. IMPROVED ADAPIVE UKF A. Adaptv Algorthm of Procss Nos Cova-Ranc Matrx Q() h algorthm mntond abov s affctd by amax and a max gratly. If th absolut valus of amax and a max ar small, th tracng accuracy s hgh, but th systm s on wth slow rspons whn th targt s moton changs trmndously. If th absolut valus of amax and a max ar larg, th systm s on wth quc rspons and lowr tracng accuracy. o avod th ngatv nflunc of th lmtd acclraton prsupposd n th targt tracng, th functonal rlaton btwn th manuvrng status of targt and th stmaton of th nghborng poston nformaton s usd to carry out th adaptaton of th procss nos covaranc. a th cas of x, snc th prdctd quantty xˆ( ) dos not ta account of th acclraton ncrmnt ax, whch th stmat xˆ( ) contans, ax can b approxmatd [3] by th dvaton rlatonshp btwn xˆ( ) and xˆ( ) usng xˆ ( ) xˆ ( ) a (5) x whr s th samplng ntrval. Sn from (7), th varanc of th manuvrng acclraton s lnar wth th acclraton ncrmnt, whl th acclraton ncrmnt ax vars lnarly wth th poston ncrmnt as shown n (5). Basd on th abov dscusson, a dvlopd adaptv Kalman algorthm [3], [4] s ntroducd. Lt ˆ( ) ˆ x x( ) (6) whr s a scal factor. hn th procss nos covaranc matrx can b rwrttn as (7), q q q3 4 Q( ) a q q q3 q3 q3 q 33 q q q xˆ ( ) xˆ ( ) q q q q q q 3 3 3 3 33 (7) Accordng to (7), whn th targt s n low-spd manuvrng or non-manuvrng condton, th valu of manuvrng acclraton varanc s small snc thr s lttl dffrnc btwn xˆ( ) and xˆ( ). On th contrary, th valu of manuvrng acclraton varanc gts largr along wth th dffrnc btwn xˆ( ) and xˆ( ) f th targt s n hgh- 05 Journal of Communcatons 58
Journal of Communcatons Vol. 0, No. 8, August 05 spd manuvrng condton. h quaton (7) can rflcts th stat of manuvrng targt corrctly, whch dos not us amax and a max. As shown n (7), th procss nos covaranc matrx Q ( ) only contans th latst nformaton of th moton. If th targt s moton changd, th old data cannot rflct th currnt moton. Howvr, f th targt s n low-spd manuvrng or non-manuvrng condton, th UKF, whch can obtan lttl nformaton of th old data, s rlatvly snstv and asly dsturbd by noss. Hnc th way of modfd Sag-Husa [0] s ntroducd, whch rducs th nflunc of th old data slowly. Assum Q ( ) ar unnown, thn th corrspondng Sag-Husa procss nos statstcs stmator [5] s gvn by q( ) [ X ( j ) ( j ) X ( j )] (8) j Q( ) [ X ( j ) ( j ) X ( j ) q( )] j (9) [ X ( j ) ( j ) X ( j ) q( )] In manuvrng targt tracng, th ffct of th latst nformaton should b mphaszd much mor. h rcursv modfd Sag-Husa stmator [0] can b obtand as shown n (30), Q( ) ( d ) Q( ) d [ K( ) V ( ) V ( ) K ( ) (30) P( ) ( ) P( ) ( )] whr Q ( ) s th procss nos covaranc matrx at tmstp - and d s th wghtng coffcnt of Q ( ). For smplcty, lt ˆ( ) ( ) ( ) ( ) Q K V V K ( ) P ( ) ( ) P( ) ( ) (3) whr Q ˆ( ) s th nformaton of th procss nos covaranc matrx at tmstp. By usng th xponntally wghtd fadng mmory mthod [3], wghtng coffcnt d can b chosn usng j j j j j0 d d b, 0 b, d (3) whr b s a forgttng factor, th ntal valu of d s st as 0.98 n th smulaton and xprmnt. hn th followng quaton can b gottn. d ( b) / ( b ) (33) Equaton (7) s th procss nos covaranc matrx at tmstp for currnt statstcal modl basd UKF and usd to rplac Q ˆ( ) hr. hn a rcursv modfd procss nos covaranc matrx can b obtand as shown n (34), 4 Q( ) ( d ) Q( ) d q q q ˆ( ) ˆ x x( ) q q q q q q 3 3 3 3 33 B. Adaptv Algorthm of Masurmnt Nos Covaranc Matrx R() (34) In ths scton, a fuzzy adaptv UKF s appld to stmat masurmnt nos covaranc matrx R ( ). Fuzzy controllr s on of th usful control paradgms for uncrtan and ll-dfnd nonlnar systms. Control actons of a fuzzy controllr ar dscrbd by som lngustc ruls. R ( ) s adjustd by montorng th nnovaton squnc { ( ),,..., }, whch [6] s dfnd by ( ) RSSI ( ) RSSI ( ) (35) whr RSSI () s th ral masurmnt and RSSI ( ) s th prdctd valu of RSSI (). h nnovaton squnc rprsnts th nformaton n th nw obsrvaton and s consdrd as th most rlvant sourc of nformaton for th fltr adaptaton. In thory, nnovaton squnc s zro man wht Gaussan nos squnc as shown n (36), E[ ( )] 0 (36) And th thortcal covaranc matrx of () can b drvd from th UKF usng N ( m) ZZ 0 P W [ RSSI ( ) RSSI ( )] [ ( ) ( )] RSSI RSSI R (37) Howvr, n practc, th nnovaton squnc s bothrd by modl uncrtanty and nos statstcal uncrtanty. h mthod n [7] s usd to obtan th man and covaranc matrx of th nnovaton squnc as shown n (38), E[ ( )] ( ) N N P[ ( )] ( ) ( ) N N (38) N s chosn mprcally to gv som statstcal smoothng. hn th rror formula btwn thortcal covaranc matrx and practcal covaranc matrx of th nnovaton squnc ar gottn by usng P[ ( )] P[ ( )] Pzz ( ) ( ) N N N ( m) W [ RSSI ( ) RSSI ( )] (39) 0 [ RSSI ( ) RSSI ( )] R( ) It s notworthy that P, whos valu should b zro n optmal stuaton, rflcts th stat of currnt Kalman 05 Journal of Communcatons 583
Journal of Communcatons Vol. 0, No. 8, August 05 fltr. Whn th valus of E and P ar not zro, t ndcats that th prdcton of RSSI ( ) s not corrct. s tracng a targt travllng n unform rctlnar moton wth a vlocty of m/s n x-drcton, y-drcton and z-drcton. h scond tas s tracng a moton whos acclraton changs sharply durng th movmnt. In th bgnnng th vlocts of x-drcton and ydrcton ar both 0m/s, whl th acclratons ar both m/s. Aftr 4 sconds, th acclratons of x-drcton and y-drcton chang to 30m/s. h vlocty of zdrcton rmans m/s durng th ntr tm. h zgzag-ln moton tracng s th thrd tas. h vlocts of x-drcton and z-drcton ar m/s and th y-drcton vlocty s 0m/s, whch changs to -0m/s aftr 9 sconds. h samplng ntrval s 0.8s. h ntal valu of th stat stmat s hn R( ) s adjustd to ma th Kalman fltr tnd towards stablty. h adjustmnt ruls of R( ) ar as follows: () If P 0, R( ) rmans unchangd. () If P 0, R( ) ncrass. (3) If P 0, R( ) dcrass. Basd on th adjustmnt ruls abov, P ar chosn as th nput varabls of fuzzy logcal controllr. h fuzzy mthod proposd hr rcvs th valu of P vry tmstp and wors out a scal paramtr calld th adjustmnt factor β. h β ndcats th amount whch th masurmnt nos covaranc matrx R( ) should b scald by, n ordr to compnsat for th varyng nos dsturbancs. h masurmnt nos covaranc [5] at tmstp s calculatd usng, Rˆ ( ) R( ) X ( ) [0 0 0 0 0 0 0 0 0] (4) whl th ntal valu of covaranc matrx s P(0) dag{0.,0.,0.,0.,0.,0.,0.,0.,0.} (4) (40) Q and R ar dsgnd to chang as h rang of β s [0.000, ] and ts ntal valu s st as n th smulaton and xprmnt, whl th rang of P s st as [-0., 0.]. h nput lngustc varabl s P and th nput lngustc valus ar N: Ngatv, ZE: Zro and P: Postv, whl trangular mmbrshp functon s usd n th nput spac. Corrspondngly, β s th output lngustc varabl and th output lngustc valus ar PS: Postv Small, PM: Postv Mdum, and PB: Postv Bg, whl trapzodal mmbrshp functon s usd. Fg. shows th mmbrshp functons of nput and output varabls. dag{0.00,0,0,0.00,0,0,0.00,0,0}, 0 t 8.4 Q(t ) dag{0.003,0,0,0.003,0,0,0.003,0,0}, 8.4 t 6.8 (43) dag{0.00,0,0,0.00,0,0,0.00,0,0},6.8 t 8 R dag{0.00,0.00,0.00,0.00 } (44) h poston stmaton rror s usd as a crtron to compar th dffrnt computaton mthods and dfnd by Error xˆ( ) x( ) yˆ ( ) y( ) zˆ( ) z( ) (45) whr x( ), y ( ) and z ( ) ar th ral masurmnt 0 N ZE -0. 0 (a) h mmbrshp functon of 0 P 0. P. PM PS 0.000 valus, whl xˆ( ), yˆ( ) and zˆ( ) ar th prdctd valus rspctvly. For comparson, th proposd algorthms ar smulatd frstly, whch contan th tradtonal CAUKF wth Q( ) n (7), th mprovd CAUKF wth adaptv algorthm of Q( ) n (34) and th fnal mprovd CAUKF wth both PB adaptv algorthm of Q( ) n (34) and R( ) mntond n 3.. h rsults ar shown n Fg.. As shown n Fg., th fnal mprovd CAUKF prforms much bttr than tradtonal CAUKF and mprovd CAUKF wth Q( ) n (34). Snc th procss (b) h mmbrshp functon of β. Fg.. h mmbrshp functons of nput and output varabls. nos Q( ) n (7) only contans th latst nformaton of th moton, th stmaton rror s asly dsturbd, whch fluctuats unstadly, spcally whn th targt hghly manuvrs. h stmaton rrors of th mprovd CAUKF wth Q( ) n (34) and fnal mprovd CAUKF IV. SIMULAION In ordr to vrfy th fasblty and ffcncy of th proposd algorthm n ths papr, th CUKF, AUKF n [0] and th fnal mprovd CAUKF ar smulatd. Smulaton wth th sam paramtrs s mplmntd on th MALAB R00a softwar. h coordnats of four rfrnc nods ar (0,0,0), (0,00m,0), (00m,0,0) and (0,0,00m) rspctvly. hr nds of tracng tas ar smulatd. h frst tas 05 Journal of Communcatons wth both adaptv algorthm of Q( ) and R( ) follow a rlatvly smooth curvs as shown n Fg.. Howvr, th accuracy of fnal mprovd CAUKF s th bst of all th thr mthods. Also, Fg. shows th fastr convrgnc spd of th proposd algorthm. 584
Journal of Communcatons Vol. 0, No. 8, August 05 th tru stat a lot, spcally whn th targt s n hghspd manuvrng condton. h prformanc of AUKF usng th mthod n [0] s much bttr than that of standard UKF. Howvr, Fg. 3 shows that th fnal mprovd CAUKF can chang along wth th manuvrng targt mor qucly and trac th targt s sharp movmnt chang mor accuratly. Also, t can b sn obvously that th fnal mprovd CAUKF can gt bttr stmaton accuracy than AUKF usng th mthod n [0]. (a) rac a targt n unform rctlnar moton. (a) rac a targt n unform rctlnar moton. (b) rac a moton whos acclraton changs sharply durng th movmnt. (b) rac a moton whos acclraton changs sharply durng th movmnt. (c) rac zgzag-ln moton Fg.. h smulaton rsults of radtonal CAUKF, Improvd CAUKF wth Q() n (34) and fnal Improvd CAUKF. hn th CUKF, AUKF usng th mthod n [0] and our fnal mprovd CAUKF ar compard wth ach othr. h rsults of th smulaton ar shown n Fg. 3. In Fg. 3(a), th rsults show that our fnal mprovd CAUKF faturs fastr rspons and smallr ovrshoot f th targt s n unform rctlnar moton. hs ffct can b obsrvd mor clarly n Fg. 3(b) and Fg. 3(c). If th targt changs ts moton mod, CUKF s much asr to b affctd than AUKF usng mthod n [0] and th fnal mprovd CAUKF, whch gts largr ovrshoot and slowr convrgnc spd. Snc th unnown procss nos can lad to larg stmaton rrors, th stat stmat of standard UKF somtms may dvat from 05 Journal of Communcatons 585 (c) rac zgzag-ln moton Fg. 3. h smulaton rsults of CUKF, AUKF usng mthod n [0] and our fnal Improvd CAUKF. V. EXPERIMENAL RESULS Exprmnts wr carrd out n an ndoor nvronmnt to tst and valdat th proposd algorthm mntond n
Journal of Communcatons Vol. 0, No. 8, August 05 prvous sctons. Error causd by rflcton du to th antnna dvrsty can b rducd by sttng th antnna of ach rfrnc nod at th angl of 90 dgrs at th mountng surfac. Sx nods ar usd n th xprmnts. On nod s dsgnatd as th targt, whch broadcasts to any rfrnc nod that s lstnng. In ordr to trac th ral-tm poston of th movng targt nod, four rfrnc nods ar placd n ndoor nvronmnt. Cartsan coordnats ar stablshd n ndoor nvronmnt, whr x-y plan s th ground. hr of th rfrnc nods ar placd on th x-y plan, whch ar (0, 0) (0,0m) (0m, 0), whl th othr on s placd m abov th nod (0, 0). h last nod s connctd to a prsonal computr that collcts RSSI data of th rfrnc nods and prforms tracng algorthms. h nods ar dsgnd basd on C430, whch s.4ghz IEEE 80.5.4 complant RF transcvr dvlopd by I. In ordr to drown out dsturbng nos, th RSSI valu btwn targt nod and ach rfrnc nod s masurd 0 tms vry tmstp and th avrag s rgardd as th fnal masurmnt valu. In ths xprmnt, two nds of tracng tass ar tstd. h frst tas s tracng a manpulator travllng n unform rctlnar moton wth a vlocty of m/s. h scond tas s tracng a manpulator travllng n unform crcular moton wth a radus of 0m and an angular vlocty of 0.5rad/s. As n th smulaton, th poston stmaton rror comparson of tradtonal CAUKF wth Q( ) n (7), stmaton rror of fnal mprovd CAUKF s smallr than thos of th othr algorthms. As shown n Fg. 5(b), whn th targt s n unform crcular moton, th stmaton rror of th fnal mprovd CAUKF rachs a small valu qucly n th frst sconds and th fnal stmaton rror rmans blow m. Howvr, th stmaton rror of th AUKF usng th mthod n [0] rmans a larg valu and th fnal stmaton rror s btwn m and 3m. Sn from abl I, th avrag RMSE of fnal mprovd CAUKF poston stmatons s obvously lss than thos of th othr algorthms. Gnrally, th xprmntal rsults show that th proposd algorthm has bttr prformanc. (a) rac a manpulator n unform rctlnar moton. mprovd CAUKF wth Q( ) n (34), and fnal mprovd CAUKF wth both adaptv algorthms n scton III s analyzd, whch s shown n Fg. 4. And Fg. 5 shows th rsults basd on th CUKF, AUKF usng th mthod n [0] and our fnal mprovd CAUKF, rspctvly. h avrag root man squar rror (RMSE) can b usd to valuat th prformancs of th algorthms as shown n (46), E RMSE N ( xˆ() x( j)) ( yˆ () y( j)) ( zˆ() z( j)) N j (46) (b) rac a manpulator n unform crcular moton. whr N s th masurmnt tms vry tmstp, whch s 0 n th xprmnt. s th traton tms. h avrag RMSE of ach algorthm s shown n abl I. Fg. 4. Exprmntal rsults of CAUKF, Improvd CAUKF wth Q() n (34) and fnal Improvd CAUKF. ABLE I: AVERAGE RMSE OF POSIION ESIMAION ERROR Avrag RMSE of unform rctlnar moton Avrag RMSE of unform crcular moton CUKF AUKF usng mthod n [0] Fnal mprovd CAUKF 0.793 0.573 0.07.0963 0.79 0.968 Fg. 4 and Fg. 5 show that our fnal mprovd CAUKF faturs fastr rspons and smallr ovrshoot f th targt s n unform rctlnar moton. h fnal 05 Journal of Communcatons (a) rac a manpulator n unform rctlnar moton. 586
Journal of Communcatons Vol. 0, No. 8, August 05 [8] [9] [0] [] [] (b) rac a manpulator n unform crcular moton. Fg. 5. Exprmntal rsults of CUKF, AUKF usng mthod n [0] and our fnal Improvd CAUKF. [3] VI. CONCLUSIONS In ths papr, an mprovd CAUKF for wrlss snsor ntwor s proposd to trac a manuvrng targt. hs mthod can not only trac a targt n low-spd manuvrng or non-manuvrng condton, but also a targt n hgh-spd manuvrng condton. In ordr to ntroduc th mprovd adaptv UKF algorthm, a currnt statstcal modl basd on RSSI s bult, whch can dscrb th trajctory of a manuvrng targt. Basd on th currnt statstcal modl, a dvlopd adaptv UKF algorthm s proposd, whch stmats th procss nos covaranc matrx Q() by th way of modfd Sag-Husa stmator. hn an mprovd fuzzy adaptv UKF s usd to stmat th covaranc matrcs R(). h smulaton and xprmntal rsults show that th fnal mprovd CAUKF can rduc th stmaton rror and sns th varaton of th moton fastr. [4] [5] [6] [7] REFERENCES [] [] [3] [4] [5] [6] [7] Xaojun Png was born n Chna n 980. H rcvd th B.S. dgr from Zhngzhou Unvrsty (ZZU), Zhngzhou, n 00 and th M.S. dgr from Wuhan Unvrsty (WHU), Wuhan, n 006, both n physcal lctroncs. H s currntly pursung th Ph.D. dgr wth th School of Optcal and Elctronc Informaton, Huazhong Unvrsty of Scnc and chnology (HUS). Hs rsarch ntrsts nclud wrlss communcaton, masurmnt and control, sgnal and mag procssng, and crcut dsgnng. Y. B. Yao, Q. Han, X. R. Xu, and N. L. Jang, A RSSI-Basd dstrbutd wghtd sarch localzaton algorthm for WSNs, Intrnatonal Journal of Dstrbutd Snsor Ntwors, vol. 05, pp. -, 05. Q. D. Dong and X. Xu, A novl wghtd cntrod localzaton algorthm basd on RSSI for an outdoor nvronmnt, Journal of Communcatons, vol. 9, no. 3, pp. 79-85, 04. H. Lu, H. S. Darab, P. Banrj, and J. Lu, Survy of wrlss ndoor postonng tchnqus and systms, IEEE ransactons on Systms, Man, and Cybrntcs-Part C: Applcatons and Rvws, vol. 37, no. 6, pp. 067-080, 007. Y. F. Zhao, H. Rn, and J. F. Hu, A smultanous localzaton and tracng algorthm basd on comprssng alman fltr, Ssors & ransducrs, vol. 77, no. 8, pp. -6, 04. S. Y. Chn, Kalman fltr for robot vson: A survy, IEEE ransactons on Industral Elctroncs, vol. 59, no., pp. 4409440, 0. F. Gustafsson and G. Hndby, Som rlatons btwn xtndd and unscntd alman fltrs, IEEE ransactons on Sgnal Procssng, vol. 60, no., pp. 545-555, 0. S. Jafarzadh C. Lascu, and M. S. Fadal, Stat stmaton of nducton motor drvs usng th unscntd Kalman fltr, IEEE 05 Journal of Communcatons ransactons on Industral Elctroncs, vol. 59, no., pp. 40746, 0. H. R. Zhou and K. S. P. Kumar, A 'currnt' statstcal modl and adaptv algorthm for stmatng manuvrng targts, Journal of Gudanc Control & Dynamcs, vol. 7, no. 5, pp. 596-60, 984. J. W, C. C. Lu, W. L. Guo, and Y. Z. Ca, Improvd currnt statstcal modl algorthm for manuvrng targt tracng, Arospac Shangha, vol. 3, no., pp. 5-56, 04. Y. Sh and C. Z. Han, Adaptv UKF mthod wth applcatons to targt tracng, Acta Automatca Snca, vol. 37, no. 6, pp. 755759, 0. Q. F. H, Y. B. L, H. Lv, and G. J. H, Swtchng multsnsor mprovd currnt statstcal modl for manuvrng targt tracng, Appld Mchancs and Matrals, vol. 385-386, pp. 585-588, 03. P. M. Santos,. E. Abrudan, A. Aguar, and J. Barros, Impact of poston rrors on path loss modl stmaton for dvc-to-dvc channls, IEEE ransactons on Wrlss Communcatons, vol. 3, no. 5, pp. 353-36, 04. J. Dun, M. Smandl, and O. Straa, Unscntd Kalman fltr: Aspcts and adaptv sttng of scalng paramtr, IEEE ransactons on Automatc Control, vol. 57, no. 9, pp. 4-46, 0. C. Lu, X. H. Huang, and M. Wang, argt tracng for vsual srvong systms basd on an adaptv Kalman fltr, Intrnatonal Journal of Advancd Robotc Systms, vol. 9, no. 49, pp. -, 0. J. H. Chng, D. D. Chn, R. J. Landry, L. Zhao, and D. X. Guan, An adaptv unscntd Kalman fltrng algorthm for MEMS/GPS ntgratd navgaton systms, Journal of Appld Mathmatcs, vol. 04, pp. -8, 04. J. P. L, X. X. Zhong, and I.. Lu, hr-dmnsonal nod localzaton algorthm for WSN basd on dffrntal RSS rrgular transmsson modl, Journal of Communcatons, vol. 9, no. 5, pp. 39-397, 04. M. Das, S. Sadhu, and. K. Ghoshal, An adaptv sgma pont fltr for nonlnar fltrng problms, Intrnatonal Journal of Elctrcal, Elctroncs and Computr Engnrng, vol., no., pp. 3-9, 03. Xuhua Yuan was born n Chna n 957. H s a profssor of th School of Optcal and Elctronc Informaton, Huazhong Unvrsty of Scnc and chnology (HUS). Hs rsarch ntrsts nclud fbr-optc communcato, fbr-optc snsng tchnology, optolctronc masurmnt and control. 587
Journal of Communcatons Vol. 0, No. 8, August 05 Chang Lu was born n Chna n 984. H rcvd th B.S. dgr n Automaton, Ph.D. dgr n Control hory and Control Engnrng from Huazhong Unvrsty of Scnc and chnology (HUS) n 007 and 0, rspctvly. Hs rsarch ntrsts nclud vsual srvong control, pattrn rcognton and mag procssng. 05 Journal of Communcatons 588