Data Association Algorithm in TBD Multiradar System

Transcription

1 Dt Associtio Algoithm i TBD Multid System Ch. Kbkchiev 1, I. Gvov 2, L. Doukovsk 2, V. Kyovtoov 2, H. Rohlig 3 1 Fculty of Mthemtics & Ifomtics, Sofi Uivesity, Jmes Bouchie St., 5, 1164 Sofi, Bulgi e-mil: ckbkchiev@yhoo.com 2 Istitute of Ifomtio Techologies, BAS Acd. G. Bochev St., bl. 2, 1113 Sofi, Bulgi e-mil: igvov@yhoo.com 3 Techicl Uivesity Hmbug-Hbug, Eibedofe St.40, D Hmbug e-mil: ohlig@tu-hbug.de Key wods: Dt Associtio, Tck-Befoe-Detect (TBD), Multid System, Sigl Pocessig, Pol Hough Tsfom, d Rdomly Aivig Impulse Itefeece Abstct I this ppe, we e studied the poblem of dt ssocitig i tck-befoe detect (TBD) multiple d system. The ifluece of tjectoy pmetes ccucy (eos) o the qulity of wok of TBD multid system is estimted. We suppose the Hough spce discetiztio to be two times lge th mx mesue eo of tget co-odite. 1. Itoductio The dt ssocitio poblem is of sigifict impotce i the pocess of buildig up multiple seso system fo detectio of tget d its tjectoy. Dt ssocitio poblem c be mthemticlly fomulted s well-studied ssigmet poblem. Covetiol ppoches fo dt ssocitio i fusio cete of multid system e: the cetlized d the decetlized ppoch [1-3]. I this ppe, we popose ew multiseso dt ssocitio ppoch with pol Hough tsfom (PHT). I cotst to the HT, poposed by Clso, Evs, d Wilso i [4], the pol Hough detectio lgoithm cosideed i the ppe, is vey effective fo tck d tget detectio becuse the iput pmetes of the tsfom e the output pmetes of the sech d [5-7]. I ou pevious esech, diffeet types of CFAR Hough detectos i pesece of domly ivig impulse itefeece wee studied ccodig to the ssumptio tht the tget tjectoy pmetes e defied without eos. I this cse, the tget detectio ws impoved [8-12]. It is well-kow tht the tget coodites (ge d zimuth) e mesuble with eos i the el d systems. It leds to eos i the tget tjectoy pmetes detemitio, which deped o the Hough pmete spce discetiztio [13,14]. The size of cells i Hough pmete spce closely elted to the eos of mesuig tget coodites. The bigge cell size bigs bigge eo i tget tjectoy pmete detemitio. The tsk fo detectio of tget tjectoy fom diffeet ds is educed to the dt ssocitio i TBD multid system. The dvtges d disdvtges both of cetlized d of decetlized thee ceso TBD detectos, which usig pol Hough tsfom, i the cse of missig mesuemet eos, wee ivestigted i [7]. We ssume tht the dt ssocitio lgoithm i TBD multid system usig the Hough tsfom will decese the equiemets fo d system sychoiztio d llow successful wok of ds, hvig diffeet ccucy pmetes. I this ppe, the ifluece of the sesos mesuemet eos o tget detectio qulity i osychoic cetlized tee seso TBD system is ivestigted. These eos mke wose Hough spce biy itegtio, educig output sigl-to-oise tio. To icese this tio d impove detecto pefomce we optimize the size of Hough detecto cells d detectio theshold vlue. The sesitivity of the Hough detecto usig this ppoch is estimted.

2 2. Netted d Hough detecto Afte ech d sc, evey oe fom the N-th ds foms the locl pol dt spce (, ) mx 0 whee [ 0, ] d [ 0, ] e the tget ge d zimuth, espectively of N-th d. All 360 co-odite systems e oieted to the Noth, d the eth cuvtue is eglected. The fist stge is dt ssocited of the N-th d co-odite systems to the globl ge-zimuth coodite system. The secod stge is Hough tsfom. The PHT mp poits (tgets) fom evey oe ssocited locl obsevtio spce (ssocited dt mp) ito cuves i the Hough pmete spce, temed s the (ρ -θ) spce, by:.cos( ), 0 ( θ ) π (1) ρ θ = whee θ is the gle d ρ is the smllest distce to the oigi of the globl pol co-odite system. If lie tjectoy exists i the globl (, ) spce, by mes of Hough tsfom it is epeseted s poit of itesectio of siusoids defied by Hough tsfom. < Fig. 1 cc()=0m, cc()=0 0, Fig. 2 cc()=0m, cc()=0 0, δ(ρ)=100m, δ(θ)=0.1 0 δ(ρ)=500m, δ(θ)=1 0 The pmetes ρ d θ peset the lie tjectoy i the Hough pmete spce d c be tsfomed bck to the globl dt spce showig the cuet distce to the tget. If the umbe of biy itegtios (BI) of dt i the Hough pmete spce exceeds the detectio theshold, both tget d its tjectoy detectios e idicted. The stuctues both of cetlized d of decetlized thee ceso TBD detectos e show i [7]. Fig. 3 Globl pol co-odite system Fig. 4 Globl ge-zimuth co-odite system

3 If the ds i cetlized thee ceso TBD detecto mesue the ge d zimuth without eos, the siusoids will be itesected i oe cell i Hough spce. The size of discetiztio defies the shpe of obtied pltfom. If the ge d zimuth e mesued without eos, the smlle size of ccumulto cells will led to smlle shpe of pltfom d poouced pick i Hough spce (Fig.1); the bigge ccumulto size will led to bigge pltfom i Hough spce (Fig. 2). I the el d system is well-kow tht the tget coodites (ge d zimuth) e mesuble with eos (Fig. 3 d 4). The ds mesuemet eos (ccucy) ( ) cc ( ) c be expessed s mesuemet oscilltios oud the cosideed tjectoy. cc d cc() Fig. 5 cc()=500m, cc()=0.5 0, Fig. 6 cc()=500m, cc()=0.5 0, δ(ρ)=500m, δ(θ)=0.5 0 δ(ρ)=1000m, δ(θ)=1 0 We ssume oml distibutio fo cc( ) N( 0 σ ) d cc( ) N( 0 σ ) E [ cc( ),cc( )] 0 d cc() δρ δθ Fig. 7 The Hough d d pmetes tget tjectoy, = is the opeto of mthemticl expecttio d [13], wee, σ, σ e the stdd devitio of the mesuemet eos. The mesuemet eos ( σ d, σ ) of co-odites ( ) decese the biy itegtio i ccumulto cells i the Hough spce. I this cse, the siusoids of oe lie tjectoy will be itesected i diffeet ccumulto cells. To obti mx biy itegtio (pick) i the Hough spce is ecessy to icese size of the ccumulto cells (Fig. 5 d 6) but it leds to bigge eo fo ρ d θ. The stip defied by the mximl vlues of these eos hs complicted shpe depedig o the mesuemet coodites (Fig.7). To impove Hough detecto pefomce by expeimets we optimize the size of Hough detecto cells d detectio theshold vlue. 3. Simultio esults By Mote Clo simultio, we study the eegetic chcteistics of o-sychoic cetlized thee seso TBD system, fte Hough pmetes optimiztio fo oe lie tjectoy. Afte 6 d scs d dt ssocitio towd globl co-odite system we e usig pol Hough tsfom. The esech is cied out fo followig iput pmetes: ge ccucy cc()=0, 100, 500m; zimuth ccucy cc()=0 0 d 1 0 ; ho discetiztio δ(ρ)=0.1-4km, thet discetiztio δ(θ)=0.5, 1, 2 0 ; Hough theshold (Ht) = 10, 12, 14; Mote Clo us

4 Fig. 8 cc()=0, 100, 500m, cc()=0 0, Fig. 9 cc()=500m, cc()=1 0, δ(ρ)=0.1-4km, δ(θ)=1 0 δ(ρ)=0.1-4km, δ(θ)=0.5, 1, 2 0 We esech the ifluece of discetiztio size i Hough spce o biy itegtio fo diffeet mesuemet eos of ge d zimuth. To hold the costt vlue of biy itegtio i the Hough spce i cse of the ehcemet mesuemet eo of ge d zimuth, is ecessy to icese size of ccumulto cells (Fig. 8). The icesble of the Hough theshold leds to decese of the umbe of cells, which exceed the theshold. The ge mesuemet eos ifluece o mx pick, while the zimuth eos ifluece smlle (Fig. 8). The umbe of cells fom pltfom (exceed Hough theshold) depeds both o the size of cells i Hough spce (Fig. 9) d o the size of Hough theshold (Fig. 10). Fig. 10 cc()=500m, cc()=1 0, δ(ρ)=0.1-4km, δ(θ)=1 0, Hough theshold (Ht) = 10, 12, 14 iceses, the umbe of exceed cells deceses. The icese of ρ leds to icese of the umbe of cells, which exceed detectio theshold. The icese of θ leds to decese of this umbe. Whe the Hough theshold 4. Coclusio I this ppe, we hve studied the ifluece of discetiztio of Hough spce fo diffeet ccucy chcteistics of o-sychoic cetlized tee seso TBD system. The esech is cied out usig Mote-Clo simultios i MATLAB computig eviomet. To hold the costt vlue of biy itegtio i Hough spce i cse of the ehcemet mesuemet eo of ge d zimuth, is ecessy to icese size of ccumulto cells. We suppose the Hough spce discetiztio to be two times lge th mx mesue eo of tget co-odite. Ackowledgmet This wok ws ptilly suppoted by pojects: IIT /2006, d MPS Ltd. - Gt IF-02-85/2005. Refeeces 1. Cheyk, V., Fudmetls of Multisite Rd System, God d Bech Sciece Publishes, 1998.

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