015 IEEE Intenational Confeence on Advanced Intelligent Mecatonic (AIM) July 7-11, 015. Buan, Koea Altitude Etiation Uing Paticle Filte wit Monopule in a Multipat Envionent Yuki Takabayai, Yaui Obata, and Ryo Kuaue Abtact Te poble of ultipat popagation in te tacking low-altitude taget wit a ada i addeed. It i well known tat ultipat fading caue bia eo to te taget altitude ove te ea. Since te bia eo caued by ultipat popagation depend on a lage nube of paaete uc a te fequency of te ada wavefo, te actual taget altitude, and ange, it i difficult to etiate te bia eo. In ti pape, we popoe an altitude etiation etod uing paticle filte and ultipat popagation odel. Te pefoance of te popoed etod i veified toug copute iulation. I. INTRODUCTION It i well known tat te poble of ultipat popagation (MP) aie in te ituation of tacking low-altitude taget wit a ada and caue lage bia eo to te eal altitude of te taget. In te peence of ultipat popagation, intefeence aong te diect pat and uface-eflected one i caued. Te intefeence affect bia eo of te taget angle. Etiation of te bia eo i noally a difficult poble due to te dependence on a lage nube of paaete uc a te fequency of te ada wavefo, ada altitude above te ea, te actual taget altitude, and te ange fo a ada to te taget and te uface eflectivity[1]. Tacking algoit fo MP poble ave been widely tudied[]-[7]. A conventional tacking etod fo MP poble i able to eliinate lage peak eo (pike eo) but i not able to eliinate contant bia eo to te eal altitude of te taget ove te ea. On te ote and, we popoed altitude etiation algoit wic calculate te eliability of aued altitude ypotei, wic i coen fo eveal peet altitude ypotei, uing bia eo baed on ultipat popagation odel[8]. Howeve, tee i a poble tat te altitude etiation etod entioned above i able to etiate only te peet altitude. Teefoe, te accuacy of te altitude etiation etod ould be degaded wen te altitude except te peet one i etiated. In ti pape, we popoe an altitude etiation etod uing a paticle filte baed on MP odel. Ou etod can copenate te contant bia eo to te eal altitude of te taget toug tacking. Copaed wit conventional tacking etod wic egad bia eo a ando eo, popoed etod calculate te ipotance weigt of aued altitude, wic coepond to paticle in paticle filte, incopoating bia eo baed on ultipat popagation odel to etiate taget altitude. Moeove, copaed wit ou conventional Yuki Takabayai and Yaui Obata ae wit Infoation Tecnology R&D cente, Mitubii Electic Copoation, 5-1-1, Ofuna Kaakua, Kanagawa, 47-8501, Japan(e-ail: Takabayai.Yuki@ dp.mitubii Electic.co.jp, Obata.Yaui@ d.mitubiielectic.co.jp). Ryo Kuaue i wit Gaduate Scool of Infoation Science and Electical Engineeing, Kyuu Univeity, 744, Motooka, Nii-ku, Fukuoka, 819-0395, Japan(e-ail: kuaue@ ait.kyuu-u.ac.jp). etod a tated above, ou popoed etod i able to etiate te altitude but te peet one by uing paticle filte teoe. Teefoe, te accuacy of altitude etiation i uc ipoved by te popoed etod. Ti pape i oganied a follow. MP odel i decibed in Section Ⅱ. Popoed etod i decibed in Section Ⅲ. Siulation eult fo 3 iulation cenaio ae peented in Section Ⅳ. Finally, a uay of te eult i given in Section Ⅴ. II. MULTIPATH PROPAGATION MODEL Te geoety of ultipat penoenon i own a Fig.1. Tee ae two epaate pat between te taget and te ada: te diect pat and te indiect pat via eflection wit gaing angleψ fo te ea (o gound) uface. g Te uface eflected ignal conit of two coponent, tat i, pecula and diffue. Te pecula eflection i caued by a oot (io-like) uface and te diffue eflection i caued by te uface iegulaitie. Wile te pecula eflection coefficient i a deteinitic nube wic depend on eveal paaete, te diffue eflection a a ando natue. Teefoe, in ti pape, we do not take into account te diffue eflection becaue a popoed tacking etod uing a paticle filte i able to eove ando eo by te diffue eflection. Unde pecondition a above, ignal-to-noie atio (SNR) and te contant bia eo to te taget altitude i depended on pecula eflection at te uface of indiect pat and elative pae between diect and indiect pat[1]. In ti Section, we peent te ateatical expeion fo te elevation angle eo, SNR, and te pobability of detection by pecula eflection. θ 0 ψ g Figue 1. ψ g Suface Geoety of ultipat popagation. Taget A. Te elevation angle eo Te elevation angle eo wit epect to te taget i given by[7] 978-1-4673-9106-1/15/$31.00 015 IEEE 0
( + co ΔΦ) ρ ρ Δ E = θ 0 (1) 1 + ρco ΔΦ+ ρ wee ρ i te pecula eflection coefficient, ΔΦ i te elative pae between te diect pat and te indiect pat and θ0 i te angle diffeence between te two pat in Fig.1. Te pecula eflection coefficient ρ in (1) i copoed of tee facto: Fenel eflection coefficient Γ, pecula catteing facto ρ and divegence facto D and i given by[7] ρ =Γ ρ D () Te Fenel eflection coefficient fo a oot uface i deteined by te electoagnetic popetie of te uface. Te Fenel eflection coefficient fo vetical polaiation i given by[7][9] ε inψ ε co ψ Γ= ε inψ + ε co ψ c g c g c g c g In te above equation, ψ g i te gaing angle in Fig.1 and ε i te coplex dielectic contant, given by[9] c (3) wee 1 and ae te gound ditance fo te eflection point to te ada noal pojection and te taget noal pojection point, epectively, = 1 +,and e i Eat adiu. Fig. ow an exaple of te eaued taget altitude including Δ E. Te oiontal axi i te ange fo te ada to te taget, te vetical axi i te taget altitude, olid line epeent te tue altitude and olid line wit co ign epeent te eaued taget altitude. A can be een fo Fig., te elevation angle eo Δ E in (1) depend on te taget poition. Contant bia eo Spike eo ε = ε jε (4) c i ε ε ε 0 = + ( π fτ) 1+ ε ( 0 ) ( π fτ) π fτ ε ε σ i εi = + 1+ f wee f i ada fequency, ε 0 i contant( ε 0 =4.9), ε i tatic dielectic contant, τ i attenuation coefficient, andσ i i ion conductivity. In te following iulation, ε,τ andσ i i et to be 69.1, 9. 10-1, 4.7 10-10, epectively[9]. Te pecula catteing facto ρ in () i given by [7] πσ inψ g ρ = exp λ wee te gaing angle i te angle between indiect pat and uface wic depend on taget altitude, and λ i te wavelengt of te wavefo. σ i te (oot-ean-quae) of te waveeigt. Divegence facto i anote quantity tat affect te eflection coefficient. Ti facto i conideed due to te cuvatue of te Eat. Te eflected wave fo a uface divege and ti divegence caue an attenuation in te powe denity of te wave. An appoxiate value fo te divegence facto i given by[1][7] 1 1 D = + e inψ g 0 1 (5) (6) (7) (8) Figue. Tue and eaued altitude. B. SNR( ignal-to-noie atio) Te SNR on MP odel i given by[1] Rd 0 SNRlt SNR0 40log = + 10F R (9) wee SNR0 i SNR at te efeence ange R d 0, R i te ange fo te ada to te taget and F i te patten popagation facto. In addition, F i given by[1][7] F jδφ = 1+ ρe = 1+ ρcoδφ+ ρ (10) C. Pobability of Detection In ti pape, auing tat te taget fluctuate accoding to a Sweling cae І[10], detection pobability Pd i given by log Pd = fd ( R) = exp ( Pfa ) ( 1+ G) (11) wee Pfa i fale-ala pobability and G i antilogait of SNR in (9). III. PROPOSED METHOD MP eo depend on te eal altitude of te taget and te ange fo te ada to te taget wic ae unknown. Teefoe, we popoe a etod wic ubtitute aued altitude fo te actual altitude utiliing paticle filte, wee 03
te aued altitude i egaded a paticle, to etiate te taget altitude. Ou popoed etod calculate te ipotance weigt w of an aued altitude a, wic i calculated by uing etiated oiontal tate vecto, te altitude lt, including te contant bia eo baed on te MP odel(wee lt, i called ultipat altitude in ti pape, in addition, te ubcipt ean te odel nube fo 1 to M wic identify an aued altitude, M ean te axiu nube of aued altitude and te ubcipt a ean te aued value). And ten, popoed etod etiate te altitude of te taget uing aued altitude and te ipotance weigt of toe. Fig.3 ow te block diaga of ou popoed etod. A own in Fig.3, ou popoed etod i copoed of 6 block (wic ae Initialiation, Tacking, Multipat popagation geneato, Ipotance calculato, Reapling and Altitude Etiato ). Te pocee of ou etod ae own a te following. a) Initialiation Initialiation poce et te aued altitude in paticle witin a pedeteined ange at equal inteval (See table Ⅱ). b) Tacking (Section A) Tacking poce calculate taget tate etiate and tei covaiance atix uing tacking filte. Ti poce alo output coelation eult (e.g., ada eaueent ae in/out of tacking gate). c) Multipat popagation geneato (Section B) Multipat popagation geneato calculate te ultipat altitude lt, fo eac aued altitude a, (wic i et in advance) uing tack etiate x, y, and ada fequency f. a ean aued altitude et, lt altitude et a follow. (,1,,,,, ) = a a a a M (,1,,,,, ) = lt lt lt lt M ean ultipat d) Ipotance weigt calculato (Section C) Ipotance weigt calculato caluculate te ipotance weigt fo all aued altitude uing eaued altitude o, te altitude eo vaiance σ and te ultipat altitude, wic ae fo Multipat popagation geneato. w ean ipotance weigt et a follow. ( w w w ) w = 1,,, M e) Reapling (Section D) Reapling poce eaple paticle wit aued altitude baed on te ipotance weigt accoding to te paticle filte teoe. Te paticle wit aued altitude wic ae te top Pu pecent in te ipotance ode ae eapled accoding to te ipotance weigt, and ando noie i added to te aued altitude. Te et of te paticle ae eoved, and new paticle wit aued altitude ae geneated accoding to unifo ando nube. f) Altitude Etiato (Section E) Altitude Etiato calculate weigted aveage altitude uing te ipotance weigt of te aued altitude wic ae te top Pu pecent in te ipotance ode, and output te weigted aveage one a te etiated altitude of te taget. Te detail of te above pocee fo a) to f) ae decibed a follow. In addition, Fig.4 ow te flowcat of popoed etod. Meaueent Tacking fequency Initialiation a Multipat popagation geneato Tack poition x, y a lt Ipotance weigt calculato Figue 3. Block diaga of popoed etod START Initialiation Tacking Tacking pae? In gate? Ye Multipat Popagation Geneato Ipotance Weigt Calculato Reapling END Figue 4. Flowcat of popoed etod A. Tacking Tacking poce ue two coodinate yte wic ae Not-Eat-Up (NEU) coodinate and Pola (POL) coodinate (ee Fig.5). Ye Altitude Etiation Meaued altitude o, Altitude eo vaiance w, a Altitude Etiation No No σ Paticle Filte Reapling Etiated altitude 04
Figue 5. NEU and POL coodinate In Fig.4, te ada poition vecto i defined a[ x ] T y, o tat te elationip between NEU and POL i defined a ( x x) + ( y y) + ( ) R 1 E tan = A ( x x) + ( y y) 1 x x tan y y (1) Ou popoed etod ue tacking filte to ipove te poition accuacy in XY coodinate and to eove abnoal eaueent wic ave pike eo. Tacking gate can eove te eaueent wic ave pike eo. Te tacking gate egad te eaueent wic atify (13) a in gate, otewie a out of gate[11]. ν S ν (13) T 1 k k k d wee v k i eaueent eidual (te diffeence between te poition vecto of a eaueent and pedicted poition vecto fo tacking), S k i eidual covaiance, and d i gate ie wic i deteined ci-quae ditibuted wit 3 degee of feedo. In addition, tacking begin afte at leat 3 eaueent ae obeved toug all tie. We call te tie afte tacking tated tacking pae. B. Multipat popagation geneato Te ultipat altitude lt, of an aued altitude a, at tie t k i defined a follow. ( ) ( ) { } = x x + y y E + (14) lt, ( k ) k k tan ok E ( x, y, ) x X(Eat) tan Z (Up) 1 a, ok = +Δ k ( xk x ) + ( yk y ) R E 0(oigin) A Taget E (15) wee te elevation angle eo ΔEk i calculated by uing (1) T and taget poition vecto = xk yk a,. Note tat, a can be een fo Fig., te elevation angle eo ΔEk contain y Y (Not) pike eo and contant bia eo. Tacking in ou popoed etod a eoved te pike eo befoe ti poce Multipat popagation geneato, o tat te pike eo ae not needed to be odeled. C. Ipotance weigt calculato In cae of tat eaued altitude ok i given at tie t k, te ipotance weigt w ( = 1,,, M) wic coepond to te pobability of te eaued altitude unde te aued altitude a, [1], i given by w = γ M γ = 1 wee γ i defined a (, ) γ = P ok a 1 1 = g( ok; lt k, σ k ) = exp ( ok lt, ( k )), ( ) πσ σ k k (16) (17) D. Reapling Te eapling take place wit pobabilitie popotional to te ipotance weigt of te top Pu pecent in te ipotance ode. Wee Pu i one of te paaete in popoed etod and only Pu pecent of all aued altitude ae eapled. In addition, ou popoed etod add te value dawn fo Gauian ando ditibution wit tandad deviation σ (wic i o called popoed ditibution in paticle filte[1]) to te eapled aued altitude, fo intance, wic i j-t aued altitude fo next apling tie a follow. a, j( k+ 1) = a, j( k) + (18) wee i Gauian ando vaiable wit ean 0 and vaiance σ. Moeove, popoed etod delete te et of aued altitude (wic coepond to 100-Pu pecent of all aued altitude), and geneate new aued altitude te ae nube a te deleted one. Note tat new aued altitude ae geneated fo unifo ditibution in te inteval [a,b], tat i, te pobability denity function i given by 1 p( ) = b a 0 [ a, b] elewee (19) wee i new aued altitude fo next apling tie, a i te ae etting value a te lowet liit, b i te ae etting value a te uppe liit of te peet aued altitude in Initialiation poce (See table Ⅱ). E. Altitude Etiato We calculate weigted aveage altitude uing te ipotance weigt of te aued altitude wic ae te top Pu pecent in te ipotance ode. Te weigted aveage altitude i given by 05
ˆ = w Mt a, (0) wee Mt i te index et wic coepond to te top Pu pecent in te ipotance ode. IV. SIMULATION RESULTS Te validity of ou popoed etod a been exained toug copute iulation a follow. A. Siulation Scenaio Fig.6 ow te geoety in iulation cenaio. In all cenaio, a taget tat fo te point A (40k ditance fo te ada) to te point B wit contant oiontal peed 50/. Te taget a a contant altitude of t (100, 50 and 700) above te ea uface. Te ada i located at te point C wic a altitude of 4. O Z B 4[] C Figue 6. Siulation cenaio B. Siulation Paaete Te ada paaete ae uaied in table I. Te paaete of te tacking filte ae et to be a follow. Te ange, te aiut and te elevation eaueent noie tandad deviation ae 50, 10ad, and 10ad epectively. Te poce noie tandad deviation at axi x, y and ae 1/, 1/, and 0.01/ epectively. Te gate ie d i deteined by ci-quae ditibution wit ignificance level 0.01% and 3 degee of feedo. TABLE I. 39.5[k] 40[k] 50/ RADAR PARAMETERS Taget Paaete Value Range eo tandad deviation () 50 Aiut eo tandad deviation (ad) 10 Elevation eo tandad deviation (ad) 10 Sapling ate() Fale-ala pobability 10-6 Te paaete of te popoed etod ae uaied in table Ⅱ. In table Ⅱ, te aued altitude of a popoed etod ae in te ange of fo 100 to 600 at inteval of 0.5 and te nube of toe i 1001. Note tat toe paaete ae et in Initialiation poce. Alo, Pu epeent te pecentage of te aued altitude eapled fo all te one. A t X In addition, we copae te popoed etod wit te conventional etod[8]. Te conventional etod calculate te eliability of aued altitude wic ae pedeteined and fixed to output te one wit iget eliability a etiated altitude. Te conventional etod paaete ae uaied in table Ⅲ. Te aued altitude of a conventional etod ae in te ange of fo 100 to 600 at inteval of 0 and te nube of toe i 6. In table Ⅲ, T SNR i teold fo deleting ultipat altitude wic contain pike eo a own in Fig., T β and T Cnt ae teold fo electing a equential aued altitude wit ige eliability tan pecified value a etiated altitude. T β i te pecified value tated above fo judging te eliability, T Cnt i teold fo judging te continuity[8]. TABLE II. PROPOSED METHOD PARAMETERS Paaete Value Te nube M 1001 Aued Te lowet liit () 100 altitude Te uppe liit () 600 Inteval () 0.5 Pu (%) 99 Standad deviation σ () 10 TABLE III. CONVENTIONAL METHOD PARAMETERS Paaete Value Te nube M 6 Aued Te lowet liit () 100 altitude Te uppe liit () 600 Inteval () 0 Fale-ala pobability 10-6 T SNR (db) 3 T β 0.95 T Cnt C. Reult Te pefoance of ou popoed etod i evaluated by te RMSE (Root Mean Squae Eo) of te taget poition etiate in 50 Mote Calo un. Fig.7, 8 and 9 ow te RMSE of taget poition etiate wee te tue altitude of te taget i epectively 100, 50 and 700. In te figue, te oiontal axi epeent te iulation tie, te vetical axi epeent te RMSE, te olid line wit tiangle ign epeent popoed etod, and te daed line wit plu ign epeent conventional etod. A eult, te RMSE of popoed etod i about a alf of tat of conventional etod at te tie 80 in Fig.8, at te tie 140 in Fig.9. Howeve, in Fig.7, te RMSE of popoed etod i alot ae a tat of conventional etod becaue te tue altitude of 100 i one of te peet aued altitude in conventional etod. 06
Fo tee iulation eult, it i veified tat te accuacy of altitude etiation i ipoved by te popoed etod copaed wit te conventional etod. Figue 7. RMSE of poition etiate (taget altitude=100). V. CONCLUSION In ti pape, we popoed a new altitude etiation etod uing a paticle filte fo te poble of ultipat popagation ove te ea. A conventional etod wic calculate te eliability of te peet aued altitude wa not able to etiate te altitude but te peet taget altitude. Teefoe, te altitude accuacy deteioate. On te ote and, ou popoed etod calculated te ipotance weigt of aued altitude, wic coepond to paticle in paticle filte, baed on ultipat popagation odel to etiate taget altitude. Copaed wit conventional etod, ou popoed etod a te advantage of being able to etiate te altitude but te peet one by uing paticle filte teoe. Siulation eult owed tat ou popoed etod educed altitude etiation eo to a alf of tat of conventional etod, paticulaly in te fa ditance fo a ada. Toug copute iulation tial, ou popoed etod owed te ig tack accuacy copaed wit conventional etod. REFERENCES Figue 8. RMSE of poition etiate (taget altitude=50). [1] B.R. Maafa, Syte Analyi and Deign Uing MATLAB. Capan & Hall, 000. [] Y. Ba-Salo, A. Kua,W.D. Blai, and G.W. Gove, Tacking Low Elevation Taget in te Peence of Multipat Popagation, IEEE Tan. Aeo. Elect. Sy.,Vol.30, No.3, pp.973-979, 1994. [3] Y. Ba-Salo, W.D. Blai,E.Daeipou and G.W. Gove, Fequency Agility and Fuion fo Tacking Taget in te Peence of Multipat Popagation, in poceeding of IEEE 1994 National Confeence,pp.166-170, Ma. 1994. [4] M.D.Syond and J.M.Sit, Multi-fequency Coplex Angle Tacking of Low Elevation Taget, IEEE Intenational Conf., no.105,pp.166-171,1973. [5] J.A.Bude and J.A.Saffold, Multipat Effect on Low-angle Tacking at illiete-wave Fequencie, IEE poceeding-f, Vol.138, no., pp.17-184, Ap.1991. [6] W.D.Blai and M.Bandt-Peace, Static of Monopule Meaueent of Rayleig Taget in te Peence of Specula and Diffue Multipat, IEEE Conf., pp.369-375, Ap.001. [7] E.Daeipou, W.D. Blai, and Y. Ba-Salo, Bia Copenation and Tacking wit onopule in te Peence of Multipat, IEEE Tan. Aeo. Elect. Sy.,Vol.33, No.3, pp.863-88, Jul. 1997. [8] Y. Takabayai,T. Matuaki and H. Kaeda, Altitude Etiation Metod uing Aued Altitude Reliability Baed on in Multipat Popagation Model, in poceeding of SICE Annual Confeence 010, pp.196-01, Ma. 010. [9] L. V. Blake, Range-Pefoance Analyi, Atec Houe, 1986. [10] S. Blackan and R. Popoli, Deign and Analyi of Moden Tacking Syte. Atec Houe, 1999. [11] Y.Ba-Salo,X.R. Li and T. Kiubaajan, Etiation wit Application to Tacking and Navigation,Jon Wiley & Son,New Yok,001. [1] S. Tun, W. Bugad and D. Fox, Pobabilitic Robotic. MIT Pe, 006. Figue 9. RMSE of poition etiate (taget altitude=700). 07