Moving Target Hough Detector in Pulse Jamming*

Transcription

1 BULGARIA ACADEMY OF SCIECES CYBEREICS AD IFORMAIO ECHOLOGIES Volum 7 o Sofa 7 Movng agt Hough Dtcto n ul Jammng* Lyuba Douova Inttut of Infomaton chnolog 3 Sofa Abtact: h Hough dtcto wth two typ of a Contant Fal Alam Rat (CFAR) poco a Cll Avagng (CA CFAR) poco and an Excon (EXC CFAR) poco n th pnc of pul ammng nvtgatd n th pnt pap. h dtcton pobablty and th avag dtcton thhold of a Hough dtcto wth th two typ of CFAR poco a tudd. h xpmntal ult a obtand by numcal analy. hy val that th u of Hough dtcto allow ducng datcally dtctablty lo n compaon to th convntonal CFAR dtcto and that t ffctv fo mall gnal-to-no ato. h ach wo pfomd n MALAB computatonal nvonmnt. h obtand analytcal ult fo Hough dtcto can b ud n both ada and communcaton cv ntwo. Kywod: Rada Dtcto Hough dtcto ul Jammng obablty of dtcton obablty of fal alam Dtctablty poft (lo).. Intoducton Dung th lat fw ya mathmatcal mthod fo xtacton of uful data about th bhavo of obvd tagt by mathmatcal tanfomaton of cvd gnal a bng wdly ud n th dgn of nw hghly ffctv algothm fo pocng ada nfomaton. Such a mathmatcal appoach th Hough anfom (H). h concpt of ung th H fo mpovng th tagt dtcton n wht Gauan no ntoducd by Calon Evan and Wlon n [ 3]. h appoach ud by Calon n [3] fo a hghly fluctuatng tagt Swlng II typ tagt modl and tatonay homognou ntfnc. In modn ada th tagt dtcton dclad f th gnal valu xcd a plmnay dtmnd adaptv thhold. h cunt tmaton of th no lvl n th fnc wndow fom th thhold. o tmat th no lvl fo ada gnal dtcton n clutt nvonmnt wth unnown avag pow lvl th tchnqu popod by Fnn and Johnon n [4] oftn ud. Avagng th output * h wo uppotd by poct II 89/7 MS Ltd. Gant IF--85/5 and Gant MI-56/5. 6 7

2 of th fnc cll uoundng th tt cll fom th tmat. h dtcton thhold dtmnd a a poduct of th no lvl tmat n th fnc wndow and a cal facto to achv th dd pobablty of fal alam. hu a contant fal alam at mantand n th poc of dtcton. h CA CFAR poco (Cll Avagng Contant Fal Alam Rat oco) a vy ffctv n ca of tatonay and homognou ntfnc. h pnc of pul ammng n both tt oluton cll and th fnc cll can cau datc dgadaton n th pfomanc of th CA CFAR poco [6]. Such typ of ntfnc non-tatonay and non-homognou and oftn caud by adacnt ada o oth ado-lctonc dvc. A tchnqu that may b ud to allvat th poblm th xcon of tong pul bfo a cll-avagng pocdu. h appoach fo an EXC CFAR dtcto pntd by Goldman and Ba-Davd and analyzd fo multpl tagt tuaton n [8 9]. h analytcal xpon fo th pobablty of dtcton and th pobablty of fal alam of EXC CFAR and EXC CFAR BI dtcto n th pnc of oon dtbuton pul ammng and Ralgh ampltud dtbuton n both tt and fnc wndow a pntd n []. h gnal modl bad on th fact that th law of dtbuton of mpul ntfnc chang fom oon to bnomal wth th ncang of th pobablty of appaanc of andomly avng mpul gat than. []. h bnomnal modl mo gnal than oon dtbuton modl. hfo all mathmatcal fomula fo valuaton of both pobablty mau th pobablty of dtcton and th pobablty of fal alam hould b dvd fo bnomnal dtbuton fo a Hough dtcto. In th pnt pap on tuaton fo a hghly fluctuatng tagt Swlng II typ tagt modl dtcton n condton of pul ammng tudd. h ffctvn of Hough dtcto wth CA CFAR o EXC CFAR poco n pul ammng fo valu of pobablty of dtcton D =.5 achd. h ffctvn of Hough dtcto wth th mthod fom [3].. th nblty towad pul ammng tmatd. h tmat allow th compaon of Hough dtcto towad ondmnonal CFAR poco and th compaon towad anoth pattn achd fom oth autho []. h pnt ult how that Hough dtcto ffctv n condton of dcad pul ammng.. Stattcal analy of Hough dtcto Ung Calon appoach [ 3] w obtan a nw ult fo dtcton pfomanc n Hough pac fo tagt modl of th typ Swlng II n condton of pul ammng dcbd wth th pobablty dnty functon (pdf) of th fnc wndow output [5]: () f x xp x xp wh th p pul avag gnal-to-no ato th avag pow of th cv no th avag ntfnc-to-no ato th pobablty fo th appaanc of pul ammng wth avag lngth n th ang cll. x 6 8

3 6 9 In condton of bnomal dtbuton of pul ntfnc th bacgound nvonmnt nclud th ntfnc-plu-no tuaton []. Conquntly th pobablty dnty functon (pdf) of th fnc wndow output may b dfnd by () x x x x f xp xp xp wh λ th avag pow of th cv no and /λ th p pul avag ntfnc-to-no ato (IR). h pobablty of dtcton fo CA CFAR poco fo tagt of ca Swlng II n pul ammng [7] (3) CA CA CA CA SW d C wh th gnal-to-no ato CA th thhold contant and th avag ntfnc-to-no ato (IR). h pobablty of fal alam fo a CA CFAR dtcto fo ca Swlng II n pul ammng [5] obtand fo valu of th pobablty of dtcton d =. h pobablty of tagt dtcton of an EXC CFAR dtcto valuatd by: (4) EXC V EXC V EXC V E E SW M M M C d wh M V (.) th momnt gnatng functon accodng to [] and EXC a pdtmnd cal facto that povd a contant fal alam at ( fa ) dsw th pobablty of pul dtcton of an EXC CFAR dtcto n th pnc of bnomnal dtbuton mpul ntfnc. h pobablty of fal alam of an EXC CFAR poco valuatd by (4) ttng =. All ndcaton fo gnal dtcton obtand fom ang oluton cll and can a aangd n a matx of z n t pac. In th pac tatonay o contant ada vlocty tagt pa a a taght ln whch cont of nonzo lmnt of. Lt u aum that nm a t of uch nonzo lmnt of that conttut a taght ln n t pac that ( ) nm. h ln may b pntd n Hough paamt pac a a pont (n m). Dnotng nm a th maxmal z of th cumulatv fal alam pobablty fo a cll wttn accodng to [3]: (5) nm nm K l l l nm nm l fa fa fa wh K a lna tactoy dtcton thhold.

4 h total fal alam pobablty n Hough paamt pac qual to on mnu th pobablty that no fal alam occud n any of th Hough cll. Fo ndpndnt Hough cll th pobablty max( nm ) nm W (6) fa fa nm K ( nm ) wh max nm th accbl Hough pac maxmum and nm of cll fom Hough paamt pac who valu a qual to W th numb nm. h cumulatv pobablty of tagt dtcton n Hough paamt pac D cannot b wttn n th fom of a mpl Bnoull um. A th tagt mov wth pct to th ada th SR of th cvd gnal chang dpndng on th dtanc to th tagt and th pobablty of a pul D () chang a wll. hn th pobablty D can by calculatd by Bunn mthod. By man of Bunn mthod [3] a matx of z th lmnt of whch a th pmtv pobablty of dtcton fom th -th tm lc fomd. Ung (3) (4) t pobl all th ( ) ndd to calculat D to b obtand. Fo can of ada th followng vald: (7) d ( S ) SW S D. M h a not many ca n pactc whn ada quppd wth a Hough dtcto wong n pul ammng. In uch tuaton t would b dabl to now th Hough lo dpndng on th paamt of th pul ammng fo atng th bhavo of th ada. Fo th calculaton of Hough dtcto lo ud th ato btwn th two valu of gnal-to-no-ato (SR) maud n db. h compaon a mad and towad Hough dtcto wth CA CFAR poco and Hough dtcto wth EXC CFAR poco n pul ammng. 3. umcal ult In od to analyz th qualty of th Hough dtcto w cond ada wth paamt mla to tho n []: th ach can tm 6 ; th ang oluton R = 3 n. m ( n. m = 85 m); th bam ang-tm pac ha 8 ang cll and tm lc. In th analy condd taght ln ncomng tagt wth a pd of Mach 3 and m ada co cton. In th analy th SR avag valu calculatd a S=K/R 4 wh K=.6 th gnalzd ngy paamt of th ada and R th dtanc to th tagt maud n nautcal ml. Calon appoach ung Bunn mthod fo calculatng th pobablty of dtcton n Hough paamt pac futh dvlopd n od to mantan contant fal alam pobablty at th output of th Hough dtcto. h utabl cal facto chon tatvly. h nflunc of th thhold contant on th qud gnalto-no ato tudd. h nvtgaton pfomd fo pobablty of dtcton ( D =.5) and dffnt valu of th pobablty fo th appaanc of pul ammng wth avag lngth n th cll n ang. 7

5 In od to achv a contant valu of th pobablty of fal alam ( fa ) th valu of th thhold contant whch guaant that a dtmnd fo dffnt numb of obvaton n th fnc wndow an avag ntfnc-to-no ato (IR) and a pobablty fo th appaanc of pul ammng wth avag lngth n th cll n ang. h poft (lo) of th CA Hough dtcto n pul ammng a dtmnd towad th CA CFAR dtcto followng th algothm popod n [3] fo pobablty of dtcton 5. In tabl a pntd ult fo avag dtcton thhold fo CA Hough 4 CFAR dtcto wth th pobablty of fal alam ( fa ) fo numb of obvaton n th fnc wndow ( 6 ) avag ntfnc-to-no ato (IR=3 db) and two dfnt valu fo a pobablty fo th appaanc of pul ammng wth avag lngth n th cll n ang. abl M CA fo = CA fo =. AD fo = AD fo = h autho n [3] u appoach popod by Baton to dtmn th thhold n Hough paamt pac. hy aum M =7 a optmal thhold n th bnay ntgaton and apply t n Hough paamt pac. In th pap aft tatv analy th optmal thhold n Hough paamt pac alo dtmnd to b M =7 fo th valu of th pobablty of appaanc of pul ammng wth avag lngth n th ang cll =. Dffnt valu of th dtcton thhold n Hough paamt pac M a hown on Fg.. h optmal valu fo th thhold M =7 of can ( M =7/) fo valu of th pobablty fo th appaanc of pul ammng wth avag lngth n th ang cll ε =. Fo ε =. th optmal valu fo dtcton thhold n Hough paamt pac M = 8 of can ( M =8/). h pobablt of dtcton of Hough dtcto wth a CA CFAR poco a hown on Fg. and Fg. 3 fo valu of th dtcton thhold M = and fo optmal valu of th dtcton thhold M = 7 fo = and fo M = 8 fo =.. h poft of ung a Hough dtcto wth CA CFAR poco calculatd fo th thhold valu M = and fo optmal valu of th dtcton thhold M =7 fo 7

6 = and M =8 fo =. compad to a CA CFAR poco fo th numb of tt oluton cll =6 and th valu fo pobablty of fal alam fa 4 a hown on Fg. 4. h CA Hough dtcto wth th optmal Hough ul M -out-of- qual to 7 of btt n ca of low valu of th pobablty fo appaanc of mpul ntfnc up to.6. Fo hgh valu of th pobablty fo appaanc of mpul ntfnc abov.6 th uag of th optmal Hough ul M -out-of- =8 of can ult n low lo. Fg.. Avag dtcton thhold of a CA Hough CFAR dtcto Fg.. obablty of dtcton of a Hough dtcto wth CA CFAR poco n pul ammng fo can M = M =7 and = Fg. 3. obablty of dtcton of a Hough dtcto wth CA CFAR poco n pul ammng fo can M = M =8 and =. Fg. 4. oft of a Hough dtcto (dahd ln) wth CA CFAR poco fo can M = and two optmal valu of th dtcton thhold M =7 fo = and M =8 fo =. compad to a CA CFAR dtcto (old ln) fo =6 A dtald pfomanc analy of Hough dtcto wth an EXC CFAR poco pntd n th pap. It bhavo ha bn tudd fo dffnt valu of th thhold contant and fo dffnt valu of th pobablty fo th appaanc of mpul ntfnc n Hough paamt pac. h xpmntal ult a obtand fo th followng nput paamt: avag pow of th cv no λ = avag 7

7 ntfnc-to-no ato (IR=3 db) pobablty fo appaanc of mpul ntfnc wth avag lngth n th ang cll fom. to.9 numb of fnc cll =6 (o 3) numb of tt cll L=6 pobablty of fal alam fa = 4 xcon thhold B E = numb of can = optmal valu of Hough dtcton thhold M =7 M =3 and bnay ul M-out-of-L=/6 M-out-of-L=6/6. In abl a pntd ult fo avag dtcton thhold fo EXC Hough CFAR dtcto wth pobablty of fal alam ( fa = 4 ) xcon contant B E = fo numb of obvaton n th fnc wndow ( 6 ) an avag ntfncto-no ato (IR=3 db) and two dfnt valu fo pobablty of appaanc of pul ammng wth avag lngth n th cll n ang. h avag dtcton thhold fo EXC Hough CFAR dtcto n condton of pul ammng and fo dffnt valu of th dtcton thhold n Hough paamt pac M hown on Fg. 5. h avag dtcton thhold fo Hough dtcto wth an EXC CFAR poco fo two dffnt valu of th numb of fnc wndow (=6 and =3) and fo th valu M = of th Hough dtcton thhold a hown on Fg. 6. h ncang of th fnc wndow numb lad to lo dmnhng. h pobablty of dtcton of th EXC Hough CFAR dtcto hown on Fg. 7 fo optmal valu of th dtcton thhold M =3 by valu fo pobablty of appaanc =.. On Fg. 8 hown th pobablty of dtcton of th EXC Hough CFAR dtcto fo two valu of th dtcton thhold M = and M =7 fo valu of pobablty of appaanc =.9. h AD of Hough dtcto wth an EXC CFAR poco fo th optmal valu of th dtcton thhold M =7 fo =.9 M =3 fo =. and fo th thhold valu M = a hown on Fg. 9. Fo compaon on Fg. th ult obtand fo th Hough dtcto wth th two typ of on-dmnonal CFAR poco a hown CA CFAR and EXC CFAR. abl M EXC fo =. EXC fo =.9 AD fo =. AD fo =

8 Fg. 5. Avag dtcton thhold of an EXC Hough CFAR dtcto fo two valu of th pobablty of appaanc Fg. 6. Avag dtcton thhold of an EXC Hough CFAR dtcto fo two valu of th numb of tt oluton cll Fg. 7. obablty of dtcton of a Hough Fg. 8. obablty of dtcton of a Hough dtcto wth EXC CFAR poco n pul dtcto wth EXC CFAR poco n pul ammng fo can M = M =3 and =. ammng fo can M = M =7 and =.9 Fg. 9. Avag dtcton thhold of an EXC Hough CFAR dtcto fo two optmal valu of dtcton thhold M =7 fo =.9 M =3 fo =. and fo thhold valu M = 7 4 Fg.. obablty of dtcton fo Hough dtcto wth two on-dmnonal CFAR poco

9 4. Concluon h xpmntal ult val th nflunc of th ntfnc on th dtcton poc whn havng contant fal alam at n pul ammng. A mthod fo lo tmaton whch allow choong optmal dtcto paamt dvlopd. h tmat of th ffctvn of a Hough dtcto (CA Hough CFAR o EXC Hough CFAR) n pul ammng a cvd fo dffnt tam chaacttc. Ung Matlab th avag dtcton thhold fo th two typ of Hough dtcto fo a hghly fluctuatng tagt Swlng II typ tagt modl dtcton n condton of pul ammng calculatd n accodanc wth th appoach pntd n [3]. Ung th appoach t vy ay to pcly dtmn th ngy bnft whn ung a gvn dtcto. h ult achvd how that Hough dtcto wth on-dmnonal poco ffctv n condton of dcang pul ammng. h pfomanc of a Hough dtcto dgnd fo non-homognou ntfnc tudd. h optmal thhold valu fo dffnt nput condton a tmatd. h valu of th tt oluton cll and th pobablty of fal alam ov th avag dtcton thhold a tudd. h ult how lo n th gnal to no ato of about 37 db fo th Hough dtcto wth EXC CFAR poco and 4 db fo th Hough dtcto wth CA CFAR poco wth pct to th Hough dtcto wth a fxd thhold []. Applcaton of cnong tchnqu n th dtcton algothm mpov th Hough dtcto ffctvn. h ult obtand n th pap could pactcally b ud n ada and communcaton ntwo. R f n c. C a l o n B. E. E v a n S. W l o n. Sach Rada Dtcton and ac wth th Hough anfom. at I. IEEE an. Vol. AES o -8.. C a l o n B. E. E v a n. S. W l o n. Sach Rada Dtcton and ac wth th Hough anfom. at II. IEEE an. Vol. AES o C a l o n B. E. E v a n S. W l o n. Sach Rada Dtcton and ac wth th Hough anfom. at III. IEEE an. Vol. AES o F n n H. M. R. S. J o h n o n. Adaptv Dtcton Mod wth hhold Contol a a Functon of Spatally Sampld Clutt Etmaton. RCA Rvw B h a V. CA CFAR ada gnal dtcton n pul ammng. Compt. Rnd. Acad. Bulg. Sc. Vol o K a b a c h v C h. L. D o u o v a I. G a v a n o v. Compaatv Analy of Lo of CA CFAR oco n ul Jammng Cybntc and Infomaton chnolog Vol K a b a c h v C h. L. D o u o v a I. G a v a n o v. Cll Avagng Contant Fal Alam Rat Dtcto wth Hough anfom n Randomly Avng Impul Intfnc. Cybntc and Infomaton chnolog Vol. 6 6 o G o l d m a n H. I. B a -D a v d. Analy and Applcaton of th Excon CFAR Dtcto. In: IEE oc. Vol. 35 t.f. (6) G o l d m a n H. fomanc of th Excon CFAR dtcto n th pnc of ntf. In: IEE oc. Vol. 37 t.f. (3) B h a V. C h. K a b a c h v. Excon CFAR Bnay Intgaton oco. Compt. Rnd. Acad. Bulg. Sc. Vol o /

10 . K a b a c h v C h. I. G a v a n o v L. D o u o v a. Excon CFAR BI Dtcto wth Hough anfom n nc of Randomly Avng Impul Intfnc. In: oc. of Intnatonal Rada Sympoum IRS 5 Bln Gmany D o u o v a L. Hough Dtcto wth On-dmnonal CFAR oco n Randomly Avng Impul Intfnc. In: oc. of Dtbutd Comput and Communcaton two Intnatonal Wohop Sofa Bulgaa R o h l n g H. Rada CFAR hholdng n Clutt and Multpl agt Stuaton. IEEE an. Vol. AES o