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BLIND SEPARATION OF OPTICAL TRACKER RESPONSES INTO INDEPENDENT

COMPONENTS DISCRIMINATES OPTICAL SOURCES

Ivica Kopriva, Antun Perin

Institute for Defense Studies, R&D, Bijenika 46, 10000 Zagreb, CroatiaInstitute !Ru"er Bo#ko$i%!, aser R&D De'art(ent, Bijenika )6, 10000 Zagreb, Croatia

e*(ai+ i$i-a.ko'ri$a/'ub+i-.sr-e.r

ABSTRACT

n o'ti-a+ s2ste( based on rotating reti-+e is used to deter(ine

'o+ar -o*ordinates of te 'ri(ari+2 infrared o'ti-a+ sour-e. Su-s2ste( fai+s to dis-ri(inate si(u+taneous+2 se$era+ o'ti-a+sour-es. 3e de(onstrate e'eri(enta++2 in a -ase of t5oo'ti-a+ sour-es tat tis dra5ba-k -an 'rin-i'a++2 be o$er-o(eb2 a''+i-ation of te b+ind signa+ se'aration BSS7 a+gorit(son data re-orded at te out'uts of an origina++2 (odified o'ti-a+s2ste(. Se'aration of (odified o'ti-a+ s2ste( res'onses intoinde'endent -o('onents 2ie+ds (odu+ating fun-tions tat -arr2infor(ation about 'o+ar -o*ordinates of te -orres'ondingsing+e o'ti-a+ sour-es.

1. INTRODUCTION

8otentia+ a''+i-ation of te BSS teor2 +ies in (an2 areas su-as s'eaker se'aration in s'ee- re-ognition 9:;,

-o((uni-ation signa+ 'ro-essing b2 'erfor(ing ada'ti$e b+inde>?,>C?, @>?7 91A;, et-. 3e be+ie$e tat for te first ti(e teBSS teor2 is a''+ied to te ne5 'rob+e( dis-ri(ination ofo'ti-a+ sour-es.

n o'ti-a+ s2ste( based on rotating reti-+e is used todete-t and deter(ine te 'osition of an obje-t fro( 5i- so(efor( of te 'ri(ari+2 infrared energ2 is e(anated 9);, 9;, seefigure 1.

igure 1 'ti-a+ tra-ker basi- -onstru-tion

ro( te reasons of -on$enien-e o'ti-a+ s2ste( so5n onfigure 1 5i++ be -a++ed o'ti-a+ tra-ker in te rest of te 'a'er.Ee rotating reti-+e, a+so -a++ed (odu+ating disk, (odu+ates

in-identa+ o'ti-a+ f+u 6 , 7t and is +o-ated at te fo-a+

'+ane of an o'ti-a+ i(aging s2ste(. Fere stands for

5a$e+engt and t (eans ti(e. De'ending on te sa'e of-+ear and o'a

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igure H Reti-+e 5it fan*b+aded 'attern

Ee ti(e fun-tion te instantaneous fre

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Ee (ain 'oint is in introdu-ing bea( s'+itter after (odu+atingdisk and ten dete-ting (odu+ated o'ti-a+ f+u 5it t5o

'otodete-tors. Eis is in agree(ent 5it te BSS teor2 tatre'ressions 1A7 and 147 re'resent (ate(ati-a+ (ode+ of te

(odified o'ti-a+ tra-ker out'ut signa+s. In 147 6 7 and 6 7 are bea( s'+itter trans(ission and ref+e-tion

-oeffi-ients res'e-ti$e+2, 5i+e R16 7 and RH 6 7 are

'oto*dete-tor s'e-tra+ res'onsi$ities. Con$o+uti$e signa+(ode+ 1A7, suitab+e for a''+i-ation of te BSS a+gorit(s, isi++ustrated 5it figure 4, 5ere #(',k), $(',k), &$#(',k) and&$$(',k) are transfor(s of te re+ated i('u+se res'onses 147.

igure 4Con$o+uti$e signa+ (ode+

B2 using on*+ine BSS a+gorit(s it sou+d be 'ossib+e to

re-o$er te sour-e signa+s s r t16 , , 7 and s r tH 6 , , 7

on te basis of te obser$ed signa+sx#(t) andx$(t) on+2.

3. INTERPRETATION OF THE BSS THEORY

REQUIREMENTS

Ee rea+*5or+d situations tat often in-+ude ti(e de+a2s

bet5een te sour-es in te (iture are des-ribed 5it-on$o+uti$e (iing (ode+ x(t)&*s(t),5ere s(t)is $e-tor ofsour-e signa+s, & is (iing (atri tat -ontains -anne+i('u+se res'onses, x(t)is $e-tor of te obser$ed signa+s and L(eans -on$o+ution. Ee goa+ is to re-onstru-t te sour-e signa+sfro( te obser$ed signa+s on+2, i.e. te (iing (atri & isassu(ed to be unkno5n. So+utions for su- 'rob+e( are gi$enin 91;, 94;, 9:;, 9;, 911;, 91H;, 91);, 91:;, 91;*9H1;. Fo5e$er,so(e of te 'ro'osed so+utions are iterati$e b2 nature, 9H;, 9:;,91H;, 9H1;. or rea+ ti(e sour-e se'aration ada'ti$e i.e.se

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{ }& & k i 0i0 i i06 7 6 7 , , = 1 H

1:7

5ere &i 6 7 is DE of te re+ated se+e-ti$e a('+ifier

i('u+se res'onsei(t), 5i+e ki0 -an be easi+2 identified fro(

147. Een -ondition 167 -an be re5ritten as

[& & k k 1 H 11 HH6 7 6 7 17

and is transfor(ed in

k k k k 11 HH H1 1H 0

17

sin-e in 17 &16 7 and &H 6 7 re'resent fre

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igure 6 8o5er s'e-tru( of te obser$ed signa+x#(t)

8o5er s'e-tru(s of te se'arated signa+s -#(t) and -$t7 are

so5n on figures : and res'e-ti$e+2. Co('ared 5it figure 6te se'aration of t5o signa+s is ob$ious. fter se'arationdeter(ination of te -o*ordinates of te o'ti-a+ sour-es is te(atter of de(odu+ation of te re-o$ered sour-e signa+s tat areof te for( 47. In order to (easure te se'aration

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igure : 8o5er s'e-tru( of signa+ -#(t)

igure 8o5er s'e-tru( of signa+-$(t)

Sin-e o'ti-a+ sour-es in our e'eri(ent 5ere not (o$ing it 5as'ossib+e to re-ord and de(odu+ate re-orded signa+s 5en ea-

o'ti-a+ sour-e 5as 'resent in te (odified o'ti-a+ (odu+atorfie+d of $ie5 a+one. n tat 5a2 5e a$e obtained referen-eddata in re+ation to 5i- a--ura-2 of te b+ind se'arationa''roa- -an be $erified. Resu+ts obtained 5it info(ase'arators 91H;, 9H0; M H17, 5it de--ore+ator 9; as 5e++ astose obtained b2 (ini(i=ing -riteria HA7*911; are re'orted in

tab+e 1. Nurtosis of te sour-e signa+s is 6 7 .s1 0 4I:=

and 6 7 .sH 1AI= . Sin-e 6 7s1 is re+ati$e+2 -+ose to=ero sour-e signa+ s# is not far fro( ?aussian and info(ase'arator 5it (-i)tanh(-i) as not di$erged. ('+itudes ofte de(odu+ated signa+s 5ere e'ressed in dBs and (easured5en de(odu+ated signa+s 5ere transfor(ed in fretre(e $a+ues for ea- statisti-s are gi$en intab+e H.

Eab+e H. e$e+ of statisti-a+ in7de'enden-e

Statisti-s >tre(e forx#,x$ >tre(e for-#,-$

C11 0.H6H *0.006:CA1 *0.10: 4.66e*)

CHH *0.11H A.)e*4

C1A *0.0)AA .)4)e*4

In tab+e H fro( A to e$en HA4 ti(es +ess +e$e+ of statisti-a+de'enden-e bet5een se'arated signa+s re+ati$e to (easuredsigna+s -an be obser$ed. Eat -an be -onsidered ase'eri(enta+ $erifi-ation of te statisti-a+ inde'enden-eassu('tion. Ee -ross*-orre+ation 7##bet5een obser$ed andse'arated signa+s are so5n on figures 11 and 1H res'e-ti$e+25en ti(e +ag 5as (o$ing fro( M)00 to )00.

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igure 11 Cross*-orre+ation bet5eenx#andx$

igure 1H Cross*-orre+ation bet5een-#and-$

5. CONCLUSION AND FUTURE WORK

so+ution for dis-ri(ination of se$era+ o'ti-a+ sour-es b2(eans of (odified o'ti-a+ tra-ker and BSS a+gorit(s is'ro'osed. >'eri(ent 'erfor(ed 5it (odified o'ti-a+ tra-kerand t5o o'ti-a+ sour-es -onfir(ed te 'rin-i'a+ 'ossibi+it2 todis-ri(inate t5o o'ti-a+ sour-es. uture 5ork 5i++ be dire-tedto5ard on*+ine BSS a+gorit(s 5orking in frerror Signa+s and Dis-ri(ination of

'ti-a+ Era-kers tat See Se$era+ Sour-es!, Proc! of theI555 ,o+. )A, Jo. 1, ''. 14A*1H, anuar2, 16).

[1)] C. Ser$iTre, !easibi+it2 of Sour-e Se'aration in

re. 3einstein, !Criteria for @u+ti-anne+ Signa+

Se'aration!,I555