第四章信号检测和信号参数估计

1、第四章信号检测和信号参数估计 1 第四章信号检测和信号参数估计 2 ( )( )( ):, (0, ), 0,1 ii r ts tn tHtTi 1 ( ). .( ). .( )0 k kii kk i r tl i m rtl i mrttT 111 0 000 0 ( )( )( ) ( )( )( ) T iiii T iiii Hrstn tt dtsn Hrstn tt dtsn ： ： 1100 |, | iiii E r HsE r Hs ( ( ). .( ) k k r tl i mr t 2 )|(Var)|(Var 0 10 N HrHr ii 第四章信号检测和信号参

2、数估计 3 2 1 1 0 0 1 2 0 0 1 0 0 ()11 exp 2/2 ( /) . ( /)()11 exp 2/2 k ii i k k ii i rs NN p R H lim p R Hrs NN 22 1001 11 00 21 . ln ( ( ).()() kk kiiiii kk ii limr tlimss rss NN 1111 000 11111 ( ) ( )( )( )( )( ) kkkkk TTT iijjijijii ijiji r t s t dtrtst dtrstt dtrs 22 0 1 ( ), 0,1 k T jijk i sst dt

3、j 00 0 1 ( )( ) k T ii i r t s t dtrs 第四章信号检测和信号参数估计 4 1 0 22 1001 00 00 21 ln ( ( )( )( )( )( )( ) ln H TT H r tr t s ts t dts ts t dt NN 充分统计量信号能量差 1 0 22 0 1010 00 1 ( )( )( )ln( )( ) 22 H TT H N r ts ts tdtststdt 1( ) s t 0( ) s t T dt 0 T dt 0 + - )(tr判决 )(tr 10 ( )( )s ts t 第四章信号检测和信号参数估计 5 (

4、)s t T dt 0 )(tr )(th l TT dttThtrdttstrl 00 )()()()( )()(tThts )()(Tsh 10 ( )( )( )0s ts ts t， * ()( ) j T H jSe 0max /2/NENS 第四章信号检测和信号参数估计 6 2 )(jS 第四章信号检测和信号参数估计 7 1 0 22 1001 00 00 21 ln( ( )( )( )( )( )( ) ln H TT H r tr ts ts tdts ts tdt NN 信号能量差充分统计量 10 ( )( )( )s ts ts t 10 2 1/2 10 0 10 1/

5、2 1010 ( )( ) ( ) ( )( ) ( )( ) (2) T s ts t t s ts tdt s ts t EEEE 第四章信号检测和信号参数估计 8 d )|( )|()|( 0 2 01 2 HlVar HlEHlE d 1 100 11 1 1/2 00 1100 ( )( ) ( |)( )( )( )( ) (2) TTE s tE s t E l HEr tt dtEE s tn tdt EE EE 2 1 0101 101 )2(EEEE EEE 第四章信号检测和信号参数估计 9 1 10 0 00 0 1/2 0 1100 ( )( ) ( |)( )( )

6、(2) TEs tE s t E l HEE s tntdt EEEE 2 )|( 0 0 N HlVar 2 11002 1100 1/2 00 1100 222 (2) (2) EE EE dEE EE NNEE EE , ， 1)()( 10 tStSd 2 1 0101 010 )2(EEEE EEE 第四章信号检测和信号参数估计 10 dARAApRa)/() ( ( ) ln(/) 0 Aa R p AR A 第四章信号检测和信号参数估计 11 )(lnApa )/(ln / ARp ar () ln(/) 0 ML A aR p R A A )/( / RAp ra )/( /

7、ARp ar )()()/()()/( / ARpApARpRpRAp aarrra / ln( / ) ln( / ) ln( ) ln( ) a rr aar pA RpR Ap Ap R 第四章信号检测和信号参数估计 12 ( )( , )( ) 0r ts t Antt T k i ii k k k trmiltrmiltr 1 )(. .)(. .)( 00 ( )( )( ,)( )( )( ) TT iiiii rr tt dts t An tt dts An 2 0 0 |()( ,)( ), |() 2 T iiiiii N E rAsAs t At dtVar rAVar

8、nE n i r 2 11 0 0 ( )11 (/ )( / )exp 2/2 kk ii ki ii rs A p RAp r A NN 第四章信号检测和信号参数估计 13 2 0 1 0 ( ) ln (/ ) 2 K ii k i rs AK p RAN N 2222 000 111 ( )( ) ( , ) , ( ) , ( )( , ) kkk TTT i iii iii rs Ar t s t A dtrr t dtsAs t A dt 0 0 ln(/)2( , ) ( )( , )0 ML T A a p R As t A r ts t Adt ANA 第四章信号检测和信号

9、参数估计 14 ) 2 exp( 2 1 )( 2 2 a a a A Ap 2 2 2 2 ln2ln 2 1 )(ln a a a a A A A A Ap 2 0 0 2( , ) ( )( , ) 0 MAP T a A a s t AA r ts t Adt NA 2 0 0 2( , ) ( )( , ) MAP T a MAP A a s t A ar ts t Adt NA 第四章信号检测和信号参数估计 15 1 1 2 2 2 ln(/)ln(/) () p R Ap R A V a r aAEE AA 2 2 0 0 ln (/)2( , ) ( )( , ) T p R

10、As t A EEr ts t Adt AA NA 2 0 0 2( ,) T s t A dt NA TT dt A Ats Edt A Ats AtstrE N 00 2 2 2 0 ),( ),( ),()( 2 第四章信号检测和信号参数估计 16 )()( )/(ln AKAa A ARp 2 221 2 0 l n( )2 () ( ) a aa p A Ea aE NA )( ),(ln AaK A ARp 1、若、若 （A为非随机量）为非随机量）( , )( )s t AAs t ( , )s t A 0 0 l n ( / )2( , ) ( )( , )0 T p R As

11、t A r ts t Ad t ANA T aa dt A Ats E 0 22 ),( T dt A Ats N Aa 0 2 0 ),( 2 )(Var 第四章信号检测和信号参数估计 17 0 0 2 ( )( )( )0 M L T A a r tA s ts t d t N 0 0 2 0 0 ( ) ( ) 1 ( ) ( ) ( ) T T M LT r t s t d t ar t s t d t E st d t 0 2 0 ( )( )( ) ( ) T MLT As tn ts t dt E aEA st dt 0 0 2 0 0 00 ln(/)2 ( )( )( ) 2

12、2 ()( )() T T MLML p R A r tAs ts t dt AN E aAs t dtaA NN 1 0 0 1 2 2 2)/(ln )( N E A ARp EAaVar 第四章信号检测和信号参数估计 18 ( ,)( )s t AAs t), 0( 2 a N 2 0 0 2 ( )( )( ) MAP T a MAP A a ar tAs ts t dt N 22 0 0 00 22 (1)( ) ( ) T aa MAP E ar t s t dt NN 0 2 0 00 2/ ( ) ( ) 1/2/ MAP T a N ar t s t d t EN 第四章信号

13、检测和信号参数估计 19 第四章信号检测和信号参数估计 20 2 11 0 0 ( )1 (/ )( / )e x p kk ii ki ii rs A p RAp r A NN 2 0 1 0 22 000 000 1 l n ( /).l n( ) 121 ( ) () ( )() k ii k i TTT r t p R AlimkNrs A N kr t d td ts tA NN At N tds a ( ,)()s t As tA 第四章信号检测和信号参数估计 21 t t t 0 ( ) () T r t s tA dt MLa ()s tA ( )r t A ( )s t)(t

14、r MLa 第四章信号检测和信号参数估计 22 00 ( ) ()( ) ()0 TT r t s tA dtr t s tA dt A 00 2 2 0 0 () () 2() 2 T T NN Var A s tA s tAdt dt A ()s tA ()s tA ()s tA 00 2 2 21 2 2 j A NN S jd j S jed 第四章信号检测和信号参数估计 23 EdjS 2 2 1 2 0 1 () 2 Var E N 2 2 2 2 S jd S jd 2 0 2 1 )( T N E Var 22 2 2 | ( )| | ( )| ts tdt T s tdt

15、， 第四章信号检测和信号参数估计 24 0 ( , )sin()s t AKtA( )( , )( )r ts t An t 0 (0,/2)NN 0 0 l n(|)2( , ) ( )( , ) 0 M L T A a p R As t A r ts t Ad t ANA 00 0 0 2 ( )s i n () c o s ()0 T r tKtAKtA d t N 000 00 ( )c o s ()s i n ()c o s ()0 TT r ttA d tKtAtA d t 0|)cos()( 0 0 T aA ML dtAttr T ML T ML tdttratdttra 0

16、0 0 0 sin)(sincos)(cos sin)( cos)( 0 0 0 0 1 T T ML tdttr tdttr tga )(tr t 0 cos t 0 sin ML a 第四章信号检测和信号参数估计 25 第四章信号检测和信号参数估计 26 第四章信号检测和信号参数估计 27 1 0 ( )( ) :,0 ( ) ( ) :,0 s tn tHtT r t n tHtT ( , ) c K t u 0 () 2 N tu ( , ): w h t u 0 ( , )()( , ) 2 nc N K t utuK t u *1 * *0 ( )( ) :,0 ( ) ( ) :

17、,0 s tn tHtT r t n tHtT * * ( , )( )( )() n Kt uE n tutun ( , ) w h t u )()()(tntwtn c TT duusduusurtr 0 2 * 0 * )( 2 1 )()()(ln 第四章信号检测和信号参数估计 28 0000 1 ln ( )( )( , ) ( )( )( , ) ( ) 2 TTTT nn r ts v dvQ z v r z dzs z dzQ z v s v dv 0000 1 ln ( )( )( , ) ( )( )( , ) ( ) 2 TTTT nn r tr z dzQ z v s

18、v dvs z dzQ z v s v dv TT dzzgzsdzzgzrtr 00 )()( 2 1 )()()(ln TzdvvsvzQzg T n 0,)(),()( 0 T w T w T T w T w T dvvsvuhdzzszuhdu dvvsvuhdzzrzuhdutr 000 000 )(),()(),( 2 1 )(),()(),()(ln TvzduvuhzuhvzQ T wwn ,0,),(),(),( 0 第四章信号检测和信号参数估计 29 第四章信号检测和信号参数估计 30 0 ( , )( , )( , ) T nww Qz vh u z h u v d u

19、与与 ( , )( ) ( ) n Kz vE n z n v 第四章信号检测和信号参数估计 31 Ttdxxnxthtn T w 0)(),()( 0 * T wwn dxdzznxnzuhxthEututKuntnE 0 * )()(),(),()(),()()( T nn T w T ww T n T ww dxxvQzxKzuhdz dtxthvthdxzxKzuhdzvuh 00 000 ),(),(),( ),(),(),(),(),( T nww dxdzzxKzuhxth 0 ),(),(),( TvzdxxvQzxKvz T nn ,0,),(),()( 0 第四章信号检测和

20、信号参数估计 32 )( 2 ),(),( 0 zx N zxKzxK cn 0 00 0 0 00 2 ()( , )( , )( , )() ()( , ) 2 22 ( , )()( , ) ( , )( , ) 0, TT nnco T ccoo N zvK x z Q v x dxK x zxzvxh v x dx N K v zzvK x z h v x dxh v zz vT NN ( ) c n t Tu Tt 0 0 Txvxvhxv N xvQ on ,0),()( 2 ),( 0 Tttntatr0),()()( TvzzvKdxzxKxvhzvh N c T coo ,

21、0),(),(),(),( 2 0 0 ),(),(),(),( 2 0 0 utKdvvuKvthuth N a T aoo 第四章信号检测和信号参数估计 33 c i ( , ) c K t u duuutKt i T ci c i )(),()( 0 ( ) i t 0 2 Tc ii N Tutut N uth i ii c i c i o ,0),()( 2/ ),( 1 0 )()( 2/ )( 2 ),( 1 00 ut N ut N utQ i ii c i c i n )()()( 1 utut i ii )()( 1 )()( 2 ),( 11 1 0 utut N utQ

22、 i ii T i i ii c in 第四章信号检测和信号参数估计 34 2 2 * * 0 0* 2 ( ) T E dEs tdt N 000 ( )( , ) ( )( ) ( ) TTT n s uQ u z s z dzdus u g u du T ii i c i i dtttss N s d 0 1 0 2 2 )()( 2 T w T w T dzzszthduusuthdtd 000 2 )(),()(),( 第四章信号检测和信号参数估计 35 ( , ) c K t u min cc j ( ), j t 0min 1 /2 c N c j ( )( ) j s tt (

23、 ),1, i t ik ( ) j t 0 i i sEij sij 0 min c 2 0 2/dE N 第四章信号检测和信号参数估计 36 0 0 ln(/)2( , ) ( )( , )0 ML T A a p R As t A r ts t Adt ANA A ARp)(ln 0 ( ,) ( )( )|0 ML T gA a s u A rug udu A dtAtstrutQugur T ng 0 ),()(),()()( 0 2 ( , )() n Q t utu N ml aA T n T A Aus utQAtstrdudt 00 ),( ),(),()( 第四章信号检测和

24、信号参数估计 37 1 00 2 2 ),( ),( ),(1 )( T n T a a A Aus utQ A Ats dudtEaaE map 00 2 map ),( ),(),()( aA TT na A Aus utQduAtstrdta 1 0 1 0 ),(),(),( ),( ),( )(Var T T n dt A Atg A Ats dtdu A Aus utQ A Ats Aa 第四章信号检测和信号参数估计 38 （复合假设检验）（复合假设检验） x HrHrHr x HrHrHr dHpHpHp dHpHpHp ), (), |R()|R( ), (), |R()|R(

25、 0|0,|0| 1|1,|1| 000 111 00 11 :),(),()( :),(),()( Htntstr Htntstr 第四章信号检测和信号参数估计 39 TttwtrH TttwtttfEtrH cr 0),()(: 0),()(cos()(2)(: 0 1 T r T r dtts N dttstr N dptr 0 2 0 0 0 ),( 1 ),()( 2 exp)()( T r dttstr N dptr 0 0 ),()( 2 exp)()( T cs T cc dttttftrL dttttftrL 0 0 )(sin)()(2 )(cos)()(2 sin)(sincos)(cos)(costttttt ccc )sin