/936 Chapter 9 Nonparametric detection UESTC 1
1 UESTC Chapter 9 Nonparametric detection
Previous detection theories are based upon the underlying statistical models of the measurements. This chapter focuses on nonparametric detection. UESTC 2
2 Previous detection theories are based upon the underlying statistical models of the measurements. This chapter focuses on nonparametric detection. 2 UESTC
Two simple nonparametric detectors 5 Let x,X2,,xy are observation samples which are mutually independent. 1 Correlation detector Binary detection: Ho:x(t)=n(t) H:x(t)=s(t)+n(t) Sample points: Ho x=n i=1,2,…,W H1:x,=S,+n D Correlation detector: ∑x ≥ t D For AWGN,it is an optimum detector. 3
3 Let are observation samples which are mutually independent. 1、Correlation detector Binary detection： 1 2 N x x x , , , 0 1 : ( ) ( ) : ( ) ( ) ( ) H x t n t H x t s t n t = = + 0 1 : 1,2, , : i i i i i H x n i N H x s n = = = + Sample points: Correlation detector: 1 0 1 D N i i i D x s =1 Two simple nonparametric detectors For AWGN, it is an optimum detector
2.Linear detector (average detector) Ho:x;=n i=1,2,…,N H1:X,=S,+n Linear detector: H ≥ X 2 i=1 Ho For AWGN,and s;is a constant,it is an optimum detector
4 2、Linear detector (average detector) 0 1 : 1,2, , : i i i i i H x n i N H x s n = = = + Linear detector: 1 0 2 1 H N i i H x = For AWGN, and si is a constant, it is an optimum detector
9.2 Sign tests Consider k independent measurements under a null hypothesis Ho yi=n,j=1,...k (9.2) And the ones under hypothesis H for the case of a signal present yi=s,+n,j=1,...k (9.3) 5
5 9.2 Sign tests Consider k independent measurements under a null hypothesis H0 , And the ones under hypothesis H1 for the case of a signal present , 1,..., (9.2) j j y n j k = = , 1,..., (9.3) j j j y s n j k = + =