39 7 Vol. 39, No ACTA AUTOMATICA SINICA July, ,.,, (Adaptive detector, AD)., (Sample covariance matrix, SCM) (Normalized sample co

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1 39 7 Vol. 39, No ACTA AUTOMATICA SINICA July, ,.,, (Adaptive detector, AD)., (Sample covariance matrix, SCM) (Normalized sample covariance matrix, NSCM), AD-SCM AD-NSCM., AD-NSCM AD-SCM.,. DOI,,,,,,.., 203, 39(7): /SP.J Sparsely Range-spread Target Detector and Performance Assessment WEI Guang-Fen SU Feng 2 JIAN Tao 2 Abstract In the background where the clutter is modeled as a spherically invariant random vector, the adaptive detection of sparsely range-spread targets is addressed. By exploiting the order statistics and the covariance matrix estimators, the adaptive detector (AD) is assessed. Herein, the detectors of AD-SCM and AD-NSCM are proposed based on the sample covariance matrix (SCM) and normalized sample covariance matrix (NSCM), respectively. In terms of constant false alarm rate properties and detection performance, the AD-NSCM outperforms the AD-SCM and the existing detector of modified generalized likelihood ratio. Finally, the performance assessment conducted by simulation confirms the effectiveness of the proposed detectors. Key words Sparsely range-spread target, adaptive detection (AD), sample covariance matrix (SCM), normalized sample covariance matrix (NSCM), order statistics Citation Wei Guang-Fen, Su Feng, Jian Tao. Sparsely range-spread target detector and performance assessment. Acta Automatica Sinica, 203, 39(7): 26 32, []., [2 3],, [4].,,., Manuscript received December 28, 20; accepted August 27, 202 (674007, 60266), (BS200DX022) Supported by National Natural Science Foundation of China (674007, 60266) and the Scientific Research Foundation for Outstanding Young Scientists of Shandong Province (BS200DX022) Recommended by Associate Editor HAN Chong-Zhao School of Information and Electronics, Shandong Institute of Business and Technology, Yantai Research Institute of Information Fusion, Naval Aeronautical and Astronautical University, Yantai 26400,,, [5], (Modified generalized likelihood ratio test, MGLRT), (Constant false alarm rate, CFAR)., [],., [6] ;, [7] [8]., [7 8].,. [9],,,.

2 7 : 27,,,.,,,, ;,, (Adaptive detector, AD),. N, K z t, t =,, K,.,.,. H 0 : z t = c t, H : z t = α t p + c t, t =,, K t =,, K (), p = (, e jφ, e j2φ,, e j(n )φ ) T / N, p H p =, ( ) H, φ, ( ) T, α t, t =,, K. [0],, :,., t N c t c t = τ t η t, t =,, K (2), η t = (η t (), η t (2),, η t (N)) T Σ, τ t η t,, f τ., Σ Σ = E{η t η H t } (3) K,,.,,. h 0, Θ h0., h 0,, []., Θ h0, () H 0 : z t = c t, t Θ h0 (4) H : z t = α t p + c t, t Θ h0 f τ, t, τ t. α t p,, z t f(z t τ t, H 0 ) = t Θ h0 π N τ t Θ t N det(σ) exp[ z H t Σ z t ] (5) τ t h0 f(z t α t, τ t, H ) = π N τ t Θ h0 t Θ t N det(σ) h0 [ exp ] (z t α t p) H Σ (z t α t p) (6) τ t, det( ). 2 Θ h0, ˆΘ h0, Σ. α = {α t t Θ h0 } τ = {τ t t Θ h0 }, (GLRT) [2]. Σ, GLRT,, (Maximum likelihood, ML), : max max f(z t α t, τ t, H ) H τ α t Θ h0 > T 0 (7) max f(z t τ t, H 0 ) < τ t Θ h0 H 0 H α t ML [3] ˆα t = ph Σ z t p H Σ p (8) ˆα t (7), τ t ML : H 0 : ˆτ t = N zh t Σ z t (9) H : ˆτ t = N (z t ˆα t p) H Σ (z t ˆα t p) (0)

3 28 39 (8) (0) (7), GLRT λ = N [ ln t Θ h0 w t = p H Σ z t 2 (z H t Σ z t )(p H Σ p) p H Σ z t 2 (z H t Σ z t )(p H Σ p) ] H > T < H 0 () (2), w t ( Σ p) [4]., (2) p H Σ z t z t [4]. z H t Σ z t p H Σ p,, w t z t,. K,,, w t, t =,, K h 0 ˆΘ h0. Σ, ˆΘ h0,., τ t f τ,, Σ ML [3].. (Sample covariance matrix, SCM), ˆΣ SCM = R R y r y H r (3) r=, y r, r =,, R R. R N, SCM, Hermitian [2].,, (Normalized sample covariance matrix, NSCM), ˆΣ NSCM = R R ( N r= y H r y r ) y r y H r (4) [9],, AD.. SCM NSCM, K ˆΣ, ˆΣ (2), ŵ () t. ŵ () t, t =,, K, : 0 ŵ () () ŵ() (t) ŵ() (K) (5) 2. K h 0 ( ŵ (), t =,, K h (t) 0), Ω h0., K h 0 N., Ω h0, Ω h0, Σ, (SCM NSCM), ˆΣ 2. ˆΣ 2 (2) Σ, w t ŵ (2) (t). ŵ(2) (t), t =,, K, : 0 ŵ (2) () ŵ(2) (t) ŵ(2) (K) (6) h 0 ( ŵ (2), t = K h (t) 0 +,, K), ˆΘ h0. 3. ˆΘ h0 ˆΣ 2 (), AD λ 2 = N N K t=k h 0+ ln( ŵ (2) (t) ) = p H ˆΣ 2 z t 2 ] ˆΣ 2 z t )(ph ˆΣ 2 p) H > T 2 < H 0 ln[ t ˆΘ h0 (z H t (7),,, 2,.,, N [5]. K, (K h 0 ),, (K h 0 ) 2N., (K h 0 )/N,.,, SCM NSCM AD-SCM AD- NSCM. ˆΘ h0 ˆΣ 2,, CFAR,.

4 7 : 29 3 AD- SCM AD-NSCM CFAR, MGLRT [5]. Toeplitz Σ,, γ, m n [Σ] m,n = γ m n, m, n N (8) Γ f τ : ( ) L L b f τ (x) = Γ(L) xl e ( L b )x, x 0 (9), Γ( ) Gamma, b ; L f τ,, L, f τ,. P d P fa.,, h 0,. K, σs 2 σc 2. (t Θ h0 ),, ; E{ α t 2 } = ε t σs 2 K (ε t ). α t 2, t =,, K,.., Model h 0 ; Model 2 4,. Model 5, Model 2 4. (Signal to clutter ratio, SCR) K, SCR = σ2 s p H Σ p (20) σc 2 CFAR, ( b) ( L) ( γ),. [9], MGLRT CFAR, MGLRT., K = 5, h 0 = 3, N = 2, L = 0.,, γ = 0, 0.5, 0.9 b =, 0, 2 AD-SCM AD-NSCM (Detection threshold) (False alarm probability)., AD-SCM,. 2, AD- NSCM CFAR,., AD-NSCM. K = 5, N = 2, L = 0.,, γ = 0, 0.5, 0.9, b =, 0, h 0 = 3, AD-SCM CFAR Fig. CFAR curves of AD-SCM for K = 5, N = 2, L = 0.,, γ = 0, 0.5, 0.9, b =, 0, h 0 = 3 ε t Table Values of ε t for typical scatters models 2 h 0 Model h 0 h 0 h 0 h 0 Model h 0 h 0 h 0 Model h 0 h 0 h 0 Model h 0 h 0 h 0 Model

5 30 39,,,, AD-NSCM. h 0 7,,,,,,,., h 0 < K/2, AD-NSCM. 2 K = 5, N = 2, L = 0.,, γ = 0, 0.5, 0.9, b =, 0, h 0 = 3, AD-NSCM CFAR Fig. 2 CFAR curves of AD-NSCM for K = 5, N = 2, L = 0.,, γ = 0, 0.5, 0.9, b =, 0, h 0 = 3 AD. 3 MGLRT AD-SCM AD-NSCM., AD-NSCM, MGLRT, AD-SCM., MGLRT AD-SCM, AD-NSCM CFAR. AD-NSCM. 4 K = 5, N = 2, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model 5 AD-NSCM Fig. 4 Detectability curves of AD-NSCM for K = 5, N = 2, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model 5 3 K = 5, N = 2, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model, MGLRT, AD-SCM AD-NSCM Fig. 3 Detectability curves of MGLRT, AD-SCM and AD-NSCM for K = 5, N = 2, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model, 5, 4 AD-NSCM.,,., Model.,, 5 AD-NSCM. 5, h 0 < 7, 5 K = 5, N = 2, L =, γ = 0.9, P fa = 0 4, Model, h 0 = 2, 4, 6, 7, 8, 0, 2 AD-NSCM Fig. 5 Detectability curves of AD-NSCM for K = 5, N = 2, L =, γ = 0.9, P fa = 0 4, Model, h 0 = 2, 4, 6, 7, 8, 0, 2, 6 AD- NSCM. 6, L,, AD-NSCM. 7.,, AD-NSCM

6 7 : 3. 8 (N = 2, 4, 6, 8) AD-NSCM., N 4, N, ; N > 4, N,., (R = K h 0 = 2), N,,,., K h 0 3N, AD-NSCM.,, AD-NSCM,., h 0 < K/2, K h 0 3N, AD-NSCM., [9], AD-NSCM, CFAR.,. 6 K = 5, N = 2, γ = 0.9, h 0 = 3, P fa = 0 4, Model, L = 0.5,, 2, 0 AD-NSCM Fig. 6 Detectability curves of AD-NSCM for K = 5, N = 2, γ = 0.9, h 0 = 3, P fa = 0 4, Model, L = 0.5,, 2, 0 8 K = 5, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model, N = 2, 4, 6, 8 AD-NSCM Fig. 8 Detectability curves of AD-NSCM for K = 5, L =, γ = 0.9, h 0 = 3, P fa = 0 4, Model, N = 2, 4, 6, 8 References Zhou Yu, Zhang Lin-Rang, Liu Xin, Liu Nan. Adaptive detection based on Bayesian approach in heterogeneous environments. Acta Automatica Sinica, 20, 37(0): (,,,.., 20, 37(0): ) 2 He Chu, Liu Ming, Feng Qian, Deng Xin-Ping. PolIn- SAR image classification based on compressed sensing and multi-scale pyramid. Acta Automatica Sinica, 20, 37(7): (,,,. SAR., 20, 37(7): ) 7 K = 5, N = 2, L =, h 0 = 3, P fa = 0 4, Model, γ = 0, 0.5, 0.9 AD-NSCM Fig. 7 Detectability curves of AD-NSCM for K = 5, N = 2, L =, h 0 = 3, P fa = 0 4, Model, γ = 0, 0.5, , SCM NSCM, AD-SCM AD- NSCM. CFAR, AD-NSCM AD-SCM MGLRT. 3 Zhu Yi-Long, Fan Hong-Qi, Lu Zai-Qi, Fu Qiang. A radar target maneuver detection algorithm based on the onedimensional high resolution Doppler profile. Acta Automatica Sinica, 20, 37(8): (,,,.., 20, 37(8): 90 94) 4 Jian T, He Y, Su F, Qu C W, Ping D F. High resolution radar target adaptive detector and performance assessment. Journal of Systems Engineering and Electronics, 20, 22(2): Gerlach K, Steiner M J. Adaptive detection of range distributed targets. IEEE Transactions on Signal Processing, 999, 47(7):

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7 Gerlach K. Spatially distributed target detection in non- Gaussian clutter. IEEE Transactions on Aerospace and Electronic Systems, 999, 35(3): Conte E, De Maio A, Ricci G. CFAR detection of distributed targets in non-gaussian disturbance. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(2): Bon N, Khenchaf A, Garello R. GLRT subspace detection for range and Doppler distributed targets. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(2): Jian Tao, Su Feng, He You, Li Bing-Rong, Gu Xue- Feng. Distributed target detection without secondary data. Acta Aeronautica et Astronautica Sinica, 20, 32(8): (,,,,.., 20, 32(8): ) 0 Jian T, He Y, Su F, Qu C W, Gu X F. Performance characterization of two adaptive range-spread target detectors for unwanted signal. In: Proceedings of the 9th International Conference on Signal Processing. Beijing, China: IEEE, Gini F, Bordoni F, Farina A. Multiple radar targets detection by exploiting induced amplitude modulation. IEEE Transactions on Signal Processing, 2004, 52(4): Kay S M. Fundamentals of Statistical Signal Processing, vol. 2: Detection Theory. New York: Prentice-Hall, Kay S M. Fundamentals of Statistical Signal Processing, vol. : Estimation Theory. New York: Prentice-Hall, Kraut S, Scharf L L, McWhorter L T. Adaptive subspace detectors. IEEE Transactions on Signal Processing, 200, 49(): 6 5 Reed I S, Mallett J D, Brennan L E. Rapid convergence rate in adaptive arrays. IEEE Transactions on Aerospace and Electronic Systems, 974, 0(6): , eegingkowei@tom.com (WEI Guang-Fen Ph. D., associate professor at Shandong Institute of Business and Technology. She received her Ph. D. degree from Dalian University of Technology in Her research interest covers theory and technology of sensor detection and signal processing. Corresponding author of this paper.),.. sufengwei@tom.com (SU Feng Ph. D., lecturer at Naval Aeronautical and Astronautical University. His research interest covers radar signal detection and signal processing.),.. iamjiantao@yahoo.com.cn (JIAN Tao Ph. D., lecturer at Naval Aeronautical and Astronautical University. His research interest covers radar signal detection and signal processing.)

* CUSUM EWMA PCA TS79 A DOI /j. issn X Incipient Fault Detection in Papermaking Wa

* CUSUM EWMA PCA TS79 A DOI /j. issn X Incipient Fault Detection in Papermaking Wa 2 *. 20037 2. 50640 CUSUM EWMA PCA TS79 A DOI 0. 980 /j. issn. 0254-508X. 207. 08. 004 Incipient Fault Detection in Papermaking Wastewater Treatment Processes WANG Ling-song MA Pu-fan YE Feng-ying XIONG