29 1 2012 1 : 1000 8152(2012)01 0079 06 Control Theory & Applications Vol. 29 No. 1 Jan. 2012 Dezert-Smarandache 1,2, 2,3, 2 (1., 102249; 2., 264001; 3., 410073) :, Dezert-Smarandache (DSmT),. DSmT 3 :.,, DSm.. : D-S ; Dezert-Smarandache ; ; : TP273 : A Recursive target identification fusion methods based on Dezert-Smarandache theory HU Li-fang 1,2, GUAN Xin 2,3, HE You 2 (1. Navy Armament Academy, Beijing 102249, China; 2. Research Institute of Information Fusion, Naval Aeronautical and Astronautical University, Yantai Shandong 264001, China; 3. The Institute of Electronic Science and Engineering, National University of Defense Technology, Changsha Hunan 410073, China) Abstract: Target identification is a major practical application of information fusion, in which Dezert-Smarandache theory (DSmT) is a useful method for dealing with problems with uncertainties and is efficient in combining conflicting evidences. We put forward three temporal-spatial information fusion approaches including the centralized fusion approach, the distributed approach without-feedback and the distributed approach with-feedback. Especially, when integrity constraints are introduced to the system, it is necessary to employ the conflict distance parameter to determine the combination order of evidences. This will in some extent overcome the deficiency in noncommitative property in the hybrid DSm rule of combination. Numerical examples are provided to show the validity in applications of the proposed approach. Key words: Dempster-Shafer evidence theory; Dezert-Smarandache theory; target identification; information fusion 1 (Introduction),,, [1-2],,. [1-2],,.,.,.,,,,.,, Bayes D-S Dezert-Smarandache theory(dsmt) [3 5],. DSmT D-S, D-S. DSmT,,,, DSmT D-S. : 2010 07 06; : 2011 05 24. : (61032001); (60572161, 60972160); (200443).
80 29 DSmT. DSmT, DSmT, [6 9]. DSmT DSmT DSmT,,., DSmT DSmT,, DSmT. 2 DSmT (Basic theory of DSmT), DSmT, [3]. 1) DSmT. 1 U k(k 2) ( ) ( ), m M f (U)( ) = [m 1 m k ]( ) k m M (U)(A) = m f i (X i ), (1) X 1,,X k D U (X 1 X k )=A m M f (U)(φ) = 0,. DSmT. 2) DSmT., DSmT, DSmT M(U) (M(U) M f (U)) DSmT. k(k 2) DSmT DSmT. 2 DSmT M(U), k (k 2), m M(U) (A) = ϕ(a) [S 1 (A) + S 2 (A) + S 3 (A)], (2) S 1 (A) m M f (U)(A) = S 2 (A) = S 3 (A) = X 1,X 2,,X k D U X 1 X 2 X k =A k m i (X i ), (3) X 1,X 2,,X k φ [u(x 1 ) u(x k )=A] [(u(x 1 ) u(x k ) φ) (A=I t )] X 1,X 2,,X k D U (X 1 X 2 X k )=A X 1 X 2 X k φ k m i (X i ), (4) k m i (X i ). (5) k DSmT : Step 1 DSmT M f (U) k DSmT, A D U, S 1 (A) m M f (U)(A).. DSmT,, DSmT DSmT. Step 2 (2) DSmT., Step 2. DSmT M(U) A = M ϕ, ϕ(a) = 0, S 1 (A), S 2 (A) S 3 (A), ϕ(a)[s 1 (A)+S 2 (A)+S 3 (A)]=0,. A M ϕ, ϕ(a) = 1, S 1 (A), S 2 (A) S 3 (A), m M(U) (A). DSmT,. Step 2,,. 3 DSmT (Block scheme of fusion processes based on DSmT) DSmT DSmT,, DSmT M(U), DSmT DSmT,, 1. 1 DSmT Fig. 1 Block scheme of fusion processes based on DSmT DSmT,, (2) Step 2, : N
1 : Dezert-Smarandache 81, DSmT N,, DSmT N ; N,. DSmT N 1,, DSmT N 1,. N, DSmT N,, DSmT N. 4 (Recursive target identification data fusion) N ( U), n, D U.,. DSmT,.. : N,, 2, k 1 m(k 1) k N k. N,,.,,.,,. ( 3) ( 4)., m i (k 1) m i (k), N m i (k) (i = 1, 2,, N).,,., m(k 1), N, m(k).,,,,. 2 Fig. 2 Block scheme of centralized and recursive target identification data fusion 3 Fig. 3 Block scheme of recursive and distributed-without-feedback target identification data fusion
82 29 4 Fig. 4 Block scheme of recursive and distributed-with-feedback target identification data fusion 5 (Definition of combination order of evidences) DSmT DSmT, DSmT,.,.,,,, DSmT,.,. 3 n S 1,, S n U m 1,, m n, G U G U D. m i m j Jousselme [10], d conflict (m i, m j ) = 1 2 (m i m j )D(m i m j ) T, (6) : G U, G U = U ; G U = 2 U DST [2] ; G U = D U DSmT [3] ; G U = S U UFT(unification of fusion theories) [4]. n = 2, (6). D G U, G U. A i B j A D(A, B) = i B j, A i, B j 2 U, C M (A i B j ) C M (A i B j ), A i, B j D U, (7) : A DST A, C M (A) DSmT Venn A, D U A DSmT, ( DSmT DSmT ) [3]. 4 R = {1,, n}, i m i conf(i, R) = 1 n d conflict (m i, m j ). (8) n 1 j=1 j i G U 2 U,, [11]. 6 (Practical cases) 1 θ 1, θ 2, θ 3, U = {θ 1, θ 2, θ 3 }. (ESM) (IR) (EO) 3, 1. θ 1 θ 2 θ 3 =φ, D U = 2 U. D S, : m({θ 1 }) = 0.3576, m({θ 2 }) = 0.564, m({θ 3 }) = 0.0785.
1 : Dezert-Smarandache 83, θ 1, 1 θ 2,, θ 1., D-S. 2. 1 3 Table 1 GBPAs determined by three sensors θ 1 θ 2 θ 3 ESM(m 1 ) 0.003 0.97 0.027 IR(m 2 ) 0.82 0.08 0.1 EO(m 3 ) 0.8 0.04 0.16 2 DSmT Table 2 Fusion results obtained using DSmT and different fusion orders θ 1 θ 2 θ 3 θ 1 θ 2 θ 1 θ 3 θ 2 θ 3 θ 1 θ 2 θ 3 123 0.6564 0.0389 0.0199 0.0622 0.0026 0.0125 0.2075 132 0.6565 0.0777 0.0183 0.0320 0.0038 0.0042 0.2075 231 0.0029 0.1133 0.0066 0.6363 0.0178 0.0156 0.2075 3, : conf(1, R)= 0.8635, conf(2, R) = 0.4544, conf(3, R) = 0.462., m 1, m 3 m 2., : m 1 m 3, m 2. 2,,. 2 θ 1, θ 2, θ 3, U = {θ 1, θ 2, θ 3 }. ESM, IR EO 3, 3. θ 1 θ 2 θ 3 = ϕ, D U = 2 U. 3 3 3 Table 3 GBPAs of three sensors under three different cycles ESM(m 1 ) IR(m 2 ) EO(m 3 ) θ1 θ 2 θ 2 θ 3 θ 1 θ 2 θ 2 θ 3 θ 1 θ 2 θ 2 θ 3 1 0.6 0.1 0.3 0.9056 0.0943 0 0.6762 0.0966 0.2272 2 0.7 0.011 0.289 0.0166 0.2651 0.7184 0 0.0106 0.9894 3 0.61 0.09 0.3 0.7 0.2121 0.0879 0.67 0.0966 0.2314 4 5. 3, 3 1, 2 3., : 1 2, 3. 3, m 2, m 3 m 1. : m 2 m 3, m 1. 4 3 Table 4 Values of conflict measure coefficient of three sensors fused in time-domain 1 2 3 conf(1, R) 0.0538 0.0925 0.0488 conf(2, R) 0.5233 0.7625 0.4319 conf(3, R) 0.3531 0.6969 0.3500 5 3 Table 5 Values of conflict measure coefficient of three sensors fused in space-domain conf(1, R) conf(2, R) conf(3, R) 0.1201 0.1746 0.1388, θ 1,, θ 1. D- S [1] [1]. 6,,.
84 29 6 Table 6 Different fusion results D-S DSmT θ 1 0 0 0.546 0.6734 θ 2 1 1 0.1375 0.0908 θ 3 0 0 0 0 θ 1 θ 2 0 0 0.1834 0.2152 θ 1 θ 3 0 0 0 0 θ 2 θ 3 0 0 0.029 0.0011 θ 1 θ 2 θ 3 0 0 0.104 0.0194 7 (Conclusion) DSmT, DSmT,., DSmT.,,.,,,,. (References): [1],,. [M]. 2. :, 2007. (HE You, WANG Guohong, GUAN Xin. Multisensor Information Fusion With Applications[M]. 2nd edition. Beijing: Publishing House of Electronics Industry, 2007.) [2],,. [M]. :, 2010. (HE You, WANG Guohong, GUAN Xin. Information Fusion Theory with Applications[M]. Beijing: Publishing House of Electronics Industry, 2010.) [3] DEZERT J, SMARANDACHE F. Advances and Applications of DSmT for Information Fusion[M]. Rehoboth: American Research Press, 2004, Vol 1. [4] DEZERT J, SMARANDACHE F. Advances and Applications of DSmT for Information Fusion[M]. Rehoboth: American Research Press, 2006, Vol 2. [5] DEZERT J, SMARANDACHE F. Advances and Applications of DSmT for Information Fusion[M]. Rehoboth: American Research Press, 2009, Vol 3. [6],,. DSmT [J]., 2006: 31(7): 53 56. (HOU Jun, MIAO Zhuang, PAN Quan. Target recognition a method of sequential images based on the weight-dsmt[j]. Fire Control and Command Control, 2006, 31(7): 53 56.) [7],,,. DSmT [J]., 2005: 25(9): 2044 2046. (MIAO Zhuang, CHEN Yongmei, LIANG Yan, et al. Improved Dezert-Smarandache theory and its application in target recognition[j]. Computer Applications, 2005, 25(9): 2044 2046.) [8]. [D]. :, 2007. (LI Xinde. Research on fusion method of imperfect information from multi-source and its application[d]. Wuhan: Huazhong University of Science and Technology, 2007.) [9] JOUSSELME A, GRENIER D, BOSSE E. A new distance between two bodies of evidence[j]. Information Fusion, 2001, 2(1): 91 101. [10] MARTIN A, JOUSSELME A, OSSWALD C. Conflict measure for the discounting operation on belief functions[c] //The 11th International Conference on Information Fusion. Piscataway, NJ: IEEE, 2008: 10.1109/ICIF.2008.4632320. : (1983 ),,,, E-mail: hlf1983622@163.com; (1978 ),,,, ; (1956 ),,,,,,.