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According to deterministic character and geometric property of chaotic system, the predictive method of neighborhood selection and the approach of neighborhood selection based on Delaunay triangulation were presented, and a new orthogonal local projective algorithm was derived by improvement of local projective method for noise reduction in chaotic time series, and rules of selection of optimal parameters were suggested. The method was successfully applied to extract weak signals in Lorenz chaos， that provided signal to noise ratio not lower than -80 dB. Computer simulation shows that this projective filtering method has great stability and reliability, and is effective for extracting weak signals in chaos.
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Keywords:
- extraction of signals /
- orthogonal local projection /
- chaos /
- parameters optimization
[1] ［1］Stark J, Arumugaw B 1992 International Journal of Bifurcation and Chaos 2 413
[2] ［2］Haykin S, Li X B 1995 Proceeding of IEEE 83 94
[3] ［3］Leung Henry, Huang X P 1995 ICASSP 2 1344
[4] ［4］Short K M 1994 International Journal of Bifurcation and Chaos 4 959
[5] ［5］Huang X G, Xu J X 2001 International Journal of Bifurcation and Chaos 11 561
[6] ［6］Wang G G, Wang S X 2006 Journal of Jilin University (Science Edition) 44 439 (in Chinese) ［王国光、王树勋 2006 吉林大学学报（理学版） 44 439］
[7] ［7］Wang G G, Wang S X 2006 Journal of Jilin University (Engineering and Technology Edition) 36 422 (in Chinese) ［王国光、王树勋 2006 吉林大学学报（工学版） 36 422］
[8] ［8］Tim Sauer 1992 Physic D 58 193
[9] ［9］Robert Cawley 1992 Phys. Rev. A 46 3057
[10] ］Kern A, Blank D, Stoop R 2000 Int. J. Mod. Phys. C 11 125
[11] ］Mera M E, Moran M 2006 Chaos 16 013116
[12] ］Grassberger P, Hegger R, Kantz H, Schaffrath C, Schreiber T 1993 Chaos 3 127
[13] ］Takens F 1981 Lecture Notes in Math. (New York:SpringerVerlag) 1 898
[14] ］Allie S, Mees A, Judd K, Watson D 1997 Phys. Rev. E 55 87
[15] ］Broomhead D J, King G P 1986 Physica D 20 217
[16] ］Buzug T, Pflister G 1992 Physica D 58 127
[17] ］Fraser A M, Swinney H 1986 Physical Review A 33 1134
[18] ］Kugiurmtzis D 1996 Physica D 95 13
[19] ］Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[20] ］Kennel M B, Brown R, Abarbanel H D I 1992 Physical Review A 45 3403
[21] ］Gibson John F, Doyne Farmer J, Casdagli Martin，Eubank Stephen 1992 Physica D 57 1
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[1] ［1］Stark J, Arumugaw B 1992 International Journal of Bifurcation and Chaos 2 413
[2] ［2］Haykin S, Li X B 1995 Proceeding of IEEE 83 94
[3] ［3］Leung Henry, Huang X P 1995 ICASSP 2 1344
[4] ［4］Short K M 1994 International Journal of Bifurcation and Chaos 4 959
[5] ［5］Huang X G, Xu J X 2001 International Journal of Bifurcation and Chaos 11 561
[6] ［6］Wang G G, Wang S X 2006 Journal of Jilin University (Science Edition) 44 439 (in Chinese) ［王国光、王树勋 2006 吉林大学学报（理学版） 44 439］
[7] ［7］Wang G G, Wang S X 2006 Journal of Jilin University (Engineering and Technology Edition) 36 422 (in Chinese) ［王国光、王树勋 2006 吉林大学学报（工学版） 36 422］
[8] ［8］Tim Sauer 1992 Physic D 58 193
[9] ［9］Robert Cawley 1992 Phys. Rev. A 46 3057
[10] ］Kern A, Blank D, Stoop R 2000 Int. J. Mod. Phys. C 11 125
[11] ］Mera M E, Moran M 2006 Chaos 16 013116
[12] ］Grassberger P, Hegger R, Kantz H, Schaffrath C, Schreiber T 1993 Chaos 3 127
[13] ］Takens F 1981 Lecture Notes in Math. (New York:SpringerVerlag) 1 898
[14] ］Allie S, Mees A, Judd K, Watson D 1997 Phys. Rev. E 55 87
[15] ］Broomhead D J, King G P 1986 Physica D 20 217
[16] ］Buzug T, Pflister G 1992 Physica D 58 127
[17] ］Fraser A M, Swinney H 1986 Physical Review A 33 1134
[18] ］Kugiurmtzis D 1996 Physica D 95 13
[19] ］Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[20] ］Kennel M B, Brown R, Abarbanel H D I 1992 Physical Review A 45 3403
[21] ］Gibson John F, Doyne Farmer J, Casdagli Martin，Eubank Stephen 1992 Physica D 57 1
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