Noise: a nonstandard analysis.

被引：118
作者：
Fliess, M [1 ]
机构：
[1] Ecole Polytech, CNRS, UMR 7161, Project ALIEN,INRIA Futurs,Equipe MAX,LIX, F-91128 Palaiseau, France
来源：
COMPTES RENDUS MATHEMATIQUE | 2006年 / 342卷 / 10期
关键词：
D O I：
10.1016/j.crma.2006.02.037
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Noise: a nonstandard analysis. Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noise corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of the parametric estimation windows, and for burst errors.
引用
收藏
页码：797 / 802
页数：6
相关论文
共 23 条
[1]  
[Anonymous], QUANTUM FLUCTUATIONS
[2]   Quantum derivatives and the Schrodinger equation [J].
Ben Adda, F ;
Cresson, J .
CHAOS SOLITONS & FRACTALS, 2004, 19 (05) :1323-1334
[3]  
Cartier P., 1995, NONSTANDARD ANAL PRA, P195
[4]  
DIENER F, 1989, ANAL NON STANDARD
[5]  
Fliess M, 2005, LECT NOTES CONTR INF, V322, P217, DOI 10.1007/11529798_14
[6]   Differential compression of noisy transient signals. [J].
Fliess, M ;
Join, C ;
Mboup, M ;
Sira-Ramírez, H .
COMPTES RENDUS MATHEMATIQUE, 2004, 339 (11) :821-826
[7]   State reconstructors. [J].
Fliess, M ;
Sira-Ramírez, H .
COMPTES RENDUS MATHEMATIQUE, 2004, 338 (01) :91-96
[8]   An algebraic framework for linear identification [J].
Fliess, M ;
Sira-Ramírez, H .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2003, 9 (09) :151-168
[9]  
FLIESS M, 2005, REFLEXIONS QUESTION
[10]  
FLIESS M, 20 C GRETSI LOUV LAN
123