Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
z2=∗(xc+1) ;
z3=∗(xc+2) ;
V=∗(xc+3) ;
∗( xcdot )=(V−Res∗z1−K1∗ z2 ) /L ;
∗( xcdot +1)=(V∗ z2 /z1−Res∗z2−K1∗ z2∗ z2 / z1 ) /L+(K2∗ z1∗ z1∗z1−B∗z2−..
z3−p∗pow( z2 , 2 . 0 8 ) /pow( z1 , 1 . 0 8 ) ) /J ;
∗( xcdot +2)=(V∗ z3 /z1−Res∗z3−K1∗ z2∗ z3 / z1 ) /L ;
return ; }
C.5 Ornstein-Ulhenbeck Process
C.5 Ornstein-Ulhenbeck Process
The facts compiled in this section are mainly taken from the book [28] and the article [59].
A note from S. Finch ([1]) and the book [100] were also convenient sources of information.
Introductory books on probability and stochastic processes can also be useful (e.g. [29,
49, 81]) 3 .
A stochastic process represents the state of a system that depends both on time and on
random events. It is represented as a collection of random variables indexed by the time. We
denote it {Xt : t ≥ 0}.
Definition 99
− A Brownian motion or Wiener process with variance parameter σ 2 , starting
at 0, is a stochastic process {Bt : t ≥ 0} taking values in R, and having the properties:
1. B0 =0,
2. for any t1