Adaptative high-gain extended Kalman filter and applications
Adaptative high-gain extended Kalman filter and applications
Adaptative high-gain extended Kalman filter and applications
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tel-00559107, version 1 - 24 Jan 2011<br />
Nomenclature<br />
χ a compact subset of the state space<br />
δt<br />
sampling time<br />
˙x(t) the time derivative of the time variable x(t): dx<br />
dt (t)<br />
F adaptation function<br />
Id(t) innovation for a window of length d, at time t (continuous time framework)<br />
Id,k<br />
innovation for a window of length dδt, at epoch k (discrete time framework)<br />
θ, θ(t), θk <strong>high</strong>-<strong>gain</strong> parameter<br />
A ′<br />
transpose of the matrix A<br />
diag(v) a dim(v) × dim(v) matrix, such that (diag(v))i,j = δijvi<br />
L 1 b (Uadm) the set of integrable (thus measurable), bounded functions having their values<br />
in Uadm.<br />
n dimension of the state space<br />
nu<br />
ny<br />
P (t) S −1 (t)<br />
dimension of the input space<br />
dimension of the output space<br />
S(t) Riccati matrix<br />
t time variable<br />
u(t) input space<br />
X a n-dimensional analytic differentiable manifold<br />
x(t) state space<br />
y(t) output space<br />
z(t) estimated state (continuous time framework)<br />
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