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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 />

xxix

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