October 2011
Intermediate to advanced
749 pages
23h 36m
English
Content preview from Optimal Estimation of Dynamic Systems, 2nd Edition
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370 Optimal Estimation of Dynamic Systems
5.4.1.2 Continuous-Time Formulation
The continuous-time formulation is much easier to derive than the discrete-time
system. Consider minimizing the following continuous-time loss function:
J[w(t)] =
1
2
t
N
t
0
[
˜
y(t) −H(t)x(t)]
T
R
−1
(t)[
˜
y(t) −H(t)x(t)]
+w
T
(t)Q
−1
(t)w(t)
dt
+
1
2
[
ˆ
x
f
(t
0
) −x(t
0
)]
T
P
−1
f
(t
0
)[
ˆ
x
f
(t
0
) −x(t
0
)]
(5.208)
subject to the dynamic constraint
d
dt
x(t)=F(t)x(t)+B(t)u(t)+G(t) w(t) (5.209)
Note that for the continuous-time case the loss function in Equation (5.208) becomes
infinite if the measurement and process noises are represented by white noise. How-
ever, since white noise can be formulated as a limiting ...
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