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h
11
h
12
h
13
h
21
h
22
h
23
h
31
h
32
h
33
Fig. 8.3
Instability of critical points. Plain line: the measured homography matrix
H
.Dashed
line: the observed homography
H
Equation 8.29 follows by setting (
H
1
A
1
)=(
H
(
t
)
,
,
0) with
t
∈
(0
,
t
1
) chosen small
enough so as to have (
H
(
t
)
,
∈U
0)
. This concludes the proof of part
iii)
and the
proof of the theorem.
8.4
Simulations with Ground Truth
We validated the proposed observer with several simulations. In this section, we
illustrate and discuss two simulations results. We use the known ground truth to
assess the quality of the homography and velocity estimations.
In order to simulate a real experiment, we build a sequence of reference ho-
mographies, starting from an initial homography
H
0
∈
SL
(3). The reference set of
homographies was built using the following formula:
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