Image Processing Reference
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We can now see the influence of the various parameters. It is, however, preferable
to give a more physical interpretation of the results given in equation [6.42]. We thus
define the quantities
T bas as follows 3 :
A bas =2 md cos( θ ) ,
T bas =(2 n +1) v sin( θ
A bas
and
γ ) ,
we make the following approximations:
1
4 A bas 2
m ( m +1) d 2 cos 2 θ
1)(2 n +3) v 2 sin 2 ( θ
T bas 2 ,
(2 n
γ )
and in the end we get:
12 σ 2 r 4 sin 2 ( θ )
(2 n + 1)(2 m +1)
var( r x )=
A bas 2 ,
12 σ 2 r 4 cos 2 ( θ )
(2 n + 1)(2 m +1)
var( r y )=
T bas 2 ,
180 σ 2 r 4 sin 2 ( θ )
n ( n + 1)(2 n + 1)(2 m +1) 5
var( v x )=
T bas 2
,
A bas 2 +4
180 σ 2 r 4 cos 2 ( θ )
n ( n + 1)(2 n + 1)(2 m +1) 5
var( v y )=
T bas 2
.
A bas 2 +4
With these approximations, we have a good idea of the influence the various
parameters have on multi-platform target motion analysis systems. See [LEC 99] for
a more comprehensive presentation.
6.9.3. Target motion analysis by fusion of active and passive measurements
Again, we will restrict ourselves to the case of a single target, in uniform rectilinear
motion.
We have at our disposal passive measurements at every instant β ( t )=
tan 1 [ r x ( t ) /r y ( t )] and at the transmission times, for example, for the radar or
the active sonar, the measurements r ( t )= r x ( t )+ r y ( t )] 1 / 2 . Of course, these
measurements are affected by noise that we will assume to be an independent,
3.
A bas for array baseline and
T bas for target baseline .

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