Image Processing Reference

In-Depth Information

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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