Probabilistic and Statistical Methods - Information Fusion in Signal and Image Processing - page 84

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 .