Probabilistic and Statistical Methods - Information Fusion in Signal and Image Processing - page 83

- constant gyration rate model ( ω is known):

⎡ ⎤

010 0
000

⎣ ⎦

ω
000 1
0

−

x ( t )= A ( ω ) x + w ( t ) , with: A ( ω )= . [6.41]

ω 00

Finally, in the context of image analysis, the problem of target motion analysis
often leads to considering more complex models such as:
- contour models;
- more complex kinematic equations (rigid body, for example);
- object dilation factors;
- more subtle measurement models (luminance, for example).

We are now going to examine some of the implications of data fusion in the field
of target motion analysis.

6.9.2. Multi-platform target motion analysis

As we have just seen, there are many advantages to considering target motion
analysis problems from the multi-platform perspective. We will see, in particular, that
the performances can be decently estimated. However, in what follows, we will always
assume that there is only one target. In other words, multi-target and multi-sensor
association problems will not be considered at all in this section. The following results
have been obtained [TRE 96]:

var( r x )= 3 σ 2 r 4 tan 2 ( θ )

(2 n +1)( m (2 m +1)( m +1) d 2 ,
var( r y )= 3 σ 2 r 4

(2 n +1)( m (2 m +1)( m +1) d 2 ,
var( v x )= 45 σ 2 r 4 sin 2 ( θ )

n ( n +1)(2 n +1)(2 m +1)[5 m ( m +1) d 2 cos 2 ( θ )+(2 n − 1)(2 n +3) v 2 sin 2 ( θ − γ )] ,
var( v y )= 45 σ 2 r 4 cos 2 ( θ )

n ( n +1)(2 n +1)(2 m +1)[5 m ( m +1) d 2 cos 2 ( θ )+(2 n − 1)(2 n +3) v 2 sin 2 ( θ − γ )] .

The parameters in these equations have the following meaning:
⎧
⎨

θ : target's azimuth,
γ : target's bearing, with the North as reference,
v : modulus of the target's speed, r : distance,
m : number of platforms, n : integration time ,
d : inter-platform distance, σ 2 : estimated noise variance .

[6.42]

⎩