Image Processing Reference
In-Depth Information
U are two vectors
2 ,
This calls for the following important comment. If
U = u x u y
u x u y ,
=det U
U ,
and as a result:
=det R
V ,
W k X
+ k V
+ k
det R k ,
R k
R k R k
= r k
r k
sin R k ,
R k
= r k
r k
, R k R
+ k V
R k R
+ k
We now simply have to point out that sin( R k ,
R k )=sin( β k β k ).
This calculation can be applied, not without some difficulties, to the case of a target
and an observer that are maneuvering. We then have the following convergence result
[LEC 99].
Convergence of the iterative methods
Let us assume that the maneuvering times of the target are known, then the deriva-
tive with respect to time
L ( ˆ
) of the Liapunov function L ( ˆ
) is:
L ˆ
X =2 ˆ
G L ˆ
X =
r k β k
β k sin β k
β k .
r k
k =1
G L ( ˆ
) of the likelihood
functional that cannot be equal to zero if all of the β k and β k coincide, i.e. if the model
is perfectly estimated. This analysis can be generalized without difficulty to the case
of multiple sensors and most importantly to multi-leg cases 2 .
As you can see, there is a functional of the gradient vector
This type of calculation can actually easily be applied to the case of a constantly
accelerating target and, more generally, to an observation model of the type tan( β t )=
A t X
B t X
A t X
B t X
where f is a monotonic and continuously
differentiable function. Thus, the non-linearity has a relatively simple structure. This is
and even f ( β t )=
2. A leg is a section of the trajectory over which the target has a uniform rectilinear motion.
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