Graphics Programs Reference
In-Depth Information
Swerling I targets have constant amplitude over one antenna scan; however,
a Swerling I target amplitude varies independently from scan to scan according
to a Chi-square probability density function with two degrees of freedom. The
amplitude of Swerling II targets fluctuates independently from pulse to pulse
according to a Chi-square probability density function with two degrees of
freedom. Target fluctuation associated with a Swerling III model is similar to
Swerling I, except in this case the target power fluctuates independently from
pulse to pulse according to a Chi-square probability density function with four
degrees of freedom. Finally, the fluctuation of Swerling IV targets is from
pulse to pulse according to a Chi-square probability density function with four
degrees of freedom. Swerling showed that the statistics associated with Swer-
ling I and II models apply to targets consisting of many small scatterers of
comparable RCS values, while the statistics associated with Swerling III and
IV models apply to targets consisting of one large RCS scatterer and many
small equal RCS scatterers. Non-coherent integration can be applied to all four
Swerling models; however, coherent integration cannot be used when the tar-
get fluctuation is either Swerling II or Swerling IV. This is because the target
amplitude decorrelates from pulse to pulse (fast fluctuation) for Swerling II
and IV models, and thus phase coherency cannot be maintained.
The Chi-square
pdf
with
2
N
degrees of freedom can be written as
N
N
N
σ
σ
1
N
σ
σ
------------------------
---
------
f
()
=
exp
-------
(2.52)
(
N
1
)! σ
where is the average RCS value. Using this equation, the
pdf
associated with
Swerling I and II targets can be obtained by letting
σ
N
=
1
, which yields a
Rayleigh
pdf
. More precisely,
f
()
1
σ
---
=
---
exp
σ 0
≥
(2.53)
Letting
N
=
2
yields the
pdf
for Swerling III and IV type targets,
f
()
4σ
σ
2
2σ
σ
------
=
exp
------
σ 0
≥
(2.54)
The probability of detection for a fluctuating target is computed in a similar
fashion to Eq. (2.23), except in this case is replaced by the conditional
pdf
. Performing the analysis for the general case (i.e., using Eq. (2.47))
f
()
f r
σ
(
⁄
)
yields
σ
2
ψ
2
2
n
P
z
σ
2
ψ
2
(
n
P
1
)
⁄
2
2
z
n
P
σ
2
1
---
n
P
----------------------
------
------
f z
σ
(
⁄
)
=
exp
z
I
n
P
(2.55)
1
ψ
2
⁄
Search WWH ::
Custom Search