Aerospace and Electronic Systems Magazine July 2017 - 44
Automatic Target Recognition in Missing Data Case
FIAA output images. SLIM is formulated around a hierarchical Bayesq
2
ian model: y α,η ~ ( Dα,η I ) , f ( α ) ∝ ∏exp − α pr ,l − 1 ,
r ,l
q
and f (η ) ∝ 1. The SLIM algorithm finds estimates of {α,η} by adopting the cost function:
in g ( α,η )
{αˆ ,ηˆ} = arg m
η
α,
(14)
q
and
y − Dα
g q ( α,η ) =
η
2
R L
2
+ α pr ,l
q
r =1 l =1
q
− 1 + MN p logη , (15)
for 0 < q ≤ 1.
To minimize the cost function in (14), the estimates of the reflection coefficients and variance at each iteration are given by
(
αˆ = AD H DAD H + η I
)
−1
(16)
y
and
ηˆ =
Figure 7.
2
1
y − Dαˆ ,
MN p
(17)
2−q
where A = diag (a) and a = αˆ . The matrix inversion in (16)
is calculated via the conjugate-gradient (CG) method [13]. Initial
estimates of {α,η} are given by
αˆ ini = γˆ
(18)
and
ηˆini =
2
1
y − Dγˆ ,
MN p
(19)
where γˆ is the reflection coefficient estimate from (13) of FIAA.
The final wide-angle SAR image is acquired by combining the various subaperture images of each target using a noncoherent maximum magnitude operation. In Figures 5 and 6, we show hybrid
and BP SAR images of civilian vehicles including a sedan, SUV,
and van formed from the full data record, as well as 30% and 50%
missing data rates.
As expected, increasing amounts of
missing data yield severe image degradations, especially in the BP imagery.
However, the hybrid SAR imaging
method is capable of mitigating the deleterious effects of data loss.
Two approximately straight parallel lines marked in red (SAR image
obtained from 30% missing data).
if not compensated. The target pose estimation process uses the
two approximately straight parallel lines (marked in red) shown in
Figure 7. If the lines in Figure 7 are not present, the pose estimation
may fail. These lines correspond to the dihedral reflection formed
between the vehicle's body and the ground. Thus, the highlighted
lines in Figure 7 indicate the orientation of the vehicle.
A hybrid pose estimation method (specifically, a 2-D FFT and
the PST) [12] is applied to estimate the target's orientation from
the SAR images.
The hybrid pose estimation method first computes the 2-D
Fourier transform of the modulus of the SAR image after removing any constant offset from the modulus of the image. The size of
the FFT on each dimension is the nearest power of 2 value greater
than that of the image dimension. The initial pose angle estimate
θˆini is obtained as the slope of a line along which the majority of the
energy in the Fourier domain lies, as shown in Figure 8(a). Mathematically, this estimate can be expressed as
POSE ESTIMATION
Target pose estimation is a significant
preprocessing step prior to target classification. Indeed, the random pose of
targets about the scene of interest will
significantly degrade ATR performance
44
Figure 8.
Hybrid pose estimation process using 2-D FFT + PST (in 30% missing data).
IEEE A&E SYSTEMS MAGAZINE
JULY 2017
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