IEEE Geoscience and Remote Sensing Magazine - June 2020 - 56

24.48
16.32
8.16
0
-8.16
-16.32
-24.48

6,750
6,800
Azimuth Sample

6,850
6,900
6,950
7,000

(m/s)

Large ocean-going vessels have strong returns in relation
to the weak reflections from the relatively smooth water surface, especially in lower sea states or in far range. By analyzing
hundreds of vessels, it was confirmed that a commonly low
CNR together with a generally large SNR permits vessel estimation standard deviations on the order of fewer than two
knots [47]. Furthermore, low correlation was found between
the size as well as the heading of the ship and the radial velocity estimation error, which implies that, for any detected vessel, one can estimate its radial speed reasonably well.
For land vehicles, extended experimental benchmark
tests using RDS-2 have been conducted over the last decade,
whereby GPS-equipped vehicles as ground truth as well
as many targets of opportunity were analyzed to confirm
the theoretically predicted performance. Figure 11 presents
the results of one of these benchmark trials from the fall
of 2010. The circles indicate three different convoys with
a total of 16 GPS-equipped control vehicles, and the dots
represent targets of opportunity.
As discussed previously, the velocity estimation error
accuracy (and with it the accuracy of the relocation error)

7,050
7,100
7,150
7,200
1,450

1,500
1,550
Range Sample

1,600

greatly depends on the size (strength) of the targets as well
as their individual velocities. The positioning error of a
large assembly of similar vehicles, however, illustrates that
the expected accuracy was achieved. The velocity estimation error of these cars is on the order of a few meters per
second, and the relocation accuracy is on the order of a few
hundred meters. In this way, for instance, the theoretical
prediction has confirmed that RDS-2 is capable of detecting a midsize car with 90% probability when traveling with
a 40-km/h radial velocity in a semiurban area for a false
alarm rate of PFA = 10 -6 [24].
AMPLITUDE AND PHASE METHODS
Many techniques that employ ATI data use both the amplitude and phase of the acquired images. This choice leads to
the following advantages.
◗ The joint statistical distribution of the complex data
can be easily written in closed form for any value of the
number N of the interferometric channels when clutter
and noise are assumed Gaussian.
◗ The detection performance can be improved, exploiting
additional amplitude information.
◗ Twice as much data is being used compared to that of the
phase-only case, because the amplitude of the acquired
data also contains information on the velocity (see Figure 3), and as a result the velocity estimation can be improved. Note, however, that, in this case, the number of
parameters to be estimated increases. In addition to the
target velocity, the target complex amplitude response
and two additional parameters must be estimated. For
this reason, an improvement in velocity estimation accuracy can be obtained only for N 2 2 [45].
One of the best known examples of the use of amplitude
and phase is based on the concept of Displaced Phase Center Antenna (DPCA), whose test metric T results from the
difference of the complex pixels, namely,
L

FIGURE 10. A relocated commercial vessel in an RDS-2 SAR image.

17.34
8.67
0
-8.67
-17.34
-26

2.01
4.02
6.04
8.05

(m/s)

Colors code the average estimated radial velocity.

10.06
12.07
14.08

13
1.
6
1.
06
0.
53

16.1

FIGURE 11. The detected and relocated moving targets in an RDS-2
image of an area near Ottawa. Colors code the slant-range velocity.

1
T = L / Z 1 ^ k h - Z 2 ^ k h 2.
K=1

(25)

It was established that, in a two-channel system, DPCA
is the optimum. It especially outperforms ATI for homogeneous clutter, that is, under the Gaussian assumption
[41]. However, this reverses when the clutter is heterogeneous; for instance, the SAR image contains various image
features or textures. In contrast to ATI, the multiplicative
texture random variable T in (19) does not cancel out and
has a strong impact on the detection performance of T,
particularly in strong, heterogeneous background clutter.
The statistics of T were analyzed in [48] when T follows
an inverse chi-square distribution. Compared to other
choices, e.g., the chi-square distribution, which leads to
the classical K-distribution for the DPCA detector, the
inverse chi-square permits even longer tails of the pdf
(severs nonhomogeneity) and leads to a simple analytical expression for the pdf involving only elementary functions [26]. For instance, for a given false alarm rate and
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

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