IEEE Geoscience and Remote Sensing Magazine - June 2020 - 54

d offers insight into the detection gain provided by BATI
versus ATI. Figure 6 depicts the PD of a deterministic target
with an SCR = 3 dB single-look and a coherence magnitude
c H0 of 0.98 for four different values of d.
Figure 7 shows an SAR image collected 24 June 1997
with the four-channel airborne experimental SAR-GMTI
system Airborne Experimental Radar (AER)-II of Forschungsgesellschaft fur Angewandte Naturwissenschaften
MEASURING THE PHASE
(FGAN) [now Fraunhofer InDIFFERENCE BETWEEN
stitut fur HochfrequenztechTHE SAME PIXELS IN
nik und Radar (FHR)] [43]. It
THE SAR IMAGE AFTER
is known from ground truth
COREGISTRATION YIELDS
that a convoy of eight veTHE ATI PHASE ESTIMATE.
hicles of different sizes was
moving along a dirt track in
the center of the image. The
PFA = 10 -5 was chosen sufficiently small enough to avoid any false alarm by either
metric. Red crosses mark detections by the BATI, while no
detections were found by ATI. Experimentally confirming
the theoretical results, e.g., Figure 6, ATI fails to declare
any pixel as belonging to a target, whereas BATI succeeds
in finding all eight vehicles.
In conclusion, target detection using BATI is superior to
that of ATI under all circumstances and outperforms classical techniques such as DPCA (see the "Velocity Estimation
From Phase-Only Data" section), especially in a nonhomogeneous textured background. Values of d ranging from one
to roughly six have yielded good results in most circumstances, but the estimation of an optimum parameter with
regard to clutter properties and power levels, particularly
for space-based SAR data, is still an open task.

VELOCITY ESTIMATION FROM PHASE-ONLY DATA
Although adding constant d is beneficial for detecting a
target in virtually all cases, this is generally not the case
when determining the target's velocity, i.e., estimating the
true underlying ATI phase value. This is due to the incorporated bias toward the clutter (zero phase) when a real
valued constant is added to the target phase contribution.
Hence, for the estimation of radial velocity, the original
ATI phase is used.
Measuring the phase difference between the same pixels
in the SAR image after coregistration yields the ATI phase
estimate zt = arg (Z 1 Z 2) ). Figure 8 shows the estimated ATI
phase for each image pixel superimposed as color onto an
AER-II SAR image of the Rhine River in Germany. Green
depicts zero phase and, as expected, can be observed over
stationary land, while the vessels in blue clearly indicate
motion. Characteristically, the rainbow colors of the wakes
reveal various velocity components and appear displaced
compared to the ships due to the difference in radial velocity. Some cars traveling on the south shore road are also
visibly displaced onto the water.
The inclusion of clutter and noise compromises the accuracy of the estimated ATI phase value. In fact, the estimates can be biased and show statistical fluctuations dependent on the signal-to-clutter plus noise ratio (SCNR) as
well as true underlying radial velocity of the target, e.g., see
pdf simulations in Figure 4 and [22]. To gain deeper insight
into the functional dependencies and best possible estimation accuracy, the CRLB may be analyzed [44]. The variance
of any unbiased estimator for a given signal model is larger
or equal to that of the CRLB. For mathematical simplicity,
let us focus on homogeneous Gaussian clutter (heterogeneous clutter follows the same characteristics) and on a
deterministic target with unknown, complex-valued reflectivity ; A ; e jz A. The target phase vector contains, as a third
unknown parameter, the interferometric phase z 2. Denoting SCNR =; A ; 2 / (v 2C + v 2W ), the upper-left element of the

Range (m)

1,850
1,900
1,950
2,000

40
0
1,

35
0
1,

30
0
1,

25
0
1,

20
0
1,

15
0

10
0

2,050

Azimuth (m)
FIGURE 8. A color-coded ATI phase superimposed onto an SAR
FIGURE 7. Experimental BATI (and ATI) detections for L = 1 and

d = 4.
54

intensity image collected by AER II. (Source: J. Ender/FHR; used
with permission.)
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2020