IEEE Geoscience and Remote Sensing Magazine - June 2020 - 59

clutter and a deterministic target with an SCR = 3 dB, single-look coherence magnitude c H0 of 0.98 and PFA = 10 -4
using RDS-2 parameters obtained with the GLRT (29).
The LRT is also shown as reference and can be compared
with the detection performance of BATI displayed in Figure 6, verifying that the amplitude information enables
improved performance.
As far as velocity estimation accuracy is concerned, in
Figure 15, the CRLB for the radial velocity and root-meansquare error of estimate obtained through the maximization
of (29) are compared with that obtained from phase-only
data, in the case of both single- and dual-baseline systems.
As shown in [45], for single-baseline systems, the use of
complex data does not improve the CRLB of the accuracy
of the radial velocity estimation for phase-only approaches.
For dual-baseline (three-channel) ATI systems, the performance of radial velocity estimation based on complex
data is much better than the one achievable using phaseonly data, as depicted in [45].

r

CRLB1/2
v , RMSE (m/s)

25
20

10
5

5

r

CRLB Ampl/Phase
CRLB Phase Only
RMSE Ampl/Phase
RMSE Phase Only

15

0

CRLB1/2
v , RMSE (m/s)

Single Baseline
SCR = 10 dB

Note that the estimation error has an impact on the
target repositioning; for example, a target with a radial
velocity of 14 m/s with TerraSAR-X parameters has a
CRLB 1/2 of 5 m/s with an SCR = 10 dB and so will suffer,
on average, a repositioning error of 410 m. To improve
the reposition, an additional baseline should be added;
in this case, the reposition error is halved, as displayed
in Figure 15(b).
Figure 16 presents the results based on real data from
TerraSAR-X in DRA mode; the targets detected assuming a
PFA equal to 10 -4 are highlighted with cyan squares [27].
Once the target's velocity is estimated, it can be replaced at
its original position (green triangle).
We note that with TerraSAR-X parameters, the azimuth
shift associated with even a low radial velocity value is
large (the shift corresponding to a target moving with
v r = 50 km/h = 14 m/s is in the order of 1.2 km). The road
network is dense in the area, so it is difficult to use the road
map as a priori information for the radial velocity estimation, but knowing where the principal roads are can be
useful to assess the performance. We have highlighted in
yellow the principal road, a highway, which is also easily
visible in the Google Earth image in Figure 17. The majority
of the targets have been positioned along the highway; in
absence of a ground truth, this ensures the reliability of the
detections. The average value of the estimated velocities is
87.5 km/h, and the average shift in azimuth is 2 km, corresponding in this case to a displacement of roughly 1,050
pixels in the TerraSAR-X SAR image.

-40

-20

Dual Baseline
SCR = 10 dB

0
vr (m/s)
(a)

20

40

CRLB Ampl/Phase
RMSE Ampl/Phase
RMSE Phase Only

4
3
2
1
0

-40

-20

0
vr (m/s)
(b)

20

40

az
Range

FIGURE 15. A CRLB 1/2 and root mean square error (RMSE) versus

FIGURE 16. The detected targets (cyan square) and targets

target radial velocity, for phase only and amplitude (Ampl)/
phase approaches, TerraSAR-X parameters, CNR = 10 dB, and
SCR = 10 dB for (a) a single baseline b 2 = 1.2 m and for (b) a dual
baseline (b 2 = 1.2 m and b 3 = 3.1m).

displaced from their original position (green triangle), with the
principal road highlighted in yellow, as shown in [27]. A singlelook, TerraSAR-X amplitude image of an area around Thessaloniki,
Greece. (Source: DLR; used with permission.)

JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - June 2020

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