Aerospace and Electronic Systems - December 2018 - 11

Antoniou et al.

Figure 6.

Figure 5.

Critical orthogonal baseline vs receiver incidence angle and considering
both a single and three DVB-T channels. Simulation parameters listed
in Table 1.

As expected, coherent techniques for resolution improvement
and advanced coherent radar imaging modes can be applied where
the signals gathered by different parts of the distributed system
can be combined coherently. This sets a limit on the maximum allowable separation among the satellites both in along-track and in
cross-track/radial direction [28]. On the other hand, non-coherent
combination can be fruitfully used when multistatic data are collected from extremely different incidence and looking angles [25].
Hence, the joint exploitation of all the introduced imaging modes
and techniques can be performed by a constellation of close satellites formations. Namely, formations provide the system with
multi-static coherent data and constellation with the required multiple acquisition geometry.

FORMATION ANALYSIS AND DESIGN
The formation examined here includes receivers separated in both
the along-track and the cross-track/vertical direction. The alongtrack separation provides the formation with MTI capabilities [40],
and it can also be used to improve the image quality, for example
by improving the signal to noise ratio since this is linearly proportional to the number of receiving antennas. Separation in this
dimension can also improve the azimuth resolution by coherent
combination of shifted Doppler spectra [28]. The cross-track separation, on the other hand, enables range resolution improvements
[27]-[29] and paves the way for single-pass SAR tomography [39].
Constraints are set on maximum allowable satellite separation or
baseline by the introduced coherent SAR techniques. Figure 5
shows the critical baseline orthogonal [28], [39] to the receiver
line of sight, i.e., indicates the inter-satellite separation which leads
to complete loss of coherence. The critical baseline was computed
using the parameters listed in Table 1. The satellite formation is
DECEMBER 2018

Nominal slant range resolution improvement resulting from coherent
combination of data collected by two receivers separated in cross-track
direction. Percentage improvement evaluated with respect to the case of
3 DVB-T; 30° receiver incidence angle assumed.

also, of course, expected to work with shorter baselines than the
critical one, but the low carrier frequencies used in the PASSAT
concept allow longer critical baselines to be established than in
the case of more traditional, shorter wavelength, interferometric
applications [12].
Figure 6 quantifies the slant range resolution improvement
identified above for the case of three DVB-T channels. It is worth
noting that 2-3 km orthogonal separation, i.e., representing less
than 25% critical baseline length, can potentially lead to the same
resolution improvement as the processing on a further DVB-T
channel.
From the orbit dynamics point of view, such a range of usable
baselines justifies the adoption of linearized relative motion model
for formation/trajectory design (and control). Furthermore, besides
ensuring a proper signal acquisition geometry, as stated above,
formation design shall be also aimed at maximizing formation geometry stability, thus minimizing both control efforts and collision
risks. In terms of orbit parameters, a reasonable choice consists
in nullifying the nominal difference in mean semimajor axis and
inclination among the satellite's orbits. Even assuming these constraints, natural relative dynamics offer several possibilities. First
of all, satellites can be separated in along-track direction by imposing very small differences in mean anomaly and/or argument of
perigee. In this case, the baseline is nominally constant, though in
practical cases active formation control has to be used to reduce
the differential drift of different satellites. Instead, relative motion
in radial or cross-track direction (which allows observations under
slightly different angles) is oscillatory by nature, thus generating
acquisition geometries that change along the orbit. In particular,
the vertical oscillation is always coupled with an along-track oscillation so that the trajectory projection in the radial/along-track
plane is a 2 × 1 ellipse. Cross-track oscillation is instead activated

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Aerospace and Electronic Systems - December 2018

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