IEEE - Aerospace and Electronic Systems - October 2021 - 27

Hennessy et al.
Figure 11.
Detection level IOD for the WISE, propagated 30 s forward. The left subplot shows the Doppler-corrected ODBD estimates, matching
Figure 10. The middle subplot shows the Herrick-Gibbs method. The right subplot shows the Doppler-analytic method.
WISE. Figure 11 shows the results for using the Dopplercorrected
ODBD detection-level estimates, the Herrick-
Gibbs estimates, and also analytically calculating the
orbital velocity from the Doppler, Doppler-rate, and
Doppler-acceleration. For the Doppler analytic method, if
we had taken the ODBD-derived parameters directly, the
resulting orbit would be identical to the left subplot in
Figure 9. Instead, for each detection, a subsequent search
was conducted through all Doppler parameters to determine
those which maximized the detection SNR. These
Doppler parameters were those used to determine the
velocity in the Doppler analytic results in Figure 11.
Figure 11 shows that the Doppler-corrected orbits
compare favorably against other methods. This is because
the IOD estimate is intrinsically incorporating every measurement
parameter, whereas the Herrick-Gibbs is incorporating
three positions and the Doppler analytic method
only uses a position and three Doppler parameters. However,
Figure 11 shows that MWA detections are not necessarily
well suited to these other methods. The detections
are all coplanar; however, the extent of the arc is only
0.41, which will cause issues with the Herrick-Gibbs solutions.
Also, the direct analytic method of [29] is very
dependent on the second derivative of the Doppler, and a
3-s CPI provides insufficient resolution for estimating
this. Further, this estimate will be highly susceptible to
noise, clutter, and signal amplitude changes across
the CPI.
NONCIRCULAR ORBITS
The methods used to form the matched filters in the
" Surveillance Stare " section matched circular orbits in
order to reduce the search space. However, there were a
few interesting examples of slightly eccentric detections.
A Delta 2 rocket body with an eccentricity of 0.01 was
detected, as well as a Pegasus XL rocket body with an
eccentricity of 0.068. While these orbits are still quite circular,
they represent larger eccentricities than the vast
majority of the catalog.
OCTOBER 2021
Figure 12 shows the orbits of the Delta 2 rocket body
predicted out an hour. Because the detection-level orbits
will have an eccentricity of zero, there is now a noticeable
offset between the detection-level predictions and the
truth, although the cross-range error is still quite small.
Unfortunately, as the detections only span a 0.39 arc, the
Herrick-Gibbs predictions do not fare any better; however,
the eccentricities of the Herrick-Gibbs estimates
range from 0.00091 to 0.00116, which are far more
accurate.
The Delta 2 rocket body was detected 11 times,
whereas the Pegasus XL rocket body was only detected
once. Two contributing factors are that the RCS of the
Delta 2 is about 10 times larger than that of the Pegasus
XL, and the Delta 2 orbit is less eccentric.
Figure 13 shows the detected SNR of the Pegasus
XL rocket body with both the circular-uncued search as
well as the track based on apriori truth information.
Not only is the SNR attenuated past its point of closest
approach (as in Figure 8), it will also be attenuated
because the eccentricity is not zero. The measurement
parameters derived for a circular orbit will not match
well with true parameters. The object was also near its
orbital perigee, and so its velocity is considerably larger
than that of an object in a circular orbit. This means
that the bistatic geometry is changing faster than it
would otherwise, and the 0.5-s staggered offset between
Figure 12.
Detection-level IOD for the Delta 2 rocket body, propagated 60
minutes forward.
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IEEE - Aerospace and Electronic Systems - October 2021

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