IEEE - Aerospace and Electronic Systems - March 2020 - 71

Image Credit: NASA/JPL-Caltech.

between the narrowband spacecraft signal and the broadband quasar signal.
Consider the experiment shown in Figure 2. Instrumental phase response has been measured at discrete points
across an 8 MHz channel by observing a strong quasar in
1 MHz frequency bins. The smooth curve drawn through the
points is an approximation to the actual phase response. The
horizontal line at zero is the average phase response seen by
the full quasar signal. The triangle at the center frequency is
the phase response seen by the spacecraft signal. As group
delay is derived from phase, the distance of the triangle from
the average quasar line is an error in the final observable.
Local calibration techniques to the level of a tenth of a
degree of phase are not practical.
The current ΔDOR error budget carries a phase dispersion error term of 0.2 for each channel. Ref. [8] provides
formulas for each ΔDOR error source and the current
state-of-the-art estimates of error magnitudes. This phase
error causes a delay error based on the frequency separation of the recorded channels. This frequency separation is
known as the spanned bandwidth. As spanned bandwidth
increases, the resultant delay error decreases. However,
the spectrum allocation for deep space research is limited
to 50 MHz at X-band, so the permitted spanned bandwidth
is limited. A DOR tone subcarrier frequency of about 19
MHz has been in standard use at X-band for many years.
While other error terms have been reduced by state-ofthe-art technologies, the phase dispersion error has now
become the dominant error term in the ΔDOR error budget. Since the spanned bandwidth is limited, another
method must be employed to reduce phase dispersion
error and improve ΔDOR accuracy.

Fewer Doppler and range measurements are needed
to meet the same specified targeting accuracy level.
This reduces the total tracking time needed, which
is an advantage especially for CubeSat class missions that are limited in antenna time and budget.
More accurate navigation targeting for a gravity
assist flyby or to initiate a landing sequence.
Avoiding a late trajectory correction maneuver if an
accurate orbit determination is obtained at an earlier
time.
Another advantage of using PN modulation is to relax
the requirement for a priori knowledge of the trajectory.

Figure 2.

Figure 1.
Error ellipses in the targeting plane for several data combinations
for the Mars Exploration Rover.

MARCH 2020

The method proposed here is to spread the spacecraft
DOR signal by a pseudonoise (PN) code so that the spacecraft spectrum will closely resemble the quasar signal
spectrum. In this case, the ground instrumental phase
response of the two signal types will be nearly the same.
This significantly reduces the phase dispersion error. For
example, using a DOR signal spectrum that is flat over
90% of an 8 MHz bandwidth will reduce the dominant
error term by an order of magnitude. This will reduce the
total measurement error by as much as 40% under favorable conditions [8]. For Mars landings, this would improve
the ΔDOR accuracy from 300 to 215 m in the Mars target
plane. Benefits of higher accuracy ΔDOR to deep space
navigation include the following.

Illustration of phase dispersion error as the difference between the
average quasar phase response and the discrete spacecraft phase
response.

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IEEE - Aerospace and Electronic Systems - March 2020

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