On 11/25/2011 9:21 PM, Jeff Liebermann wrote:
On Fri, 25 Nov 2011 21:42:39 -0500, "Leland C. Scott"
wrote:

From time to time I've read about some interference, or deliberate jamming,
of an amateur satellite.

My question is has anybody written a nice paper where using known orbital
elements of the satellite and Doppler Shift to calculate a curve on the
earth's surface where the source maybe located?

Sorta. That's how the Transit (NAVSAT) satellite navigation system
worked, but backwards. In the Transit system, the ground station
measured the doppler shift from the satellites. In your case, you'll
need to measure the doppler shift of the ground station from the
satellite. That's going to be difficult because your ground station
will have both the ground to satellite doppler, and the satellite to
your receiver doppler to deal with simultaneously. Since both the
postion of the satellite and your station is known, the 2nd doppler
shift can be calculated. Note that the only part of the "S" curve
that's really important is where the satellite passes overhead. A
highly elliptical orbit will make that somewhat tricky.


Actually, you really need to see as much of the curve as possible.
Sure, just knowing point of closes approach (center of the S) is
commonly used in navigation solutions, but seeing the whole curve lets
you take out more of the unknowns.

One assumption is that the frequency of the oscillator is "reasonably"
stable over the observation time (100-1000 seconds for most LEO) so that
the frequency measurements have low variance, and that the drift is
small. Crummy RC oscillator with tons of phase noise wouldn't help.




The math to recover the first doppler shift involves an exercise in 3D
spherical geometry, which is non-trivial. I'm not even sure I could
still do the math. Sorry no software handy:
http://en.wikipedia.org/wiki/Transit_(satellite)
http://www.jhuapl.edu/techdigest/td/td1901/
http://www.prc68.com/I/MX4102.shtml

I would think any issue with
the satellite's transponder's frequency conversation, due to local
oscillator frequency drift, can be corrected for by calibrating the link
between two or more known stations. This I'm assuming would likely only work
for linear transponders.

Correct. The "bent pipe" satellite transponder is the only one that
will pass the uplink doppler shift. It won't work with a
demodulate-remodulate repeater.




Since the satellites are in highly elliptical orbits the Doppler Shift would
be different over several orbits. Then using multiple orbits these curves I
think would tend to intersect, or nearly so, at one point. Additionally the
time of signal acquisition and loss can be timed and compared to the
projected ground foot print of the satellite coverage zone to help zero in
on the source location.

Yep, except that from 100 miles up, the "cocked hat" pattern formed by
the lines of position is going to be rather large. I don't have a
feel for the expected accuracy, but I'll guess(tm) that you'll be
lucky if you can locate anything within a mile radius.


160km is VERY low for an orbit (that's Phoebus-Grunt kind of territory)
ISS is low (350-400 km) and has significant effects from drag. Most
LEO are at 600km and above.

Locating to within a mile should be straightforward. ARGOS regularly
gives positions of wildlife trackers and such to about 500m kinds of
accuracy.




Good luck.

Leland C. Scott
KC8LDO