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? 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.



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.

73's

Leland C. Scott
KC8LDO

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.

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.

Good luck.

Leland C. Scott
KC8LDO

--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

On 26/11/2011 02:42, 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? 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.


This is how the SARSATs calculated the position of 121.5MHz and 243 MHz
EPIRBs.

Jeff

Jeff Liebermann wrote:
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.

It should not be difficult to locate the source so accurately that you
could go to that position and hear the transmitter and locate it
using land-based direction finding.

However, this usually is not very practical. The interference comes
from countries with little amateur activity, and who wants to go there
for a fox-hunt (which you maybe cannot start right away, you have
to wait until the interfering transmitter is active again).

And then, what are you going to do once the source has been located?
The local authorities are probably not that interested in getting it
off the air...

On 11/25/2011 6:42 PM, 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?

Yes. Look for papers on the Argos system (that's what they use for
tracking things like buoys, etc.).

Here's some starting points:
3 papers by Levanon, et. al.
1985 Random Error in ARGOS and SARSAT Satellite Positioning Systems
1984 Theoretical Bounds on Random Errors in Satellite Doppler Navigation
1983 Angle-Independent Doppler Velocity Measurement

More recently
2007 Amiri & Mehdipour, "Accurate Doppler Frequency Shift Estimation for
any Satellite Orbit"
2008 Amar & Weiss, "Localization of Narrowband Radio Emitters Based on
Doppler Frequency Shifts"


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.

Actually, you don't even need that. If you think about it, what you are
trying to do is do a sort of curve fit where the unknowns are the 6
orbital elements and the frequency of the transmitter.

Simple techniques (like those you'll find in the Satellite
Experimenter's Handbook and similar works) tend to focus on things like
determining the inflection point of the Doppler curve, which tells you
the point of closest approach, and then relating that to figure out the
orbit (or position of the receiver/transmitter).

before the advent of the computational horsepower, analytical techniques
like this were popular. You could do fixes and orbit determination with
a stopwatch and slide rule.

Much like doing Celestial Navigation using Nautical Almanac and sight
reduction tables vs using a computer.

These days, iterative approaches are more useful, and have the advantage
that you can weight the individual observations by their SNR, for instance.




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.

Yes. It depends on the orbit. Some are more useful than others, i.e.
the classic 4 day repeat frozen orbit only gives you half a dozen
different paths over any given point on the surface.

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.

It's fairly straightforward, and if you think in terms of iterative
solutions, all you really need is a decent goal-seeker/optimizer engine
tied to a orbit simulator. There's a variety of Matlab/Octave packages
out there that do the orbit mechanics, and likewise, there's optimizer
engines.

For that matter, doing the orbital stuff yourself isn't that hard with
matlab/octave/mathematica or even C, BASIC, or PASCAL. Especially if you
don't need gnat's eyelash precision. Take a look at the MIT
OpenCourseWare offering for 16.07 Dynamics Fall 2008 Version 2.0 by
Widnall and Peraire.. Specifically Lectures 15 and 16


T.S. Kelso's SGP from the celestrak.com website is a defacto standard
orbit propagator. There's tons of implementations out there in pretty
much any language you want.




73's

Leland C. Scott
KC8LDO

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