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