“Satellite orbits are developed using many thousands of independent observations by multimillion dollar sensors positioned all over the globe, processed off line using large computers and sophisticated algorithms.”
So I infer it is triangulation to the Nth degree that permits such precision?
Memo to Self: do not let Barack Obama know about this capability, else he will direct GPS satellites to catch speeders all across America and use the revenue from fines to help bankroll the growing welfare state.
Orbits are determined by the method of least squares. The technique was developed by Lagrange and Gauss in the late 18th Century for determination of the orbits of comets and asteroids (and it can be applied to planets as well).
http://en.wikipedia.org/wiki/Least_squares
If you read the wiki article, in the application of non linear least squares, the numerical values of the partial derives are your “model”, gravity, drag, radiation pressure, etc. The problem is that they work soooo well for satellites and well but not quite as well for space craft in grazing orbits. Since the partial derives are the model, the “laws of physics” the problem is to figure out a set of partial derives that work for satellites and grazing orbits. Merely fitting parameters by adding convenient terms is unsatisfactory because the numbers fit a theoretical model, and fudging means abandoning a well accepted and proven model.
Orbit determination is the classical non-linear least squares problem. I actually “taught myself” the method from the book by White, Mueller and Bates on a plane ride from Boston to Anchorage.
http://www.amazon.com/Fundamentals-Astrodynamics-Roger-R-Bate/dp/0486600610
It is really quite easy to apply with modern computers.