TLE's from observations

Bruno Tilgner (100533.2016@CompuServe.COM)
03 Dec 96 18:15:03 EST

On 1 December Alphonse Pouplier wrote:

>Hi all!

>There are a lot of programs giving previsions and using TLEs.
>But does a program exist which would give the TLEs using
>observations?

Since nobody has answered yet, it appears there are not many of such
programs, perhaps none at all. Hence I would like to submit the following
suggestion:

Dan Boulet's book "Methods of Orbit Determination" contains algorithms
to compute the state vector (position and velocity in cartesian coordinates)
from observations. A computer program (in BASIC) is given as well as another
program to improve initial state vectors by further observations.

It is a relatively straightforward job to compute classical Keplerian
elements from these vectors, except in some pathological cases.

Ken Ernandes' program VEC2TLE allows to perform the next step, calculation of
TLE's from the state vectors, due consideration being given to the reference
system and units of measure.

This will still give a first approximation only because drag effects are
not taken into account. Mike McCants' program FITELEM allows refinement
of initial TLE's either by manually changing parameters or by inputting
the time delay between computed and observed positions. His program is not
terribly user-friendly because everything has to be entered through a batch
file in classical mainframe style.

I have not tried this approach myself, but that's the way I would go about
it if I couldn't find a program that does the job. Needless to say that this
is a classical problem of positional astronomy, treated thoroughly in the
18th and 19th centuries by Laplace, Gauss and Olbers, were it not for
non-gravitational forces. 

A word of caution is in order, however. The Spacetrack Report No.3, "Models
for Propagation of NORAD Element Sets", warns that NORAD element sets are
mean values obtained by removing periodic variations in a particular way
(not explained further) which must be re-introduced before using the elements. 
Using NORAD TLE's in a different model will result in degraded predictions
even if the model is intrinsically more accurate. Conversely, it could be
argued that using TLE's, constructed in the way outlined above, with a NORAD
model such as SGP4 could lead to erroneous results.

Comments are welcome!

Bruno Tilgner
100533.2016@compuserve.com
Fax +33 1 557 0042