Is it possible to update an existing TLE using new data?

Question

I'm writing a simulation a space surveillance telescope. The population of satellites it observes is initialized using TLEs, and the telescope also is given these TLEs at the beginning of the night so it knows where to look for the satellites. The telescope does not have knowledge of the underlying data used to generate the TLE.

As the simulated night progresses, the telescope obtains new observations of the satellite. Is there any way to update the TLEs with the data from these new observations? I'm new to using TLEs but from what I understand I'm guessing the answer is no.

If the answer to the above is no, but then the telescope also had the underlying data used to generate the TLE, is it then possible and advisable to "update" the TLE by generating a new TLE using both the old and the new data?

Answer 1

Is it possible to update an existing TLE using new data?

Of course it is. How do you think TLEs are updated?

That said, it's not easy. You'll need to

1. Compute the Jacobian of your new data with respect to the elements of a TLE you might want to modify.
2. Come up with a weighting matrix that indicates which of those new data are better than others. For example, azimuth near zenith is more or less worthless. Another example: Measurements with a high accuracy telescopes timestamped by an atomic clock are a lot better than measurements made with a typical backyard telescope timestamped with a kitchen clock.
3. Use a generalized least squares approach to yield an estimated correction to the TLE.
4. Repeat steps 1 to 3 until the residuals become statistically insignificant.

But you'll need to be careful of statistically insignificant corrections in step 3. You also need to be aware that the least squares approach outlined above is notoriously greedy -- you might want to use an even more advanced approach.