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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?

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    $\begingroup$ How accurate will the measure to be, and how accurate do you want the result to be? The scientific literature on this is pretty dense, but you could start here: ncbi.nlm.nih.gov/pmc/articles/PMC4970016 $\endgroup$ – Bob Jacobsen Jan 22 at 21:27
  • $\begingroup$ There is a community of satellite observers that do this regularly. They watch for objects that don't have official TLEs (e.g. spy satellites, X-37) make measurements, and issue new TLEs themselves. See for example answers to How are military satellites with (apparently) classified TLEs still showing up on sat map websites? It is possible that some of their software is open sourced. $\endgroup$ – uhoh Jan 23 at 1:15
  • $\begingroup$ But the programs will be a bit complicated because TLEs are not the same as orbital elements, they are engineered to work specifically with SGP4. $\endgroup$ – uhoh Jan 23 at 1:18
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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.

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