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I have to calculate the probability of collision at moment $t$ with space debris. I am using JSPOC algorythm described in https://www.space-track.org/documents/How_the_JSpOC_Calculates_Probability_of_Collision.pdf. I have the sizes both of the satellite and the debris. SGP4 and TLEs are used to find the position and velocity of the objects and also to calculate the covariance matrix according to algorythm described in Osweiler's dissertation, see https://apps.dtic.mil/dtic/tr/fulltext/u2/a446817.pdf(or in "Covariance Propagation of Two-Line Element Data" by HUO Yurong, Li Zhi, Han Lei).

Unfortunately, my results do not coincide with the correct ones. I see several possible reasons for it:

1) The incorrectness of TLEs. It was mentioned in different conversations on Stackexchange that TLE are not very precise. Not having any other opportunities or, probably, being unaware of them, I am obliged to use TLEs.

-Maybe, I can obtain the state vector and/or covariance from other free sources? I have seen something in comments for Covariance matrix of a satellite position, but no concrete information, unfortunately.

2) Wrong method of calculating the covariance. In the publications mentioned above the 2 weeks range was used to calculate the covariance matrix, but no explanations to it was given. I suppose that theoretically the accuracy should be increasing with the increasing of the given data, but the computation error will raise, too.

-Is this number "14" some empirical guess or there is something deeper in it?

3) The coordinate frame. In the first paper the RTC system is used.

-Can coordinate change give us some different results (in general case)? Are there any advantages of one system comparing to the other?

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    $\begingroup$ It looks like you have asked "I did a calculation, the results disagree with the correct ones, why?" As currently written it's going to be a hard question to answers correctly, Where do the "correct results" come from? If they are based on any information besides the TLEs you are using then there's no way you will get results that agree. At epoch TLEs are only accurate to order 1 km so unless you are comparing two methods using the exact same TLEs + SGP4, you are comparing apples to oranges. $\endgroup$ – uhoh Sep 2 at 10:09
  • $\begingroup$ As far as the two weeks is concerned, it's known that SGP4 loses accuracy far away from the epoch but I don't know of a hard cutoff at +/- 7 days. Slightly related and currently unanswered: Algorithmic methods or techniques to find conjunctions in large ensembles of state vectors? $\endgroup$ – uhoh Sep 2 at 10:18
  • $\begingroup$ @uhoh, maybe there are some alternatives to TLE in free access? Also, I have found in space.stackexchange.com/questions/26832/… the following links: celestrak.com/software/tskelso-sw.php, movingsatellites.com/e_gps.html. As I understood, this is the software that provides the position of the satellite. I thought about using its results to create covariation and feed them with the position to my algorythm but not sure, whether it is reasonable. $\endgroup$ – Alex Johnson Sep 6 at 7:12
  • $\begingroup$ TLEs are really the only way to get positional information about satellites that I know of. I am sure that the movingsatellites program uses them, it says so right on that page, it just calls them " NORAD 2 LINE element set" TLE = Two Line Element set. It is reasonable, but not that accurate. I can't really help much further on this though. $\endgroup$ – uhoh Sep 6 at 10:30

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