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?