I can tell you how I do it, but again I am not an impact study person. It helps to understand a bit of the background of how we fit orbits in general:
1) someone with a telescope sees something moving (typically these days these are bigger surveys)
2) These observations are submitted to the Minor Plant Center (MPC), the clearinghouse of all asteroid/comet observations.
3) Several groups pull observations from the MPC to fit orbits, including JPL Horizons (MPC also fits orbits)
4) You now have a pile of observations which you have to figure out which observation links to other observations, which is a complex math problem on its own. Solve that.
5) JPL Horizons for example then fits the orbits to the observations, and since the observations may be 100 years of data of wildly varying quality, from hand written notes in the 1920s through to modern data, this is very difficult. They publish a covariance matrix with the associated fit (IE: basically a gaussian error fit for the parameters).
6) I grab that covariance matrix and sample from it using some pretty vanilla statistics to build orbits.
7) Propagate and see what happens.
Here is an example of an observation from 1950:
https://caltech-ipac.github.io/kete/tutorials/palomar.html
The image was developed on a glass plate, this one was never even sent in to the MPC, the guy taking the observation just wrote down "Asteroid" on the cover slip for the image. It was not formally discovered until the 1980s. We now know its orbit very well, so this particular observation is not that interesting other than as a curiosity.
Here is an example of an orbit fit by JPL Horizons:
https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=c%2F2...
Note the "condition code" on the right, which is a score of how good their orbit fit matches the data, 0 means we know the orbit with high precision. This one is an 8, meaning we have a fit, but its not that great. Most likely because we only have 31 days of observations.