You can probably find all of these ingredients in the Julia ecosystem, but your description above should answer
: because you need to make a lot of decisions like this, so there is no general method for “estimation”.
That said, I am not sure why something simple like minimizing a sum of squared discrepancies would not work, but maybe your problem domain has something special.
If you want to get more specific help, post an MWE for generating the data, and the questions you have.