"Improvement in/on/of/to something"

There has been an improvement in/of Sally's performance in Mathematics from 3.0/4.0 to 3.2/4.0 and she is determined to further improve on/in her skills in this subject.

My choices: improvement in, improve on for the optional positions marked by /.

improve on may mean additions as part of improvement, whereas improve in may mean improvement in efficiency, proficiency etc. without any enhancement in techniques or functionalities.For many people however they mean the same or both interchangeably.

A thing may be improved, or made better. You can use the word in this sense by saying something along the lines of

The successful candidate is expected to contribute by improving the current calibration.

If you're not actually modifying the calibration and rather submitting an improvement, however, you'll have to use a preposition.

In that case, you "improve upon" something by making or suggesting something better. "Improve on" may be used similarly.

Some people use "improve in" to convey individuals' attainment of skill (e.g. "John improved in playing the violin"), but this isn't correct, since using improve without an object in this way would imply that John himself increased in value or became better (see definition #5 here).

I assume that "John improved at playing the violin" would be correct, but it isn't used commonly (in my part of the US, at least).

"Improve of" and "improve to" are just incorrect -- see the definitions of "of" and "to."

It could be an improvement 'of the current curriculum' an improvement 'in performance' or an improvement 'on previous attempts."

The Macmillan Dictionary's definition of improvement highlights this phrase:

an improvement on something : better than something that existed before

Using their recommendation, I would rewrite your phrase this way:

The successful candidate is expected to contribute an improvement on the current calibration method.