"This is an improvement on your last report."

"On" is the correct preposition used when talking about improvements in comparison to a previous thing or situation, such as a previous report. We use ‘improvement of,’ to refer to something becoming better. However, we mainly use this when talking about improvement in prospects. For example, ‘We anticipate the improvement of local public schools in the country.’ The prepositions "over" and "against" are not typically paired with the noun "improvement".