Iconosquare uses optimisation tools to analyze your engagement. Sign up to monitor your average number of likes, the exact time of day you should be posting, follower growth, and much more.
Another tool which I use daily for stats is called InsTrack.
InsTrack lets you track your Instagram followers, discover who unfollowed you on Instagram and who is not following you back, detect blockers, view your fans, rank your best friends plus much more. I always amazed how many people use the follow / unfollow tactic on Instagram – this tools lets you see who is doing this on your account.