There is no mobile app as traditional mouse(because of engineering problems), but there is a mouse with iphone touch or gyroscope.
How much money a person can possibly benefit if he makes a traditional mouse app for mobile
Ask HN: How much could some one make if he makes a traditional mobile mouse app? | Better HN
Accurately inferring the position of the mouse from its acceleration is a difficult problem (the integration involved will result in rather large errors that compound over time when calculating the velocity and position). I doubt that the return on a 'traditional mouse' app would reward the effort required to make this work.
I don'f quite understand what you want ot build. In general a moise only makes sense for screens bigget than a typical mouse-pad or phone screen or look arround stuff like 3D games
I thought about this a long time ago (2009) using the gyros + compass as an IMU. The thing is that the gyros were not as precise back then but things might have changed now.