I am combining two position measurements of a ball from two sensors in real time to obtain one triangulated position in x,y,z coordinates. As the data exchange of the measurements carries some latency, the data has to be extrapolated be able to obtain the current position. Due to extrapolation an error appears in the triangulated data.
I know that when the ball is in the air, the velocity of the ball should be constant in x and y directions and the velocity in the z direction should decay with g. The velocities in x and y however oscillate as function of time around a mean value which is the actual x respectively y velocity. The same goes for when I compute the acceleration in the z direction. It oscillates as function of time around g.
Given that I know how the ball should behave, i.e. that vx and vy should be constant and that the acceleration in the z direction should be z, how can I impose these conditions to better estimate the triangulated position?