1. A method comprising:(a) determining gravitational and centripetal accelerations by performing a local running mean of acceleration measurements from a drill pipe;
(b) removing the local running mean to yield corrected acceleration data due to vibration only;
(c) transforming the corrected acceleration data from a local rotating coordinate frame to a global stationary coordinate frame; and
(d) mapping in real time, the acceleration data in the global stationary coordinate frame into continuous drill-string positions,
wherein the acceleration data is mapped into the continuous drill-string positions using:
where P(x, y, z, t) is a position vector in a global stationary coordinate frame referenced at a center of the drill pipe; a(x, y, z, t) is an acceleration vector in the global stationary coordinate frame referenced at the center of the drill pipe; t is travel time of the drill pipe; and dt is time interval the drill pipe moves from P(x, y, z, t) to P(x, y, z, t+dt).