In current industrial control applications, the proportional + integral + derivative (PID) control is still used as the leading tool, but constructing controller requires precise mathematical model of plant, and tuning the parameters of controllers is not simple to implement. Motivated by the gap between theory and practice in control problems, linear active disturbance rejection control (LADRC) addresses a set of control problems in the absence of precise mathematical models. LADRC has two parameters to be tuned, namely, a closed-loop bandwidth and observer bandwidth. The performance of LADRC depends on the quick convergence of a unique state observer, known as the extended state observer, proposed by Jinqing Han ( 1994). Only one parameter, observer bandwidth, significantly affects the tracking speed of extended state observer. This paper studies numerically the optimal fast tracking observer bandwidth and the absolute tracking error estimation for a class of non-linear and uncertain motion control problems by finite difference method.