To reduce the observation noise in the traditional extend state observation (ESO) when dealing with the system with output measurement noise,
 an ARCTANFAL function was proposed to replace the commonly used FAL function in ESO. The normal form of ARCTANFAL function based ESO was given, whose observation error analysis was conducted by using a Lyapunov function. Besides, two improved ESO using the ARCTANFAL function and two ADRCs based on these two ESOs for the system with output measurement noise were proposed. Simulation results show that these two improved ESOs can minimize the observation noise, especially in the observation of the disturbance, and the two ADRCs also have good performance on dealing with systems with output measurement noise.