In our previous research, we proposed a nonlinear digital filter to Estimate the Smoothed and Differential values of the sensor inputs by using Sliding mode system (ESDS). This estimator is able to eliminate impulsive noise efficiently from time series data. We applied this filter to processing outputs of robot sensors, and it became possible to perform robust environment recognition. ESDS is designed using a theory of variable structure system (VSS) with sliding mode. In short, ESDS is a nonlinear filter. Therefore, it is very difficult to clarify the behavior of the system analytically. Consequentially, we deal with the step function with impulsive noise as an example, and we attempt to eliminate this impulsive noise by keeping the sudden shift of signals. In this case, there is a trade-off between the noise elimination ability and the tracking performance for an input signal. Although ESDS is a nonlinear filter, it has the same trade-off as linear filters such as a low-pass filter. In order to satisfy these two conditions simultaneously, we use two filters whose parameters are independent of each other. Furthermore, in order to repress the adverse affect of impulsive noise in the steady-state, we introduced the boundary layer. Generally, a boundary layer is used so as to inhibit the harmful effect of chattering. Chattering is caused in the sliding mode system when the state of the system vibrates on the switching line of a sliding mode system. By introducing the boundary layer to ESDS, we can repress the adverse effect of impulsive noise in the steady-state. According to these considerations, we clarify the relationship between these characteristics of ESDS and the arbitrary parameters.