Theoretical study of ESDS by using phase plane

In our previous research (2000), we proposed a technique to estimate the smoothed value and the differential value of the sensor inputs by using sliding mode system (ESDS). We smooth the distance value by supposing the continuity of the signal that is obtained by the sonar, and taking advantage of this continuity, we compose a robust estimator. This estimator is based on the sliding mode system. In our proposed method, there is trade-off between the ability of noise elimination and the tracking performance for the input signal. We discuss the ability of noise elimination that ESDS has by finding the solution trajectory in the phase plane. At the same time, we discuss the signal tracking performance by using the solution trajectory. According to these considerations, we clarify the relation between these characteristics and the arbitrary parameters.