Detecting and monitoring of moving and potentially hazardous slopes requires reliable estimations of velocities. Separating any movement signal from measurement noise is crucial for understanding the temporal variability of slope movements and detecting changes in the movement regime, which may be important indicators of the process. Thus, methods capable of estimating velocity and its changes reliably are required. In this paper we develop and test a method for deriving velocities based on noisy GPS (Global Positioning System) data, suitable for various movement patterns and variable signal-to-noise-ratios (SNR). We tested this method on synthetic data, designed to mimic the characteristics of diverse processes, but where we have full knowledge of the underlying velocity patterns, before applying it to explore data collected.