The aim of this paper is to prove two new uncertainty principles for the Dunkl-Gabor transform. The first of these results is a new version of Heisenberg's uncertainty inequality which states that the Dunkl-Gabor transform of a nonzero function with respect to a nonzero radial window function cannot be time and frequency concentrated around zero. The second result is an analogue of Benedicks' uncertainty principle which states that the Dunkl-Gabor transform of a nonzero function with respect to a particular window function cannot be time-frequency concentrated in a subset of the form $S\times \mathcal B(0,b)$ in the time-frequency plane $\mathbb R^d\times \widehat {\mathbb R}^d$. As a side result we generalize a related result of Donoho and Stark on stable recovery of a signal which has been truncated and corrupted by noise.
Global Navigation Satellite System (GNSS) positioning has characteristics of simple operation, high efficiency and high precision technique for landslide surface monitoring. In recent years, finalization of modern GNSS systems Galileo and BeiDou has brought a possibility of multi-GNSS positioning. The paper focuses on evaluation of possible benefits of multi-GNSS constellations in landslide monitoring. While simulating observational conditions of selected Recica landslide in the Czech Republic, one-month data from well-established permanent GNSS reference stations were processed. Besides various constellation combinations, differential and Precise Point Positioning techniques, observation data lengths and observation sampling intervals were evaluated. Based on the results, using a combination of GPS and GLONASS, or GPS, GLONASS and Galileo systems can be recommended, together with a static differential technique and observation periods for data collection exceeding eight hours. In the last step, data from GNSS repetitive campaigns realized at the Recica landslide during two years were processed with optimal setup and obtained displacement results were compared to standard geotechnical measurements.