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Geospatial data emanating from GPS-enabled pervasive devices reflects the mobility and interactions between people and places, and poses serious threats to privacy. Most of the existing location privacy works are based on the k-Anonymity privacy paradigm. In this paper, we employ a different and stronger privacy definition called Differential Privacy. We propose a novel context-aware and non context-aware differential privacy technique. Our technique couples Kalman filter and exponential mechanism to ensure differential privacy for spatio-temporal data. We demonstrate that our approach protects outliers and provides stronger privacy than state-of-the-art works.