Global Navigation Satellite System (GNSS) is the widely used technology for outdoor positioning. However, the classical GNSS navigator is vulnerable to multiple faulty measurements including multipaths and Non-Line-Of-Sight (NLOS) in harsh propagation environments such as urban canyons. In this paper, we propose a novel algorithm, the Context-Adaptive Robust Extended Kalman Filter (CAR-EKF), for robust GNSS navigation in evolving challenging conditions. This method is based on robust statistics and enabled by GNSS-based environmental context detection. M-estimators have shown promising results in this background but are limited by the fixed hyper-parameter. Our main idea is to adapt the Huber loss hyper-parameter depending on the context detected. To do so, an environmental context detection functionality module is realized through a data-driven manner which takes into account the GNSS constellation, signal quality and positioning information. Then the associated Huber hyper-parameter is chosen in order to adapt the navigator to the current context type. The context classification accuracy, the positioning performance and the generalization capability of the proposed method are evaluated in multiple contexts scenarios (open-sky, trees, urban and urban canyon), with two distinct GNSS receivers. The maximum positioning error is reduced by up to 36% with respect to M-estimators.