Smartphone receivers comprise approximately 1.5 billion global navigation satellite system receivers currently manufactured worldwide. Smartphone receivers provide measurements with lower signal levels and higher noise than commercial receivers. Because of constraints on size, weight, power consumption, and cost, it is challenging to achieve accurate positioning with these receivers, particularly in urban environments. Traditionally, global positioning system measurements are processed via model-based approaches, such as weighted least-squares and Kalman filtering approaches. While model-based approaches can provide meter-level positioning accuracy in a postprocessing manner, these approaches require strong assumptions on the corresponding noise models and require manual tuning of parameters such as covariances. In contrast, learning-based approaches have been proposed that make fewer assumptions about the data structure and can accurately model environment-specific errors. However, these approaches provide lower accuracy than model-based methods and are sensitive to initialization. In this paper, we propose a hybrid framework for learning position correction, which corresponds to the offset between the true receiver position and the estimated position. For a learning-based approach, we propose a graph convolution neural network (GCNN) that can learn different graph structures with multi-constellation and multi-frequency signals. For better initialization of the GCNN, we use a Kalman filter to estimate a coarse receiver position. We then use this coarse receiver position to condition the input features to the graph. We test our proposed approach on real-world data sets from the Google Smartphone Decimeter Challenge and show improved positioning performance over model-based methods such as the weighted least-squares and Kalman filter methods.