Particle filters for mobile robot localization must balance computational requirements and accuracy of localization. Increasing the number of particles in a particle filter improves accuracy, but also increases the computational requirements. Hence, we investigate a different paradigm to better utilize particles than to increase their numbers. To this end, we introduce the Corrective Gradient Refinement (CGR) algorithm that uses the state space gradients of the observation model to improve accuracy while maintaining low computational requirements. We develop an observation model for mobile robot localization using point cloud sensors (LIDAR and depth cameras) with vector maps. This observation model is then used to analytically compute the state space gradients necessary for CGR. We show experimentally that the resulting complete localization algorithm is more accurate than the Sampling/Importance Resampling Monte Carlo Localization algorithm, while requiring fewer particles.