Self-driving vehicles are posing new challenges as the automation level defined in the SAE International standards for autonomous driving is increased. A pivotal task in autonomous driving is building a perception of the surrounding environment using optical sensors, which is a long-standing challenge and prompts us to explore the utilization of various sensors. Radar is an older and cheaper type of sensor than alternatives such as lidar for long-range distance coverage, and it is also competitively reliable and robust in adverse weather conditions. However, sparse data and noise are inherent challenges of radar. This study explores the dynamic Gaussian process for occupancy mapping and predicting a drivable path for a self-driving vehicle within the field of view (FOV) of a radar sensor. Gaussian occupancy mapping does not need abundant data for training and is a promising alternative to data-reliant deep learning techniques. The proposed technique optimizes parameters (variational and kernel-based) of the Gaussian process to determine the allowed region within the FOV limits by means of stochastic selection of functional points (pseudoinput) and tuning of threshold values. We have tested the proposed technique in experiments performed under different environmental conditions, such as various road and traffic conditions and diverse weather and illumination conditions. The results verify the efficacy of the proposed technique in diverse weather conditions for finding a drivable path for a self-driving vehicle, with the additional benefits of requiring only a low-cost apparatus and providing coverage of a long distance range.