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Mapping the occupancy level of an environment is important for a robot to navigate in unknown and unstructured environments. To this end, continuous occupancy mapping techniques which express the probability of a location as a function are used. In this work, we provide a theoretical analysis to compare and contrast the two major branches of Bayesian continuous occupancy mapping techniques---Gaussian process occupancy maps and Bayesian Hilbert maps---considering the fact that both utilize kernel functions to operate in a rich high-dimensional implicit feature space and use variational inference to learn parameters. Then, we extend the recent Bayesian Hilbert maps framework which is so far only used for stationary robots, to map large environments with moving robots. Finally, we propose convolution of kernels as a powerful tool to improve different aspects of continuous occupancy mapping. Our claims are also experimentally validated with both simulated and real-world datasets.