Information-Preserving Continuous Occupancy Mapping with Variance-Weighted Submap Joining

Large-scale SLAM remains challenging due to accumulated trajectory drift and the increasing computational cost of maintaining global consistency. Submap joining alleviates these issues by constructing locally consistent submaps and subsequently fusing them into a global map. However, existing occupancy-based submap joining methods operate on discrete grids, resulting in non-smooth gradients during optimization and neglecting the uncertainty associated with occupancy estimates. We propose the first continuous probabilistic submap joining framework that jointly optimizes submap poses and a global occupancy field in the latent log-odds space. The framework employs an information-preserving sparse Bayesian formulation that compresses raw occupancy observations into sufficient-statistic log-odds tuples while retaining the posterior information of the original observations. This yields closed-form predictive mean and variance estimates for occupancy mapping, which directly enable a submap joining formulation with analytical Jacobians, leading to more accurate submap joining and yielding a closed-form optimal global map upon pose convergence. Experiments on both simulated and large-scale real-world datasets demonstrate that the proposed method achieves higher pose accuracy and improved global consistency than state-of-the-art grid-based submap joining approaches, while producing more compact map representations and better-calibrated uncertainty estimates than existing continuous occupancy mapping methods.