This work addresses range-only SLAM (RO-SLAM) as the Bayesian inference problem of sequentially tracking a vehicle while estimating the location of a set of beacons without any prior information. The only assumptions are the availability of odometry and a range sensor able of identifying the different beacons. We propose exploiting the conditional independence between the position distributions of each beacon within a Rao-Blackwellized Particle Filter (RBPF) for maintaining independent Sum of Gaussians (SOGs) for each beacon. Unlike other approaches, it is shown then that a proper probabilistic observation model can be derived for online operation with no need for delayed initializations. We provide a rigorous statistical comparison of this proposal with previous work of the authors where a Monte-Carlo approximation was employed instead for the conditional densities. As verified experimentally, this new proposal represents a significant improvement in accuracy, computation time, and robustness against outliers.