Rao-Blackwellised Particle Filters (RBPFs) are a class of Particle Filters (PFs) that exploit conditional dependencies between parts of the state to estimate. By doing so, RBPFs can improve the estimation quality while also reducing the overall computational load in comparison to original PFs. However, the computational complexity is still too high for many real-time applications. In this paper, we propose a modified RBPF that requires a single Kalman Filter (KF) iteration per input sample. Comparative experiments show that while good convergence can still be obtained, computational efficiency is always drastically increased, making this algorithm an option to consider for real-time implementations.