Integrated Multipath-Based SLAM: Unifying Multipath Components Extraction and State Estimation via Hybrid Message Passing

Traditional multipath-based simultaneous localization and mapping (SLAM) frameworks typically employ a sequential two-stage process: multipath component (MPC) extraction followed by recursive state estimation. The first stage identifies the number of MPCs and estimates their parameters, while the second stage updates the mobile agent and map feature (MF) states. These two stages share similar objectives as MPCs and MFs exhibit an intrinsic one-to-one correspondence governed by geometric propagation constraints, while both rely on Bayesian inference techniques representable through factor graphs and message passing (MP) algorithms. Building on these similarities, this paper proposes a unified probabilistic framework, termed integrated multipath-based SLAM, which jointly encodes MPCs and MFs within a single state variable, explicitly modeling their geometric relationships and shared sparsity patterns. We derive the posterior distribution with its corresponding factor graph representation and develop a hybrid MP algorithm combining belief propagation and mean field MP. To address practical implementation challenges, we further establish an plug-and-play data association module. Activated upon detecting potential MPC-MF mismatches, this module employs row/column-wise matrix operations to realign associations while maintaining computational efficiency. Simulation results demonstrate that the proposed algorithm outperforms conventional decoupled approaches by improving both computational efficiency and estimation accuracy.