Joint localization and synchronization (JLAS) is a technology that simultaneously determines the spatial locations of user nodes and synchronizes the clocks between user nodes (UNs) and anchor nodes (ANs). This technology is crucial for various applications in wireless sensor networks. Existing solutions for JLAS are either computationally demanding or not resilient to noise. This paper addresses the challenge of localizing and synchronizing a mobile user node in broadcast-based JLAS systems using sequential one-way time-of-arrival (TOA) measurements. The AN position uncertainty is considered along with clock offset and skew. Two redundant variables that couple the unknowns are introduced to pseudo-linearize the measurement equation. In projecting the equation to the nullspace spanned by the coefficients of the redundant variables, the affection of them can be eliminated. While the closed-form projection solution provides an initial point for iteration, it is suboptimal and may not achieve the Cramér-Rao lower bound (CRLB) when noise or AN position error is relatively large. To improve performance, we propose a novel robust iterative solution (RIS) formulated through factor graphs and developed via message passing. The RIS outperforms the common Gauss–Newton iteration, especially in high-noise scenarios. It exhibits a lower root mean-square error (RMSE) and a higher probability of converging to the optimal solution, while maintaining manageable computational complexity. Both analytical results and numerical simulations validate the superiority of the proposed solution in terms of performance, resilience, and computational load.