Baoshan Song

Baoshan Song, Matthew Giamou, Penggao Yan et al.

Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task rely on abundant satellites unavailable in GNSS-degraded environments, or use local optimization methods which cannot guarantee the optimality of a solution. This work introduces a globally optimal solver that transforms raw pseudo-range or Doppler measurements into a convexly relaxed problem. The proposed method is certifiable, meaning it can numerically verify the correctness of the result, filling a gap where existing local optimizers fail. We first formulate the original frame alignment problem as a nonconvex quadratically constrained quadratic program (QCQP) problem and relax the QCQP problem to a concave Lagrangian dual problem that provides a lower cost bound for the original problem. Then we perform relaxation tightness and observability analysis to derive criteria for certifiable optimality of the solution. Finally, simulation and real world experiments are conducted to evaluate the proposed method. The experiments show that our method provides certifiably optimal solutions even with only 2 satellites with Doppler measurements and 2D vehicle motion, while the traditional velocity-based VOBA method and the advanced GVINS alignment technique may fail or converge to local optima without notice. To support the development of GNSS-based navigation techniques in robotics, all code and data are open-sourced at https://github.com/Baoshan-Song/Certifiable-Doppler-alignment.

Baoshan Song, Ruijie Xu, Zhi Zhan et al.

Sliding window factor graph optimization (SW-FGO) is widely recognized for its robustness, yet its theoretical relationship with the extended Kalman filter (EKF) remains a subject of debate. This paper establishes the sufficient conditions to bridge SW-FGO with the iterated extended Kalman filter (IEKF). We introduce recursive FGO (Re-FGO), a conceptual perspective that employs a two-stage marginalization pipeline to mathematically degenerate the factor graph optimization to the IEKF recursive update. By enforcing the Markov assumption and a single-state window, we prove the theoretical equivalence between the IEKF and Re-FGO. This degeneration is validated through simulations and real-world urban GNSS and INS tightly coupled fusion experiments. The results confirm that Re-FGO exactly reproduces IEKF estimation behavior, demonstrating that the two-stage marginalization pipeline is foundational to enforce structural consistency, thereby successfully uniting graph-based smoothing and filtering paradigms under unified optimization principles.

Baoshan Song, Feng Huang, Li-Ta Hsu

Decentralized multi-robot LiDAR-SLAM is essential for collaborative missions but faces significant challenges in maintaining global consistency. Existing frameworks predominantly rely on local-search optimization or one-time coordinate alignment, which are prone to suboptimal convergence and long-term inconsistency, especially in large-scale or degenerate environments. To address these limitations, this paper presents the first decentralized LiDAR-SLAM system that integrates a state-of-the-art certifiably optimal Pose Graph Optimization (PGO) backend. By leveraging the Riemannian Block Coordinate Descent (RBCD) algorithm, our system ensures globally consistent trajectory estimation without requiring accurate initial guesses. Experimental results demonstrate that the proposed framework achieves superior robustness, improving trajectory RMSE by up to 48.9% compared to the state-of-the-art DiSCo-SLAM.