LARK: Learnability-Grounded Trajectory Selection for Efficient Reasoning Distillation

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor $ρ$, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a $χ^2$-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Loosely Coupled Factor Graph Optimization for Pseudolite-Augmented Navigation

In Global Navigation Satellite System (GNSS)-degraded environments, pseudolites (PLs) provide additional signal sources to enhance positioning performance, but their integration in optimization-based frameworks remains limited. This paper presents a loosely coupled factor graph optimization (FGO) framework that fuses the GNSS/PL least-squares (LS) solutions with inertial measurement unit (IMU) data. The evaluation considers low GNSS visibility scenarios with four high-elevation GNSS satellites and up to two PL transmitters over an 80~s window. FGO achieves a 22.8\% to 41.3\% reduction in mean 3D error compared to standard LS methods. Compared to a GNSS-IMU baseline, incorporating PL transmitters further improves positioning accuracy, with performance depending on geometry.

GNSS/Multi-Sensor Fusion Using Continuous-Time Factor Graph Optimization for Robust Localization

Accurate and robust vehicle localization in highly urbanized areas is challenging. Sensors are often corrupted in those complicated and large-scale environments. This paper introduces GNSS-FGO, an online and global trajectory estimator that fuses GNSS observations alongside multiple sensor measurements for robust vehicle localization. In GNSS-FGO, we fuse asynchronous sensor measurements into the graph with a continuous-time trajectory representation using Gaussian process regression. This enables querying states at arbitrary timestamps so that sensor observations are fused without requiring strict state and measurement synchronization. Thus, the proposed method presents a generalized factor graph for multi-sensor fusion. To evaluate and study different GNSS fusion strategies, we fuse GNSS measurements in loose and tight coupling with a speed sensor, IMU, and lidar-odometry. We employed datasets from measurement campaigns in Aachen, Duesseldorf, and Cologne in experimental studies and presented comprehensive discussions on sensor observations, smoother types, and hyperparameter tuning. Our results show that the proposed approach enables robust trajectory estimation in dense urban areas, where the classic multi-sensor fusion method fails due to sensor degradation. In a test sequence containing a 17km route through Aachen, the proposed method results in a mean 2D positioning error of 0.19m for loosely coupled GNSS fusion and 0.48m while fusing raw GNSS observations with lidar odometry in tight coupling.