联合转向与外参标定的可观测性分析
Observability Analysis of Joint Steering and Extrinsic Calibration
AI总结：
本文通过李导数非线性可观测性分析，证明平面自行车模型车辆在联合估计位姿、LiDAR外参与转向偏差时，直线加圆弧组合运动可实现七状态系统完全局部弱可观测，为标定轨迹选择提供理论依据。
AI中文摘要：
本技术报告研究了平面自行车模型车辆在联合估计车辆位姿、平面LiDAR外参标定和转向角偏差时的局部弱可观测性。采用基于李导数的非线性可观测性分析方法，考察了静止、直线、恒定曲率和直线加圆弧组合运动。所得可观测性矩阵和零空间描述了在不同运动基元下，位姿、LiDAR平移和偏航偏移以及转向偏差如何耦合。静止运动和单一运动基元保留了不可观测方向，而直线与曲线运动的组合消除了已识别的退化，并实现了七状态系统的完全局部弱可观测性。该分析为选择能够充分激励转向和传感器外参参数的标定轨迹提供了理论基础。
英文摘要：
This technical report studies the local weak observability of a planar bicycle-model vehicle when vehicle pose, planar LiDAR extrinsic calibration, and steering-angle bias are estimated jointly. A Lie-derivative-based nonlinear observability analysis is used to examine stationary, straight-line, constant-curvature, and combined straight-plus-arc motion. The resulting observability matrices and nullspaces describe how pose, LiDAR translation and yaw offsets, and steering bias become coupled under different motion primitives. Stationary motion and individual motion primitives retain unobservable directions, whereas the combination of straight and curved motion removes the identified degeneracies and yields full local weak observability of the seven-state system. The analysis provides a theoretical basis for selecting calibration trajectories that sufficiently excite both steering and sensor-extrinsic parameters.
