分析车辆在联合估计姿态与标定参数时的可观测性，指导轨迹设计。
Observability Analysis of Joint Steering and Extrinsic Calibration
- 用李导数法分析七维状态系统的可观测性。
- 直线加弧线组合运动可实现完全局部弱可观测性。
- 适用于需要精确标定的自动驾驶系统开发。
本技术报告研究了平面自行车模型车辆在同时估计车辆位姿、平面激光雷达外参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、恒曲率及直线加弧线组合运动下的系统表现。所得可观测性矩阵与零空间揭示了位姿、激光雷达平移与偏航误差以及转向偏差在不同运动模式下的耦合关系。静止状态和单一运动模式仍存在不可观测方向，而直线与曲线运动的组合可消除这些退化，实现七状态系统的完全局部弱可观测性。该分析为选择能充分激励转向与传感器外参的标定轨迹提供了理论依据。
原文摘要 · Abstract (English)
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.
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