解决轮式车辆定位中轮半径和天线位置未知的难题
Invariant filtering for wheeled vehicle localization with unknown wheel radius and unknown GNSS lever arm
- 基于不变扩展卡尔曼滤波，几何化设计观测器
- 误差方程自洽，雅可比矩阵与状态无关
- 适合机器人定位与自动驾驶系统开发
本文研究非完整汽车（更一般地，轮式机器人）的观测器设计问题，其配备有轮速传感器但轮半径未知，且通过安装在车体上未知位置的GNSS天线测量位置。通过教程式统一阐述，回顾了不变卡尔曼滤波领域中的双框架系统理论，并将其几何化适配至该问题，尽管初看似乎超出其适用范围。所提出的构造生成了一个具有自主误差方程和与状态无关雅可比矩阵的不变扩展卡尔曼滤波器，在仿真中表现卓越。该新方法显著拓展了不变滤波的应用范围。
原文摘要 · Abstract (English)
We consider the problem of observer design for a nonholonomic car (more generally a wheeled robot) equipped with wheel speeds with unknown wheel radius, and whose position is measured via a GNSS antenna placed at an unknown position in the car. In a tutorial and unified exposition, we recall the recent theory of two-frame systems within the field of invariant Kalman filtering. We then show how to adapt it geometrically to address the considered problem, although it seems at first sight out of its scope. This yields an invariant extended Kalman filter having autonomous error equations, and state-independent Jacobians, which is shown to work remarkably well in simulations. The proposed novel construction thus extends the application scope of invariant filtering.
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