标题： 基于流形的状态估计的可逆卡尔曼滤波 显示英文标题

标题： Reversible Kalman Filter for state estimation with Manifold

摘要： 这项工作引入了一种在卡尔曼滤波框架下的流形状态估计算法。其主要目标是提供一种方法，使能够在合成数据上以任意精度评估现有卡尔曼滤波变体的精度，这一点据我们所知，在以往的工作中尚未被解决。为此，我们开发了一种新的滤波器，表现出良好的数值特性，从而修正了先前卡尔曼滤波变体中观察到的发散问题。在这种表述中，可达到的精度不再受小速度假设的限制，仅由传感器噪声决定。此外，这种新的滤波器假设传感器具有高精度，在实际场景中需要一个我们以启发式方式定义的检测步骤，从而使该方法能够扩展到各种场景，使用9轴IMU或里程计、加速度计和压力传感器的组合。后一种配置专门用于水下环境中的轨迹重建。 显示英文摘要

摘要： This work introduces an algorithm for state estimation on manifolds within the framework of the Kalman filter. Its primary objective is to provide a methodology enabling the evaluation of the precision of existing Kalman filter variants with arbitrary accuracy on synthetic data, something that, to the best of our knowledge, has not been addressed in prior work. To this end, we develop a new filter that exhibits favorable numerical properties, thereby correcting the divergences observed in previous Kalman filter variants. In this formulation, the achievable precision is no longer constrained by the small-velocity assumption and is determined solely by sensor noise. In addition, this new filter assumes high precision on the sensors, which, in real scenarios require a detection step that we define heuristically, allowing one to extend this approach to scenarios, using either a 9-axis IMU or a combination of odometry, accelerometer, and pressure sensors. The latter configuration is designed for the reconstruction of trajectories in underwater environments.