提出可逆卡尔曼滤波，提升流形上状态估计精度
Reversible Kalman Filter for state estimation with Manifold
- 基于可逆卡尔曼滤波，在流形上实现高精度状态估计
- 精度不再受小速度假设限制，仅由传感器噪声决定
- 适用于水下轨迹重建等复杂场景，支持多传感器融合
本文提出一种在流形框架下的状态估计算法，旨在实现对现有卡尔曼滤波变体的精度评估，且精度可达任意水平，这在以往工作中尚未解决。为此，我们设计了一种新滤波器，具备优良的数值稳定性，纠正了此前滤波器存在的发散问题。该方法摆脱了小速度假设的限制，精度仅取决于传感器噪声。此外，该滤波器假设传感器具有高精度，在实际中需通过启发式检测步骤引入，从而可应用于9轴惯性测量单元（IMU）或里程计、加速度计与压力传感器组合的场景，后者专为水下轨迹重建设计。
原文摘要 · Abstract (English)
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.
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