Efficient Invariant Kalman Filter for Inertial-based Odometry with Large-sample Environmental Measurements
<|reference_start|>Efficient Invariant Kalman Filter for Inertial-based Odometry with Large-sample Environmental Measurements: A filter for inertial-based odometry is a recursive method used to estimate the pose from measurements of ego-motion and relative pose. Currently, there is no known filter that guarantees the computation of a globally optimal solution for the non-linear measurement model. In this paper, we demonstrate that an innovative filter, with the state being $SE_2(3)$ and the $\sqrt{n}$-\textit{consistent} pose as the initialization, efficiently achieves \textit{asymptotic optimality} in terms of minimum mean square error. This approach is tailored for real-time SLAM and inertial-based odometry applications.   Our first contribution is that we propose an iterative filtering method based on the Gauss-Newton method on Lie groups which is numerically to solve the estimation of states from a priori and non-linear measurements. The filtering stands out due to its iterative mechanism and adaptive initialization. Second, when dealing with environmental measurements of the surroundings, we utilize a $\sqrt{n}$-consistent pose as the initial value for the update step in a single iteration. The solution is closed in form and has computational complexity $O(n)$. Third, we theoretically show that the approach can achieve asymptotic optimality in the sense of minimum mean square error from the a priori and virtual relative pose measurements (see Problem~\ref{prob:new update problem}). Finally, to validate our method, we carry out extensive numerical and experimental evaluations. Our results consistently demonstrate that our approach outperforms other state-of-the-art filter-based methods, including the iterated extended Kalman filter and the invariant extended Kalman filter, in terms of accuracy and running time.<|reference_end|>
@article{li2024efficient,
    title={Efficient Invariant Kalman Filter for Inertial-based Odometry with
  Large-sample Environmental Measurements},
    author={Xinghan Li, Haoying Li, Guangyang Zeng, Qingcheng Zeng, Xiaoqiang Ren,
  Chao Yang, Junfeng Wu},
    journal={arXiv preprint arXiv:2402.05003},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.05003},
    primaryClass={cs.RO}
}