Fast covariance recovery in incremental nonlinear least square solvers
Fast covariance recovery in incremental nonlinear least square solvers
复制标题
增量非线性最小二乘求解器中的快速协方差恢复
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
P. Zemčík
中科院分区：
文献类型：
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作者：
V. Ila;L. Polok;Marek Solony;P. Smrz;P. Zemčík
机器人中的许多估计问题依赖于非线性最小二乘的有效求解。例如，众所周知，同时定位和映射（SLAM）问题可以表述为最大似然估计（MLE），并使用NLS解决，从而产生平均状态向量。然而，对于许多应用来说，仅仅恢复平均向量是不够的。数据关联、主动决策、次优视图只是需要快速状态协方差恢复的几个应用程序。这个问题并不简单，因为通常情况下，协方差是通过对系统矩阵求逆得到的，结果是密集的。本文的主要贡献是提出了一种新的快速增量协方差更新算法，并辅以高效的协方差恢复实现。与其他最先进的解决方案相比，这种组合使计算时间减少了两个数量级。所提出的算法适用于任何NLS求解器的实现，并且不依赖于我们以前的论文中描述的增量策略，这不是本文的主题。
Many estimation problems in robotics rely on efficiently solving nonlinear least squares (NLS). For example, it is well known that the simultaneous localisation and mapping (SLAM) problem can be formulated as a maximum likelihood estimation (MLE) and solved using NLS, yielding a mean state vector. However, for many applications recovering only the mean vector is not enough. Data association, active decisions, next best view, are only few of the applications that require fast state covariance recovery. The problem is not simple since, in general, the covariance is obtained by inverting the system matrix and the result is dense. The main contribution of this paper is a novel algorithm for fast incremental covariance update, complemented by a highly efficient implementation of the covariance recovery. This combination yields to two orders of magnitude reduction in computation time, compared to the other state of the art solutions. The proposed algorithm is applicable to any NLS solver implementation, and does not depend on incremental strategies described in our previous papers, which are not a subject of this paper.