Abstract
Fast covariance calculation is required both for SLAM (e.g.~in order to solve data association) and for evaluating the information-theoretic term for different candidate actions in belief space planning (BSP). In this paper we make two primary contributions. First, we develop a novel general-purpose incremental covariance update technique, which efficiently recovers specific covariance entries after any change in the inference problem, such as introduction of new observations/variables or re-linearization of the state vector. Our approach is shown to recover them faster than other state-of-the-art methods. Second, we present a computationally efficient approach for BSP in high-dimensional state spaces, leveraging our incremental covariance update method. State of the art BSP approaches perform belief propagation for each candidate action and then evaluate an objective function that typically includes an information-theoretic term, such as entropy or information gain. Yet, candidate actions often have similar parts (e.g. common trajectory parts), which are however evaluated separately for each candidate. Moreover, calculating the information-theoretic term involves a costly determinant computation of the entire information (covariance) matrix which is O(n^3) with n being dimension of the state or costly Schur complement operations if only marginal posterior covariance of certain variables is of interest. Our approach, rAMDL-Tree, extends our previous BSP method rAMDL, by exploiting incremental covariance calculation and performing calculation re-use between common parts of non-myopic candidate actions, such that these parts are evaluated only once, in contrast to existing approaches.
Abstract (translated)
对于SLAM（例如为了解决数据关联）和评估信念空间规划（BSP）中不同候选行动的信息理论项，都需要快速的协方差计算。在本文中，我们做出了两个主要贡献。首先，我们开发了一种新的通用增量协方差更新技术，它可以在推理问题发生任何变化后有效地恢复特定的协方差项，例如引入新的观测值/变量或状态向量的重新线性化。我们的方法比其他最先进的方法更快地恢复它们。其次，利用增量协方差更新方法，提出了一种高维状态空间中BSP的有效计算方法。最先进的BSP方法对每一个候选动作进行信念传播，然后评估一个目标函数，该目标函数通常包括信息论术语，如熵或信息增益。然而，候选动作通常有相似的部分（例如，公共轨迹部分），但是每个候选动作都要单独评估。此外，计算信息理论项涉及到整个信息（协方差）矩阵的一个代价高昂的行列式计算，该矩阵是O（n^3），n是状态的维数，或者如果只关心某个变量的边际后验协方差，则是代价高昂的舒尔补运算。我们的方法，RAMDL树，扩展了我们以前的BSP方法RAMDL，利用增量协方差计算，在非近视候选动作的公共部分之间进行计算重用，这样这些部分相对于现有方法只评估一次。
URL
https://arxiv.org/abs/1906.02249
