In modern warfare, securing time for preemptive response is recognized as an important factor of victory. The naval combat system, the core of naval forces, also strives to increase the effectiveness of engagement by improving its real-time information processing capabilities. As part of that, it is considered to use the TPR-tree in the naval combat system's target indexing because spatio-temporal searches can be performed quickly even as the number of target information increases. However, because the TPR-tree is slow to process updates, there is a limitation to handling frequent updates. In this paper, we present a method for improving the update performance of TPR-tree by applying the bottom-up update scheme, previously proposed for R-tree, to the TPR-tree. In particular, we analyze the causes of overlaps occurring when applying the bottom-up updates and propose ways to limit the MBR expansion to solve it. Our experimental results show that the proposed technique improves the update performance of TPR-tree from 3.5 times to 12 times while maintaining search performance.