The Motion Tomography (MT) algorithm maps an ocean flow field using sporadically measured positions of underwater vehicles. A key step of the MT algorithm, called trajectory tracing, is to estimate the underwater trajectories of the vehicles based on the estimated flow field and known start and end positions. This paper extends the MT algorithm by developing a set of analytical formulas to compute the underwater trajectories. These analytical formulas enable us to study the convergence of the MT algorithm, and we prove that the estimated trajectory and measured trajectory end positions converge as the MT algorithm proceeds. Experimental results are collected on the Georgia Tech Miniature Autonomous Blimps to demonstrate that the MT algorithm can be applied to reconstruct a wind field in an indoor environment using nothing but sparse position measurements. We further validate the MT algorithm using data collected by an underwater glider deployed in the South Atlantic Bight. We demonstrate MT is able to reconstruct the ocean flow field using recorded glider surfacing positions and improve the spatial distribution of a dead reckoning flow field map.

运动断层扫描 (MT) 算法使用水下航行器的零星测量位置绘制海洋流场。MT算法的一个关键步骤，称为轨迹跟踪，是根据估计的流场和已知的起点和终点位置来估计车辆的水下轨迹。本文通过开发一组用于计算水下轨迹的分析公式来扩展 MT 算法。这些解析公式使我们能够研究 MT 算法的收敛性，我们证明估计轨迹和测量轨迹末端位置随着 MT 算法的进行而收敛。在佐治亚理工学院微型自主飞艇上收集了实验结果，以证明 MT 算法可用于仅使用稀疏位置测量来重建室内环境中的风场。我们使用部署在南大西洋湾的水下滑翔机收集的数据进一步验证了 MT 算法。我们证明 MT 能够使用记录的滑翔机表面位置重建海洋流场，并改善航位推算流场图的空间分布。