In multiple target tracking, it is important to be able to evaluate the performance of different tracking algorithms. The trajectory generalized optimal sub-pattern assignment metric (TGOSPA) is a recently proposed metric for such evaluations. The TGOSPA metric is computed as the solution to an optimization problem, but for large tracking scenarios, solving this problem becomes computationally demanding. In this paper, we present an approximation algorithm for evaluating the TGOSPA metric, based on casting the TGOSPA problem as an unbalanced multimarginal optimal transport problem. Following recent advances in computational optimal transport, we introduce an entropy regularization and derive an iterative scheme for solving the Lagrangian dual of the regularized problem. Numerical results suggest that our proposed algorithm is more computationally efficient than the alternative of computing the exact metric using a linear programming solver, while still providing an adequate approximation of the metric.

翻译：在多目标跟踪领域，评估不同跟踪算法的性能至关重要。轨迹广义最优子模式分配度量(TGOSPA)是近期提出的一种用于此类评估的度量标准。TGOSPA度量的计算可归结为一个优化问题的求解，但在大规模跟踪场景中，求解该问题的计算成本极高。本文提出一种基于不平衡多边际最优传输框架的TGOSPA度量近似计算算法。借鉴计算最优传输领域的最新进展，我们引入熵正则化方法，并推导出求解正则化问题拉格朗日对偶的迭代计算框架。数值实验表明，相较于采用线性规划求解器计算精确度量的传统方法，本算法在保持度量近似精度的同时，显著提升了计算效率。