We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier maps that arise in the context of simulation based inference. We then apply these results in a filtering scenario to analyze the optimal transport filtering algorithm of Al-Jarrah et al. (2024, ICML). An extension of that algorithm along with numerical benchmarks on various non-Gaussian and high-dimensional examples are provided to demonstrate its effectiveness and practical potential.

翻译：本文系统分析了一类基于最优传输的滤波与数据同化算法的估计误差。在此过程中，我们将先前关于Brenier映射的误差分析推广至基于模拟的推断背景下出现的条件Brenier映射情形。随后，我们将这些结果应用于滤波场景，以分析Al-Jarrah等人（2024，ICML）提出的最优传输滤波算法。本文进一步扩展了该算法，并在多种非高斯和高维示例上进行了数值基准测试，以验证其有效性和实际应用潜力。