Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters -- show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

翻译：传统滤波算法（如经典卡尔曼滤波、无迹卡尔曼滤波及粒子滤波）在应用于不确定性服从任意非高斯分布（可能包含多峰分布）的非线性系统时，会出现性能退化。本研究综述了基于条件归一化流进行非线性滤波实现状态估计的最新方法，其中条件嵌入由标准MLP架构、Transformer或选择性状态空间模型（如Mamba-SSM）生成。此外，我们测试了最优传输启发的动力学损失项在缓解由大量变换构成的流中过参数化问题的有效性。我们针对自动驾驶与患者种群动力学相关应用研究了这些方法的性能，特别关注其处理时间反转与链式预测的能力。最终，我们评估了不同条件策略在真实世界COVID-19联合SIR系统预测与参数估计应用中的表现。