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：传统状态估计滤波算法——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（可能为多峰分布）的非线性系统时，其性能会出现退化。本研究综述了基于条件归一化流的非线性滤波状态估计最新方法，其中条件嵌入由标准多层感知机架构、Transformer 或选择性状态空间模型（如 Mamba-SSM）生成。此外，我们测试了一种受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模型中的过参数化问题的有效性。我们在自动驾驶和患者群体动态相关的应用场景中评估了这些方法的性能，特别关注其如何处理时间反演与链式预测。最后，针对现实世界 COVID-19 联合 SIR 系统预测与参数估计的应用，我们评估了多种条件化策略的性能表现。