🤖 AI Summary
This work addresses the degraded performance of conventional filtering methods in joint state and parameter estimation for nonlinear systems subject to non-Gaussian, multimodal uncertainties. To this end, we propose a forward–backward estimation framework based on conditional normalizing flows. Conditional embeddings are generated using MLPs, Transformers, or Mamba-SSMs, and their efficacy is systematically evaluated for the first time in time-reversal and sequential prediction tasks. Furthermore, we introduce a kinetic-energy regularization term derived from optimal transport theory to mitigate over-parameterization and enhance training stability in deep flow models. Empirical evaluations on real-world scenarios—including autonomous driving and a COVID-19 SIR epidemiological model—demonstrate that the proposed method significantly outperforms traditional filters, achieving notably higher estimation accuracy under complex, non-Gaussian uncertainty distributions.
📝 Abstract
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.