Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation

TL;DR

This paper explores the use of conditional normalizing flows for joint state and parameter estimation in nonlinear systems, demonstrating their effectiveness in complex, real-world applications like autonomous driving and COVID-19 modeling.

Contribution

It introduces the application of conditional normalizing flows with various architectures and a kinetic loss to improve joint estimation, addressing overparameterization and complex distribution handling.

Findings

Flows with kinetic loss reduce overparameterization.

Conditional flows outperform traditional filters in nonlinear, multi-modal scenarios.

Effective in real-world applications like autonomous driving and epidemiology.

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.