Real time filtering algorithms

TL;DR

The paper surveys nonlinear filtering across three principal paradigms—Kalman-type methods, Monte Carlo methods, and Yau-Yau PDE-based approaches—emphasizing their applicability to both continuous-time and discrete-time systems and the growing role of learning-based enhancements. It details classic and modern Kalman-type variants (EKF, UKF, CKF), optimization-driven filters, and multi-model hybrids, while also examining particle-filtering methods and the Feedback Particle Filter, along with the DMZ/Yau-Yau PDE-based framework for exact real-time filtering. A central theme is the integration of neural networks to augment or implement filtering algorithms, with two main approaches: hybrid model-driven/data-driven designs and end-to-end neural implementations of Yau-Yau, including convergence guarantees and potential to overcome the curse of dimensionality. The work highlights a trade-off landscape: Kalman-type filters offer real-time performance but lack universal nonlinear guarantees, Monte Carlo methods provide modeling flexibility at the expense of real-time feasibility in high dimensions, and the Yau-Yau approach—especially when combined with neural networks—promises rigorous convergence and scalability. This synthesis provides a roadmap toward unified, AI-augmented real-time nonlinear filtering for high-dimensional systems with theoretical guarantees and practical efficiency.

Abstract

This paper presents a systematic review of recent advances in nonlinear filtering algorithms, structured into three principal categories: Kalman-type methods, Monte Carlo methods, and the Yau-Yau algorithm. For each category, we provide a comprehensive synthesis of theoretical developments, algorithmic variants, and practical applications that have emerged in recent years. Importantly, this review addresses both continuous-time and discrete-time system formulations, offering a unified review of filtering methodologies across different frameworks. Furthermore, our analysis reveals the transformative influence of artificial intelligence breakthroughs on the entire nonlinear filtering field, particularly in areas such as learning-based filters, neural network-augmented algorithms, and data-driven approaches.