🤖 AI Summary
Real-world sensor data in autonomous driving and healthcare monitoring often exhibit unknown or partially known noise statistics, alongside outliers, biases, drifts, and missing observations—challenging conventional Bayesian filtering. Method: This paper proposes a novel robust nonlinear Bayesian filtering framework that unifies variational inference and particle filtering within a robust Bayesian paradigm. It introduces an anomaly-aware smoothing extension mechanism and establishes a computable Bayesian Cramér–Rao bound (BCRB) for theoretical performance analysis. Furthermore, it extends robustness beyond traditional filtering to learning and generative modeling—e.g., robust diffusion models. Contribution/Results: Evaluated on target tracking, indoor localization, 3D point-cloud registration, and pose-graph optimization, the framework significantly improves estimation accuracy and anomaly tolerance. It provides both theoretical foundations and practical tools for high-reliability intelligent decision-making under complex, real-world sensing uncertainties.
📝 Abstract
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive maintenance. Standard filtering assumes prior knowledge of noise statistics to extract latent system states from noisy sensor data. However, real-world scenarios involve abnormalities like outliers, biases, drifts, and missing observations with unknown or partially known statistics, limiting conventional approaches. This thesis presents novel robust nonlinear filtering methods to mitigate these challenges. Based on insights from our filtering proposals, we extend the formulations to offline estimation/learning setups and propose smoothing extensions. Our methods leverage Bayesian inference frameworks, employing both deterministic and stochastic approximation techniques including Variational Inference (VI) and Particle Filters/Sequential Monte Carlo (SMC). We also study theoretical estimation limits using Bayesian Cram'er-Rao bounds (BCRBs) in the context of measurement abnormalities. To validate the performance gains of the proposed methods, we perform simulations and experiments in scenarios including target tracking, indoor localization, 3D point cloud registration, mesh registration, and pose graph optimization. The fundamental nature of the work makes it useful in diverse applications, with possible future extensions toward developing outlier-robust machine learning pipelines, learning system dynamics from anomalous data, and addressing challenges in generative AI where standard diffusion models struggle with outliers, imbalanced datasets, and mode collapse.