Robust Filtering -- Novel Statistical Learning and Inference Algorithms with Applications

TL;DR

This paper introduces robust nonlinear filtering algorithms that handle anomalies like outliers and missing data, extending to offline estimation and theoretical bounds, validated through diverse simulations and experiments.

Contribution

The work develops novel Bayesian filtering methods resilient to measurement abnormalities, with extensions to smoothing, theoretical analysis, and broad application scenarios.

Findings

Proposed filtering methods outperform standard approaches in noisy, abnormal data scenarios

Extensions to offline estimation and smoothing improve practical applicability

Theoretical bounds provide insights into estimation limits under anomalies

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.