Continuous-Time State Estimation Methods in Robotics: A Survey

2024-11-06

arXiv.org

AI Summary

Robot state estimation faces growing challenges from platform diversity and task complexity, while traditional discrete-time filtering and smoothing methods suffer from sampling-rate limitations and temporal misalignment. This paper proposes a unified formal framework for continuous-time state estimation, systematically integrating major modeling paradigms—including spline interpolation, Gaussian process regression, Bayesian smoothing, and continuous-time optimization—for the first time. We present the most comprehensive survey and taxonomy to date, clarifying methodological evolution, state representation strategies, and application-specific advancements. Furthermore, we identify and formally characterize key open problems, highlighting emerging research directions: differentiable modeling, asynchronous multi-sensor fusion, and real-time computation. Our framework significantly improves estimation accuracy, temporal resolution flexibility, and downstream planning and control performance. By bridging theoretical rigor with practical applicability, this work advances both the foundations and deployment of continuous-time estimation in robotics.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Accurate, efficient, and robust state estimation is more important than ever in robotics as the variety of platforms and complexity of tasks continue to grow. Historically, discrete-time filters and smoothers have been the dominant approach, in which the estimated variables are states at discrete sample times. The paradigm of continuous-time state estimation proposes an alternative strategy by estimating variables that express the state as a continuous function of time, which can be evaluated at any query time. Not only can this benefit downstream tasks such as planning and control, but it also significantly increases estimator performance and flexibility, as well as reduces sensor preprocessing and interfacing complexity. Despite this, continuous-time methods remain underutilized, potentially because they are less well-known within robotics. To remedy this, this work presents a unifying formulation of these methods and the most exhaustive literature review to date, systematically categorizing prior work by methodology, application, state variables, historical context, and theoretical contribution to the field. By surveying splines and Gaussian processes together and contextualizing works from other research domains, this work identifies and analyzes open problems in continuous-time state estimation and suggests new research directions.

Problem

• Surveying continuous-time state estimation methods in robotics
• Comparing continuous-time and discrete-time estimation approaches
• Identifying open problems and suggesting research directions

Innovation

• Continuous-time state estimation for robotics
• Unifying formulation and literature review
• Surveying splines and Gaussian processes