# Continuous-Time State Estimation Methods in Robotics: A Survey

arXiv: https://arxiv.org/abs/2411.03951 · HTML: https://mlsanity.com/paper/2411.03951/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2024.

## Built on by (most cited first, 10 of 10)

- [ADAPT: An Autonomous Forklift for Construction Site Operation](https://mlsanity.com/paper/2503.14331/) (2025)
- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations](https://mlsanity.com/paper/2506.06780/) (2025)
- [Continuous-Time Value Iteration for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2509.09135/) (2025)
- [Holistic Fusion: Task- and Setup-Agnostic Robot Localization and State Estimation with Factor Graphs](https://mlsanity.com/paper/2504.06479/) (2025)
- [From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning](https://mlsanity.com/paper/2503.05799/) (2025)
- [Unleashing the Power of Discrete-Time State Representation: Ultrafast Target-based IMU-Camera Spatial-Temporal Calibration](https://mlsanity.com/paper/2509.12846/) (2025)
- [A Novel Multi-Timescale Stability-Preserving Hierarchical Reinforcement Learning Controller Framework for Adaptive Control in High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2510.22420/) (2025)
- [Provably Efficient Reinforcement Learning in Continuous-Time Episodic MDPs with Poisson Decision Epochs](https://mlsanity.com/paper/2609.23127/) (2026)

## Abstract (arXiv)

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.