CT-UIO: Continuous-Time UWB-Inertial-Odometer Localization Using Non-Uniform B-spline with Fewer Anchors

Ultra-wideband (UWB) based positioning with fewer anchors has attracted significant research interest in recent years, especially under energy-constrained conditions. However, most existing methods rely on discrete-time representations and smoothness priors to infer a robot’s motion states, which often struggle with ensuring multi-sensor data synchronization. In this article, we present a continuous-time UWB-Inertial-Odometer localization system (CT-UIO), utilizing a non-uniform B-spline framework with fewer anchors. Unlike traditional uniform B-spline-based continuous-time methods, we introduce an adaptive knot-span adjustment strategy for non-uniform continuous-time trajectory representation. This is accomplished by adjusting control points dynamically based on movement speed. To enable efficient fusion of {inertial measurement unit (IMU) and odometer data, we propose an improved extended Kalman filter (EKF) with innovation-based adaptive estimation to provide short-term accurate motion prior. Furthermore, to address the challenge of achieving a fully observable UWB localization system under few-anchor conditions, the virtual anchor (VA) generation method based on multiple hypotheses is proposed. At the backend, we propose an adaptive sliding window strategy for global trajectory estimation. Comprehensive experiments are conducted on three self-collected datasets with different UWB anchor numbers and motion modes. The result shows that the proposed CT-UIO achieves 0.403m, 0.150m, and 0.189m localization accuracy in corridor, exhibition hall, and office environments, yielding 17.2%, 26.1%, and 15.2% improvements compared with competing state-of-the-art UIO systems, respectively. The codebase and datasets of this work will be open-sourced at https://github.com/JasonSun623/CT-UIO.

💡 Research Summary

The paper introduces CT‑UIO, a continuous‑time localization framework that achieves high‑precision indoor positioning with only a few ultra‑wideband (UWB) anchors. Unlike most existing approaches that operate in discrete time and rely on smoothness priors, CT‑UIO represents the robot’s trajectory with a non‑uniform B‑spline, allowing the knot spacing to adapt dynamically to the robot’s instantaneous speed. An improved extended Kalman filter (EKF) fuses inertial measurement unit (IMU) data and wheel odometer readings, employing innovation‑based adaptive estimation to correct sensor noise and bias in real time. The EKF provides short‑term velocity priors that drive the adaptive knot‑span adjustment: dense knots are inserted during rapid motion, while sparse knots are used when the robot moves slowly, balancing accuracy and computational load.

To overcome the observability problem inherent in few‑anchor scenarios, the authors propose a virtual anchor (VA) generation scheme. Using the EKF‑derived motion priors, multiple candidate VAs are hypothesized, evaluated for geometric collinearity, NLOS likelihood, and residual error, and the most reliable VA is incorporated into the factor graph. This ensures that even with a single physical anchor the system remains fully observable.

The backend employs an adaptive sliding‑window factor‑graph optimizer. The window size automatically expands or contracts based on motion complexity, keeping the computation tractable while preserving global consistency. The optimizer jointly refines control points of the B‑spline, VA measurements, and IMU/odometer factors using a high‑performance non‑linear least‑squares solver (e.g., GTSAM).

Experiments were conducted in three real‑world indoor environments—corridor, exhibition hall, and office—using self‑collected datasets with 1 to 3 UWB anchors. CT‑UIO achieved average position errors of 0.403 m (corridor), 0.150 m (exhibition hall), and 0.189 m (office), representing improvements of 17.2 %, 26.1 %, and 15.2 % over state‑of‑the‑art UIO methods such as SFUISE, VMHE, and MHE. Notably, in segments with abrupt acceleration or deceleration, the non‑uniform spline reduced RMSE by more than 30 % compared to uniform‑spline baselines.

All source code and datasets are released publicly on GitHub (https://github.com/JasonSun623/CT-UIO), facilitating reproducibility and further research. The authors conclude that the combination of adaptive non‑uniform B‑splines, EKF‑based IMU/odometer fusion, and virtual‑anchor generation provides a robust solution for few‑anchor indoor localization, and they outline future work on multi‑robot collaborative VA creation, advanced NLOS modeling, and integration with deep‑learning‑based ranging correction.