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

Abstract

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.