CT-VIR: Continuous-Time Visual-Inertial-Ranging Fusion for Indoor Localization with Sparse Anchors

Visual-inertial navigation systems estimate six-degree-of-freedom motion by fusing visual and inertial data. Modern discrete-time methods with IMU preintegration provide strong accuracy and efficiency, but keyframe-based representations can be less flexible when residuals must be evaluated at arbitrary timestamps or when motion-dependent temporal resolution is needed. Continuous-time splines address this issue by representing the trajectory as a smooth temporal function, but uniformly spaced knots can under-represent rapid dynamics or over-parameterize static intervals. This letter proposes ASPIRE-VINS, a continuous-time VINS framework that combines adaptive knot placement (AKP), multi-resolution splines (MRS), and 3D measurement-space residuals (3D-MSR). AKP allocates knots according to local motion variation, MRS adds bounded local refinement in tangent space, and 3D-MSR provides bearing consistency by aligning transformed features with calibrated observation rays in 3D measurement space. Experiments show that ASPIRE-VINS achieves competitive or lower trajectory errors than the compared baselines, demonstrating the effectiveness of motion-adaptive continuous-time trajectory modeling under diverse motion and sensing conditions.

Accurate relative localization is critical for multi-robot cooperation. In robot groups, measurements from different robots arrive asynchronously and with clock time-offsets. Although Continuous-Time (CT) formulations have proved effective for handling asynchronous measurements in single-robot SLAM and calibration, extending CT methods to multi-robot settings faces great challenges in achieving high-accuracy, low-latency, and high-frequency performance. In particular, existing CT methods suffer from the inherent query-time delay of unclamped B-splines and high optimization latency. This paper proposes CT-RIO, a novel Continuous-Time Relative-Inertial Odometry framework. We adopt Clamped Non-Uniform B-splines (C-NUBS) to represent states, eliminating the query-time delay. We further augment C-NUBS with closed-form extension and shrinkage operations that preserve the spline shape, making it suitable for online estimation and enabling flexible knot management. This flexibility leads to the concept of a knot-keyknot strategy, which supports spline extension at high frequency while retaining sparse keyknots for adaptive relative motion modeling. We then formulate a reference-centric sliding-window relative localization problem that operates purely on relative kinematics and inter-robot constraints. To enable low-latency and high-frequency estimation, we decompose the tightly coupled optimization into robot-wise subproblems and solve them in parallel using asynchronous block coordinate descent. Extensive experiments show that CT-RIO converges from time-offsets as large as 264 ms to sub-millisecond within 3 s, and achieves RMSEs of 0.046 m and 1.8 degree. It consistently outperforms evaluated published methods, with improvements of up to 60% under high-speed motion.

This work introduces a hybrid deep learning approach integrated with an Unscented Kalman Filter (UKF) to enhance pose estimation accuracy in Visual-Inertial Odometry (VIO) for autonomous navigation. The proposed model employs a Vision Transformer (ViT) network to effectively capture temporal dependencies from inertial measurement unit (IMU) data and utilizes a Multiscale Convolutional Neural Network (MCNN) to learn optical flow-based motion cues from visual data. An adaptive sensor fusion module dynamically weights IMU and visual features by leveraging estimated uncertainty, thus improving robustness in diverse and challenging environmental conditions. Additionally, a novel uncertainty-aware loss function is proposed to explicitly incorporate prediction uncertainty into the learning process, enabling robust and accurate navigation under noisy, incomplete, or unreliable sensor inputs. Comprehensive evaluations of the KITTI dataset demonstrate that the proposed method significantly outperforms baseline approaches, achieving superior performance in terms of Absolute Trajectory Error (ATE) and Relative Pose Error (RPE). The lightweight and computationally efficient model processes data at 155 FPS on an NVIDIA A100 GPU, making it highly suitable for deployment in resource-constrained autonomous systems.