Relative State Estimation perform mutually localization between two mobile agents undergoing six-degree-of-freedom motion. Based on the principle of circular motion, the estimation accuracy is sensitive to nonlinear rotations of the reference platform, particularly under large inter-platform distances. This phenomenon is even obvious for linearized kinematics, because cumulative linearization errors significantly degrade precision. In virtual reality (VR) applications, this manifests as substantial positional errors in 6-DoF controller tracking during rapid rotations of the head-mounted display. The linearization errors introduce drift in the estimate and render the estimator inconsistent. In the field of odometry, IMU preintegration is proposed as a kinematic observation to enable efficient relinearization, thus mitigate linearized error. Building on this theory, we propose dual preintegration, a novel observation integrating IMU preintegration from both platforms. This method serves as kinematic constraints for consecutive relative state and supports efficient relinearization. We also perform observability analysis of the state and analytically formulate the accordingly null space. Algorithm evaluation encompasses both simulations and real-world experiments. Multiple nonlinear rotations on the reference platform are simulated to compare the precision of the proposed method with that of other state-of-the-art (SOTA) algorithms. The field test compares the proposed method and SOTA algorithms in the application of VR controller tracking from the perspectives of bias observability, nonlinear rotation, and background texture. The results demonstrate that the proposed method is more precise and robust than the SOTA algorithms.

Recently, map representations based on radiance fields such as 3D Gaussian Splatting and NeRF, which excellent for realistic depiction, have attracted considerable attention, leading to attempts to combine them with SLAM. While these approaches can build highly realistic maps, large-scale SLAM still remains a challenge because they require a large number of Gaussian images for mapping and adjacent images as keyframes for tracking. We propose a novel 3D Gaussian Splatting SLAM method, VIGS SLAM, that utilizes sensor fusion of RGB-D and IMU sensors for large-scale indoor environments. To reduce the computational load of 3DGS-based tracking, we adopt an ICP-based tracking framework that combines IMU preintegration to provide a good initial guess for accurate pose estimation. Our proposed method is the first to propose that Gaussian Splatting-based SLAM can be effectively performed in large-scale environments by integrating IMU sensor measurements. This proposal not only enhances the performance of Gaussian Splatting SLAM beyond room-scale scenarios but also achieves SLAM performance comparable to state-of-the-art methods in large-scale indoor environments.

Recent works have combined monocular event camera and inertial measurement unit to estimate the $SE(3)$ trajectory. However, the asynchronicity of event cameras brings a great challenge to conventional fusion algorithms. In this paper, we present an asynchronous event-inertial odometry under a unified Gaussian Process (GP) regression framework to naturally fuse asynchronous data associations and inertial measurements. A GP latent variable model is leveraged to build data-driven motion prior and acquire the analytical integration capacity. Then, asynchronous event-based feature associations and integral pseudo measurements are tightly coupled using the same GP framework. Subsequently, this fusion estimation problem is solved by underlying factor graph in a sliding-window manner. With consideration of sparsity, those historical states are marginalized orderly. A twin system is also designed for comparison, where the traditional inertial preintegration scheme is embedded in the GP-based framework to replace the GP latent variable model. Evaluations on public event-inertial datasets demonstrate the validity of both systems. Comparison experiments show competitive precision compared to the state-of-the-art synchronous scheme.

This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. Inspired by recent advances in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on ${\mathbf{Gal}(3) \ltimes \mathfrak{gal}(3)}$, the left-trivialization of the tangent group of the Galilean group $\mathbf{Gal}(3)$. We define a novel preintegration error that geometrically couples the navigation states and the bias leading to lower linearization error. Our method improves in consistency compared to existing preintegration approaches which treat IMU biases as a separate state-space. Extensive validation against state-of-the-art methods, both in simulation and with real-world IMU data, implementation in the Lie++ library, and open-source code are provided.

This paper proposes a versatile graph-based lifelong localization framework, LiLoc, which enhances its timeliness by maintaining a single central session while improves the accuracy through multi-modal factors between the central and subsidiary sessions. First, an adaptive submap joining strategy is employed to generate prior submaps (keyframes and poses) for the central session, and to provide priors for subsidiaries when constraints are needed for robust localization. Next, a coarse-to-fine pose initialization for subsidiary sessions is performed using vertical recognition and ICP refinement in the global coordinate frame. To elevate the accuracy of subsequent localization, we propose an egocentric factor graph (EFG) module that integrates the IMU preintegration, LiDAR odometry and scan match factors in a joint optimization manner. Specifically, the scan match factors are constructed by a novel propagation model that efficiently distributes the prior constrains as edges to the relevant prior pose nodes, weighted by noises based on keyframe registration errors. Additionally, the framework supports flexible switching between two modes: relocalization (RLM) and incremental localization (ILM) based on the proposed overlap-based mechanism to select or update the prior submaps from central session. The proposed LiLoc is tested on public and custom datasets, demonstrating accurate localization performance against state-of-the-art methods. Our codes will be publicly available on https://github.com/Yixin-F/LiLoc.

LiDAR-Inertial Odometry (LIO) is typically implemented using an optimization-based approach, with the factor graph often being employed due to its capability to seamlessly integrate residuals from both LiDAR and IMU measurements. Conversely, a recent study has demonstrated that accurate LIO can also be achieved using a loosely-coupled method. Inspired by this advancements, we present a novel LIO method that leverages the recursive Bayes filter, solved via the Extended Kalman Filter (EKF) - herein referred to as LIO-EKF. Within LIO-EKF, prior and likelihood distributions are computed using IMU preintegration and scan matching between LiDAR and local map point clouds, and the pose, velocity, and IMU biases are updated through the EKF process. Through experiments with the Newer College dataset, we demonstrate that LIO-EKF achieves precise trajectory tracking and mapping. Its accuracy is comparable to that of the state-of-the-art methods in both tightly- and loosely-coupled methods.

Multi-sensor fusion is an effective way to enhance the positioning performance of autonomous underwater vehicles (AUVs). However, underwater multi-sensor fusion faces challenges such as heterogeneous frequency and dynamic availability of sensors. Traditional filter-based algorithms suffer from low accuracy and robustness when sensors become unavailable. The factor graph optimization (FGO) can enable multi-sensor plug-and-play despite data frequency. Therefore, we present an FGO-based strapdown inertial navigation system (SINS) and long baseline location (LBL) system tightly coupled navigation system (FGO-ILNS). Sensors such as Doppler velocity log (DVL), magnetic compass pilot (MCP), pressure sensor (PS), and global navigation satellite system (GNSS) can be tightly coupled with FGO-ILNS to satisfy different navigation scenarios. In this system, we propose a floating LBL slant range difference factor model tightly coupled with IMU preintegration factor to achieve unification of global position above and below water. Furthermore, to address the issue of sensor measurements not being synchronized with the LBL during fusion, we employ forward-backward IMU preintegration to construct sensor factors such as GNSS and DVL. Moreover, we utilize the marginalization method to reduce the computational load of factor graph optimization. Simulation and public KAIST dataset experiments have verified that, compared to filter-based algorithms like the extended Kalman filter and federal Kalman filter, as well as the state-of-the-art optimization-based algorithm ORB-SLAM3, our proposed FGO-ILNS leads in accuracy and robustness.

This document is in supplement to the paper titled "Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers", available at [1]. The purpose of this document is to show how IMU biases can be incorporated into the framework presented in [1], while maintaining the differential Sylvester equation form of the process model.

Relative state estimation using exteroceptive sensors suffers from limitations of the field of view (FOV) and false detection, that the proprioceptive sensor (IMU) data are usually engaged to compensate. Recently ego-motion constraint obtained by Inertial measurement unit (IMU) preintegration has been extensively used in simultaneous localization and mapping (SLAM) to alleviate the computation burden. This paper introduces an extended preintegration incorporating the IMU preintegration of two platforms to formulate the motion constraint of relative state. One merit of this analytic constraint is that it can be seamlessly integrated into the unified graph optimization framework to implement the relative state estimation in a high-performance real-time tracking thread, another point is a full smoother design with this precise constraint to optimize the 3D coordinate and refine the state for the refinement thread. We compare extensively in simulations the proposed algorithms with two existing approaches to confirm our outperformance. In the real virtual reality (VR) application design with the proposed estimator, we properly realize the visual tracking of the six degrees of freedom (6DoF) controller suitable for almost all scenarios, including the challenging environment with missing features, light mutation, dynamic scenes, etc. The demo video is at https://www.youtube.com/watch?v=0idb9Ls2iAM. For the benefit of the community, we make the source code public.

This paper introduces the united monocular-stereo features into a visual-inertial tightly coupled odometry (UMS-VINS) for robust pose estimation. UMS-VINS requires two cameras and a low-cost inertial measurement unit (IMU). The UMS-VINS is an evolution of VINS-FUSION, which modifies the VINS-FUSION from the following three perspectives. 1) UMS-VINS extracts and tracks features from the sub-pixel plane to achieve better positions of the features. 2) UMS-VINS introduces additional 2-dimensional features from the left and/or right cameras. 3) If the visual initialization fails, the IMU propagation is directly used for pose estimation, and if the visual-IMU alignment fails, UMS-VINS estimates the pose via the visual odometry. The performances on both public datasets and new real-world experiments indicate that the proposed UMS-VINS outperforms the VINS-FUSION from the perspective of localization accuracy, localization robustness, and environmental adaptability.