Despite their widespread use in determining system attitude, Micro-Electro-Mechanical Systems (MEMS) Attitude and Heading Reference Systems (AHRS) are limited by sensor measurement biases. This paper introduces a method called MAgnetometer and GYroscope Calibration (MAGYC), leveraging three-axis angular rate measurements from an angular rate gyroscope to estimate both the hard- and soft-iron biases of magnetometers as well as the bias of gyroscopes. We present two implementation methods of this approach based on batch and online incremental factor graphs. Our method imposes fewer restrictions on instrument movements required for calibration, eliminates the need for knowledge of the local magnetic field magnitude or instrument's attitude, and facilitates integration into factor graph algorithms for Smoothing and Mapping frameworks. We validate the proposed methods through numerical simulations and in-field experimental evaluations with a sensor onboard an underwater vehicle. By implementing the proposed method in field data of a seafloor mapping dive, the dead reckoning-based position estimation error of the underwater vehicle was reduced from 10% to 0.5% of the distance traveled.

Most existing visual-inertial odometry (VIO) initialization methods rely on accurate pre-calibrated extrinsic parameters. However, during long-term use, irreversible structural deformation caused by temperature changes, mechanical squeezing, etc. will cause changes in extrinsic parameters, especially in the rotational part. Existing initialization methods that simultaneously estimate extrinsic parameters suffer from poor robustness, low precision, and long initialization latency due to the need for sufficient translational motion. To address these problems, we propose a novel VIO initialization method, which jointly considers extrinsic orientation and gyroscope bias within the normal epipolar constraints, achieving higher precision and better robustness without delayed rotational calibration. First, a rotation-only constraint is designed for extrinsic orientation and gyroscope bias estimation, which tightly couples gyroscope measurements and visual observations and can be solved in pure-rotation cases. Second, we propose a weighting strategy together with a failure detection strategy to enhance the precision and robustness of the estimator. Finally, we leverage Maximum A Posteriori to refine the results before enough translation parallax comes. Extensive experiments have demonstrated that our method outperforms the state-of-the-art methods in both accuracy and robustness while maintaining competitive efficiency.

Accurate and robust initialization is essential for Visual-Inertial Odometry (VIO), as poor initialization can severely degrade pose accuracy. During initialization, it is crucial to estimate parameters such as accelerometer bias, gyroscope bias, initial velocity, and gravity, etc. The IMU sensor requires precise estimation of gyroscope bias because gyroscope bias affects rotation, velocity and position. Most existing VIO initialization methods adopt Structure from Motion (SfM) to solve for gyroscope bias. However, SfM is not stable and efficient enough in fast motion or degenerate scenes. To overcome these limitations, we extended the rotation-translation-decoupling framework by adding new uncertainty parameters and optimization modules. First, we adopt a gyroscope bias optimizer that incorporates probabilistic normal epipolar constraints. Second, we fuse IMU and visual measurements to solve for velocity, gravity, and scale efficiently. Finally, we design an additional refinement module that effectively diminishes gravity and scale errors. Extensive initialization tests on the EuRoC dataset show that our method reduces the gyroscope bias and rotation estimation error by an average of 16% and 4% respectively. It also significantly reduces the gravity error, with an average reduction of 29%.

As the current initialization method in the state-of-the-art Stereo Visual-Inertial SLAM framework, ORB-SLAM3 has limitations. Its success depends on the performance of the pure stereo SLAM system and is based on the underlying assumption that pure visual SLAM can accurately estimate the camera trajectory, which is essential for inertial parameter estimation. Meanwhile, the further improved initialization method for ORB-SLAM3, known as Stereo-NEC, is time-consuming due to applying keypoint tracking to estimate gyroscope bias with normal epipolar constraints. To address the limitations of previous methods, this paper proposes a method aimed at enhancing translation accuracy during the initialization stage. The fundamental concept of our method is to improve the translation estimate with a 3 Degree-of-Freedom (DoF) Bundle Adjustment (BA), independently, while the rotation estimate is fixed, instead of using ORB-SLAM3's 6-DoF BA. Additionally, the rotation estimate will be updated by considering IMU measurements and gyroscope bias, unlike ORB-SLAM3's rotation, which is directly obtained from stereo visual odometry and may yield inferior results when operating in challenging scenarios. We also conduct extensive evaluations on the public benchmark, the EuRoC dataset, demonstrating that our method excels in accuracy.

We propose an accurate and robust initialization approach for stereo visual-inertial SLAM systems. Unlike the current state-of-the-art method, which heavily relies on the accuracy of a pure visual SLAM system to estimate inertial variables without updating camera poses, potentially compromising accuracy and robustness, our approach offers a different solution. We realize the crucial impact of precise gyroscope bias estimation on rotation accuracy. This, in turn, affects trajectory accuracy due to the accumulation of translation errors. To address this, we first independently estimate the gyroscope bias and use it to formulate a maximum a posteriori problem for further refinement. After this refinement, we proceed to update the rotation estimation by performing IMU integration with gyroscope bias removed from gyroscope measurements. We then leverage robust and accurate rotation estimates to enhance translation estimation via 3-DoF bundle adjustment. Moreover, we introduce a novel approach for determining the success of the initialization by evaluating the residual of the normal epipolar constraint. Extensive evaluations on the EuRoC dataset illustrate that our method excels in accuracy and robustness. It outperforms ORB-SLAM3, the current leading stereo visual-inertial initialization method, in terms of absolute trajectory error and relative rotation error, while maintaining competitive computational speed. Notably, even with 5 keyframes for initialization, our method consistently surpasses the state-of-the-art approach using 10 keyframes in rotation accuracy.

Visual-inertial SLAM is crucial in various fields, such as aerial vehicles, industrial robots, and autonomous driving. The fusion of camera and inertial measurement unit (IMU) makes up for the shortcomings of a signal sensor, which significantly improves the accuracy and robustness of localization in challenging environments. This article presents PLE-SLAM, an accurate and real-time visual-inertial SLAM algorithm based on point-line features and efficient IMU initialization. First, we use parallel computing methods to extract features and compute descriptors to ensure real-time performance. Adjacent short line segments are merged into long line segments, and isolated short line segments are directly deleted. Second, a rotation-translation-decoupled initialization method is extended to use both points and lines. Gyroscope bias is optimized by tightly coupling IMU measurements and image observations. Accelerometer bias and gravity direction are solved by an analytical method for efficiency. To improve the system's intelligence in handling complex environments, a scheme of leveraging semantic information and geometric constraints to eliminate dynamic features and A solution for loop detection and closed-loop frame pose estimation using CNN and GNN are integrated into the system. All networks are accelerated to ensure real-time performance. The experiment results on public datasets illustrate that PLE-SLAM is one of the state-of-the-art visual-inertial SLAM systems.

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.

Visual-inertial initialization can be classified into joint and disjoint approaches. Joint approaches tackle both the visual and the inertial parameters together by aligning observations from feature-bearing points based on IMU integration then use a closed-form solution with visual and acceleration observations to find initial velocity and gravity. In contrast, disjoint approaches independently solve the Structure from Motion (SFM) problem and determine inertial parameters from up-to-scale camera poses obtained from pure monocular SLAM. However, previous disjoint methods have limitations, like assuming negligible acceleration bias impact or accurate rotation estimation by pure monocular SLAM. To address these issues, we propose EDI, a novel approach for fast, accurate, and robust visual-inertial initialization. Our method incorporates an Error-state Kalman Filter (ESKF) to estimate gyroscope bias and correct rotation estimates from monocular SLAM, overcoming dependence on pure monocular SLAM for rotation estimation. To estimate the scale factor without prior information, we offer a closed-form solution for initial velocity, scale, gravity, and acceleration bias estimation. To address gravity and acceleration bias coupling, we introduce weights in the linear least-squares equations, ensuring acceleration bias observability and handling outliers. Extensive evaluation on the EuRoC dataset shows that our method achieves an average scale error of 5.8% in less than 3 seconds, outperforming other state-of-the-art disjoint visual-inertial initialization approaches, even in challenging environments and with artificial noise corruption.

The miniaturization of inertial measurement units (IMUs) facilitates their widespread use in a growing number of application domains. Orientation estimation is a prerequisite for most further data processing steps in inertial motion tracking, such as position/velocity estimation, joint angle estimation, and 3D visualization. Errors in the estimated orientations severely affect all further processing steps. Recent systematic comparisons of existing algorithms show that out-of-the-box accuracy is often low and that application-specific tuning is required to obtain high accuracy. In the present work, we propose and extensively evaluate a quaternion-based orientation estimation algorithm that is based on a novel approach of filtering the acceleration measurements in an almost-inertial frame and that includes extensions for gyroscope bias estimation and magnetic disturbance rejection, as well as a variant for offline data processing. In contrast to all existing work, we perform an extensive evaluation, using a large collection of publicly available datasets and eight literature methods for comparison. The proposed method consistently outperforms all literature methods and achieves an average RMSE of 2.9{\deg}, while the errors obtained with literature methods range from 5.3{\deg} to 16.7{\deg}. Since the evaluation was performed with one single fixed parametrization across a very diverse dataset collection, we conclude that the proposed method provides unprecedented out-of-the-box performance for a broad range of motions, sensor hardware, and environmental conditions. This gain in orientation estimation accuracy is expected to advance the field of IMU-based motion analysis and provide performance benefits in numerous applications. The provided open-source implementation makes it easy to employ the proposed method.

In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group affine and its error state model should be trajectory-independent. Moreover, with such trajectory-independent error state model, the linear Kalman filter is still effective for large initialization errors. However, the measurement model of the traditional MEKF is dependent on the attitude prediction, which is therefore trajectory-dependent. This is also the main reason why the performance of traditional MEKF is degraded for large initialization errors. Through substitution of the attitude prediction related term with the vector observation in body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, the MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations and field test of attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models.