Reliable absolute positioning remains a challenge in autonomous ground robotics, particularly in complex and dynamic real-world environments. The fusion of drift-free global positioning and precise local positioning is essential to ensure continuous and accurate localization in mobile ground robots. However, a benchmark dataset encompassing challenging scenarios for both absolute and relative positioning is still lacking, which limits further research and comprehensive evaluation of fusion-based Simultaneous Localization and Mapping (SLAM) methods for autonomous ground robots. To fill this gap, we introduce a ground robot dataset for multi-sensor navigation in diverse environments. All sensors are well calibrated, and Global Navigation Satellite System (GNSS), Inertial Measurement Unit (IMU), camera, and Light Detection and Ranging (LiDAR) measurements are hardware-synchronized. Furthermore, several auxiliary sensors are also included in our system, which are often overlooked in existing datasets but may be vital in certain applications. We perform data acquisition in a variety of challenging environments, both outdoors and indoors. In outdoor scenarios, ground truth is provided by a high-level integrated navigation system, while in indoor environments, it is obtained using a motion capture system. We evaluate the positioning performance of several baseline algorithms on our dataset, and the results show that current methods need further improvement in specific challenging scenarios. To advance relevant research, we make the dataset and associated tools publicly available. The project can be accessed at https://github.com/lizhipro/MSN-DE.git .

Orientation estimation based on magnetic-inertial measurement units is popular in fields, such as robotics, aerospace, and drones. However, the magnetometer is susceptible to external magnetic field interference, which significantly reduces the accuracy of state estimates. This article advances the partial-state updating extended Kalman filter (EKF) and proposes the partial-state updating optimization and the separate partial-state updating optimization to keep some vulnerable states unaffected by certain measurements full of gross error. These two algorithms are then applied to magnetic-inertial orientation estimation to avoid the effects of magnetic interference on the level angles and sensor biases. Simulation and experimental results demonstrate that, compared with the traditional optimization, the proposed algorithms are totally immune to the magnetic interference on the level angles and sensors' biases and have better convergence than the partial-state updating EKF, especially in scenarios with large initial orientation errors.

Pedestrian navigation systems (PNSs) based on inertial measurement units (IMUs) are popular for various applications, including but not limited to human motion tracking, emergency response, and medical monitoring. However, the inertial navigation system (INS) typically suffers from cumulative error over time due to sensor noise and bias drift. In this study, a pedestrian navigation scheme is proposed with dual commercial microelectromechanical systems (MEMSs)-based IMUs mounted on one lower limb, one shank-mounted, and the other foot-mounted. The kinematic constraints are constructed based on the biomechanical relationship, where the lower limb is assumed to be a kinematic chain with two rigid segments. The global observability of the system is analyzed to demonstrate the improvement in estimation accuracy introduced by the kinematic constraints. Both simulation and real-world experiments were conducted to validate the positioning performance and motion-capturing capability of the shank-foot system. Compared to traditional zero velocity update (ZUPT) and the geometric constraint-based method, our proposed method reduces the average positioning errors by 23.2 %-84.4 % across all tests.

Continuous-time attitude estimation methods are becoming increasingly popular because they can be evaluated at any query time and offer many other advantages by expressing the attitude as a continuous function of time. Consequently, the representation of the continuous-time attitude trajectory becomes a critical issue. This paper introduces an attitude representation method using Chebyshev polynomials defined directly on the unit quaternion manifold. The attitude trajectory is parameterized as a cumulative product of exponential-map rotational components using Lie algebra coefficients of increasing frequency. This on-manifold formulation inherently guarantees unit-norm consistency and avoids the singularities associated with minimal three-parameter representations. A recursive strategy is adapted to derive the trajectory's time derivatives (angular velocity) and its Jacobians with respect to the coefficients, including extensions for navigation frame kinematics considering Earth's rotation. The representation is applied within a polynomial optimization framework for batch or window-based attitude estimation. Comprehensive simulations and experiments evaluate the method in the inertial-magnetic attitude estimation scenario. Results demonstrate that the proposed method exhibits superior convergence and robustness compared to the standard multiplicative Extended Kalman Filter, and achieves superior or comparable accuracy while offering substantial improvements in computational efficiency over other polynomial optimization methods.

Structure from Motion (SfM) is a critical task in computer vision, aiming to recover the 3D scene structure and camera motion from a sequence of 2D images. The recent pose-only imaging geometry decouples 3D coordinates from camera poses and demonstrates significantly better SfM performance through pose adjustment. Continuing the pose-only perspective, this paper explores the critical relationship between the scene structures, rotation and translation. Notably, the translation can be expressed in terms of rotation, allowing us to condense the imaging geometry representation onto the rotation manifold. A rotation-only optimization framework based on reprojection error is proposed for both two-view and multi-view scenarios. The experiment results demonstrate superior accuracy and robustness performance over the current state-of-the-art rotation estimation methods, even comparable to multiple bundle adjustment iteration results. Hopefully, this work contributes to even more accurate, efficient and reliable 3D visual computing.

Inertial navigation is a subject of motion sensing and motion computation, and the engineered inertial navigation systems (INS) are indispensable to acquire full motion knowledge of moving objects. This paper reviews the algorithmic research history of the strapdown inertial navigation system that dates to the early 1960s. The algorithmic history is excitingly found to be inter-weaved with advances of computers and the related astronautical orbit propagation field. Notably, four historical crossroads, including one we face now, are presented that had/would have far-reaching consequences upon the current/future INSs. Hopefully, this review constitutes a thought-provoking summary of the inertial navigation computation researches and would contribute to preparing us for the next-generation INSs of meter-level accuracy in future applications.

Inertial sensor-based human motion tracking technology has many applications, including but not limited to sports, cinematic rehabilitation, and gaming. Human pose estimation is highly sensitive to the accuracy of the IMU-joint vector, which is defined from the center of rotation (COR) of joints to the inertial measurement units (IMUs). The sensor measurement error, caused by soft tissue artifacts (STAs), and the joint motion substantially impact the IMU-joint calibration. This article proposes an IMU-joint calibration method based on measurement integrals that does not need the derivative of noisy IMU measurements for angular acceleration. A number of influencing factors such as the STAs noise, IMU-joint distance, and the joint angular velocity are investigated by simulations and real tests. The proposed method demonstrates not only better calibration accuracy but higher robustness than the state-of-the-art methods.

The good estimation consistency of Invariant Extended Kalman Filter (InEKF) is mainly attributed to its excellent trajectory-independent property. However, when the InEKF is applied to multi-source inertial-based navigation that coexists left-invariant and right-invariant observations, the observation matrix would be unavoidably trajectory-dependent and might lead to the degradation of estimation performance. This paper for the first time performs theoretical analyses on the covariance switch between the left error and the right error in multi-source inertial-based navigation. Furthermore, detailed realizations of the covariance switch-based InEKF are formulated in this work, which are lacked in previous works. Numerical simulations and experiments demonstrate that the covariance switch significantly reduces the attitude errors during the transient phase in contrast with the original method using the incompatible error definition.

Offline camera calibration techniques typically employ parametric or generic camera models. Selecting parametric models relies heavily on user experience, and an inappropriate camera model can significantly affect calibration accuracy. Meanwhile, generic calibration methods involve complex procedures and cannot provide traditional intrinsic parameters. This paper reveals a pose ambiguity in the pose solutions of generic calibration methods that irreversibly impacts subsequent pose estimation. A linear solver and a nonlinear optimization are proposed to address this ambiguity issue. Then a global optimization hybrid calibration method is introduced to integrate generic and parametric models together, which improves extrinsic parameter accuracy of generic calibration and mitigates overfitting and numerical instability in parametric calibration. Simulation and real-world experimental results demonstrate that the generic-parametric hybrid calibration method consistently excels across various lens types and noise contamination, hopefully serving as a reliable and accurate solution for camera calibration in complex scenarios.

Invariant extended Kalman filter (InEKF) possesses excellent trajectory-independent property and better consistency compared to conventional extended Kalman filter (EKF). However, when applied to scenarios involving both global-frame and body-frame observations, InEKF may fail to preserve its trajectory-independent property. This work introduces the concept of equivalence between error states and covariance matrices among different error-state Kalman filters, and shows that although InEKF exhibits trajectory independence, its covariance propagation is actually equivalent to EKF. A covariance transformation-based error-state Kalman filter (CT-ESKF) framework is proposed that unifies various error-state Kalman filtering algorithms. The framework gives birth to novel filtering algorithms that demonstrate improved performance in integrated navigation systems that incorporate both global and body-frame observations. Experimental results show that the EKF with covariance transformation outperforms both InEKF and original EKF in a representative INS/GNSS/Odometer integrated navigation system.

The lightweight Multi-state Constraint Kalman Filter (MSCKF) has been well-known for its high efficiency, in which the delayed update has been usually adopted since its proposal. This work investigates the immediate update strategy of MSCKF based on timely reconstructed 3D feature points and measurement constraints. The differences between the delayed update and the immediate update are theoretically analyzed in detail. It is found that the immediate update helps construct more observation constraints and employ more filtering updates than the delayed update, which improves the linearization point of the measurement model and therefore enhances the estimation accuracy. Numerical simulations and experiments show that the immediate update strategy significantly enhances MSCKF even with a small amount of feature observations.

The acquisition of attitude, velocity, and position is an essential task in the field of inertial navigation, achieved by integrating the measurements from inertial sensors. Recently, the ultra-precision inertial navigation computation has been tackled by the functional iteration approach (iNavFIter) that drives the non-commutativity errors almost to the computer truncation error level. This paper proposes a computationally efficient matrix formulation of the functional iteration approach, named the iNavFIter-M. The Chebyshev polynomial coefficients in two consecutive iterations are explicitly connected through the matrix formulation, in contrast to the implicit iterative relationship in the original iNavFIter. By so doing, it allows a straightforward algorithmic implementation and a number of matrix factors can be pre-calculated for more efficient computation. Numerical results demonstrate that the proposed iNavFIter-M algorithm is able to achieve the same high computation accuracy as the original iNavFIter does, at the computational cost comparable to the typical two-sample algorithm. The iNavFIter-M algorithm is also implemented on a FPGA board to demonstrate its potential in real time applications.

The goal of this paper is to solve the low-orbit pseudolite self-interference problem. The low-orbit pseudolite navigation signals will interference satellite navigation as they broadcast at the same frequency and same time. However, the low-orbit pseudolite also needs satellite navigation to get continuous and effective high-precision positioning. So, while effectively filtering the self-interference, the GNSS navigation signals need low distortion. In this paper, we propose an anti-self-interference method which ensures that GNSS navigation signals are not distorted. Specifically, the method uses the known characteristics of self-interference signals to establish an optimization problem. By solving this problem, self-interference filtering can be achieved without estimating the direction of satellite navigation signal and without the assistance of the receiver channel amplitude-frequency and phase-frequency characteristics. The simulation test results show that the algorithm can filter self-interference without additional distortion of the satellite navigation signals. The application test results show that, the algorithm can filter self-interference with high-precision carrier observation of the satellite navigation signal which statistical standard deviation is only 0.01 times of the carrier wavelength. The method could help in achieving high-precision satellite navigation and positioning of pseudolite terminals and providing high-precision position information for low-orbit pseudolites.

This paper proposes an innovative state estimation method for visual-inertial fusion based on Chebyshev polynomial optimization. Specifically, the pose is modeled as a Chebyshev polynomial of a certain order, and its time derivatives are used to calculate linear acceleration and angular velocity, which, along with inertial measurements, constitute dynamic constraints. This is coupled with a visual measurement model to construct a visual-inertial bundle adjustment formulation. Simulation and public dataset experiments show that the proposed method has better accuracy than the discrete-form preintegration method.

Space-time adaptive processing (STAP) is a classic anti-interference algorithm for satellite navigation. In engineering applications, the number of time-domain taps of STAP not only determines the anti-jamming performance, but also determines the FPGA logic resource required for engineering implementation. In order to reduce application costs, it is urgent to predict the minimum number of time-domain taps required to achieve specified anti-interference indicators, so as to select the lowest cost FPGA chip. Unlike traditional dimensionality reduction algorithms such as Multistage Wiener Filter (MSWF), this paper proposes a method for determining the minimum number of time-domain taps without digital sampling data. To provide such a method, this paper construct an optimization problem and a solution method that determines the minimum number of time-domain taps based on the amplitude-frequency and phase-frequency characteristics of the specific receiver channels. Moreover, this method use interference to noise ratio (INR) to estimated minimum number of time-domain taps, which ensure the minimum number meet anti-interference performance. Finally, this paper verifies the effectiveness of the method through simulation by collecting amplitude-frequency and phase-frequency characteristics of 30 sets channels, and engineering test with three 2-element space time anti-jamming receivers.

The defects of the traditional strapdown inertial navigation algorithms become well acknowledged and the corresponding enhanced algorithms have been quite recently proposed trying to mitigate both theoretical and algorithmic defects. In this paper, the analytical accuracy evaluation of both the traditional algorithms and the enhanced algorithms is investigated, against the true reference for the first time enabled by the functional iteration approach having provable convergence. The analyses by the help of MATLAB Symbolic Toolbox show that the resultant error orders of all algorithms under investigation are consistent with those in the existing literatures, and the enhanced attitude algorithm notably reduces error orders of the traditional counterpart, while the impact of the enhanced velocity algorithm on error order reduction is insignificant. Simulation results agree with analyses that the superiority of the enhanced algorithm over the traditional one in the body-frame attitude computation scenario diminishes significantly in the entire inertial navigation computation scenario, while the functional iteration approach possesses significant accuracy superiority even under sustained lowly dynamic conditions.

The lightweight Multi-state Constraint Kalman Filter (MSCKF) has been well-known for its high efficiency, in which the delayed update has been usually adopted since its proposal. This work investigates the immediate update strategy of MSCKF based on timely reconstructed 3D feature points and measurement constraints. The differences between the delayed update and the immediate update are theoretically analyzed in detail. It is found that the immediate update helps construct more observation constraints and employ more filtering updates than the delayed update, which improves the linearization point of the measurement model and therefore enhances the estimation accuracy. Numerical simulations and experiments show that the immediate update strategy significantly enhances MSCKF even with a small amount of feature observations.

Optimization-based visual-inertial simultaneous localization and mapping system (VI-SLAM) focuses on the establishment of the loss function using both inertial and visual constraints. Preintegration theory is commonly used to express inertial constraints, but it lacks the merging equation between keyframes, challenging VI-SLAM from culling and merging redundant keyframes. To address this, we establish an on-manifold preintegration merging theory, including the merging of preintegrated terms, noise covariance, and Jacobians for bias updating, which significantly improves the preintegration theory and provides theoretical support for the keyframe management function of VI-SLAM. Visual constraints are typically expressed using multiple view geometry with 3-D points optimized as scene structure parameters. However, the excessive dimensionality of the optimization parameters generated by 3-D points can lead to computational bottlenecks. Through the recent pose-only imaging geometry representation, we construct a lightweight optimization algorithm for SLAM that avoids the dimensional explosion in bundle adjustment. Based on the above, we propose a 3-D points-free SLAM optimizer. The proposed algorithms are validated on simulation, public datasets, and real-world experiments, and compared against advanced open-source systems, such as ORB-SLAM3 and VINS.

How to efficiently and accurately handle image matching outliers is a critical issue in two-view relative estimation. The prevailing RANSAC method necessitates that the minimal point pairs be inliers. This paper introduces a linear relative pose estimation algorithm for n $( n \geq 6$) point pairs, which is founded on the recent pose-only imaging geometry to filter out outliers by proper reweighting. The proposed algorithm is able to handle planar degenerate scenes, and enhance robustness and accuracy in the presence of a substantial ratio of outliers. Specifically, we embed the linear global translation (LiGT) constraint into the strategies of iteratively reweighted least-squares (IRLS) and RANSAC so as to realize robust outlier removal. Simulations and real tests of the Strecha dataset show that the proposed algorithm achieves relative rotation accuracy improvement of 2 $\sim$ 10 times in face of as large as 80% outliers.