arXiv subjects

Yuanxin Wu

Publications and source records attributed to Yuanxin Wu.

At least 19 recordsLinked to original sources

arXiv2025

Towards Rotation-only Imaging Geometry: Rotation Estimation

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.

cs.CV↗

arXiv2025

CT-ESKF: A General Framework of Covariance Transformation-Based Error-State Kalman Filter

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.

eess.SY↗

arXiv2025

Generic Calibration: Pose Ambiguity/Linear Solution and Parametric-hybrid Pipeline

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.

cs.CV↗

arXiv2024

An Immediate Update Strategy of Multi-State Constraint Kalman Filter

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.

cs.RO↗

arXiv2024

Visual-inertial state estimation based on Chebyshev polynomial optimization

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.

cs.RO↗

arXiv2024

Investigation of Enhanced Inertial Navigation Algorithms by Functional Iteration

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.

cs.RO↗

arXiv2024

Linear Relative Pose Estimation Founded on Pose-only Imaging Geometry

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.

cs.CV↗

arXiv2023

Clifford Algebra-Based Iterated Extended Kalman Filter with Application to Low-Cost INS/GNSS Navigation

The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial attitude, this work generalizes the previously proposed trident quaternion within the framework of Clifford algebra to represent the extended pose, IMU biases and lever arms on the Lie group. Consequently, a quasi-group-affine system is established for the low-cost INS/GNSS integrated navigation system, and the right-error Clifford algebra-based EKF (Clifford-RQEKF) is accordingly developed. The iterated filtering approach is further applied to significantly improve the performances of the Clifford-RQEKF and the previously proposed trident quaternion-based EKFs. Numerical simulations and experiments show that all iterated filtering approaches fulfill the fast and global convergence without the prior attitude information, whereas the iterated Clifford-RQEKF performs much better than the others under especially large IMU biases.

eess.SY↗

arXiv2023

Inertial-based Navigation by Polynomial Optimization: Inertial-Magnetic Attitude Estimation

Inertial-based navigation refers to the navigation methods or systems that have inertial information or sensors as the core part and integrate a spectrum of other kinds of sensors for enhanced performance. Through a series of papers, the authors attempt to explore information blending of inertial-based navigation by a polynomial optimization method. The basic idea is to model rigid motions as finite-order polynomials and then attacks the involved navigation problems by optimally solving their coefficients, taking into considerations the constraints posed by inertial sensors and others. In the current paper, a continuous-time attitude estimation approach is proposed, which transforms the attitude estimation into a constant parameter determination problem by the polynomial optimization. Specifically, the continuous attitude is first approximated by a Chebyshev polynomial, of which the unknown Chebyshev coefficients are determined by minimizing the weighted residuals of initial conditions, dynamics and measurements. We apply the derived estimator to the attitude estimation with the magnetic and inertial sensors. Simulation and field tests show that the estimator has much better stability and faster convergence than the traditional extended Kalman filter does, especially in the challenging large initial state error scenarios.

cs.RO↗

arXiv2022

iNavFIter-M: Matrix Formulation of Functional Iteration for Inertial Navigation Computation

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.

eess.SY↗

arXiv2022

ChevOpt: Continuous-time State Estimation by Chebyshev Polynomial Optimization

In this paper, a new framework for continuous-time maximum a posteriori estimation based on the Chebyshev polynomial optimization (ChevOpt) is proposed, which transforms the nonlinear continuous-time state estimation into a problem of constant parameter optimization. Specifically, the time-varying system state is represented by a Chebyshev polynomial and the unknown Chebyshev coefficients are optimized by minimizing the weighted sum of the prior, dynamics and measurements. The proposed ChevOpt is an optimal continuous-time estimation in the least squares sense and needs a batch processing. A recursive sliding-window version is proposed as well to meet the requirement of real-time applications. Comparing with the well-known Gaussian filters, the ChevOpt better resolves the nonlinearities in both dynamics and measurements. Numerical results of demonstrative examples show that the proposed ChevOpt achieves remarkably improved accuracy over the extended/unscented Kalman filters and extended batch/fixed-lag smoother, closes to the Cramer-Rao lower bound.

cs.RO↗

arXiv2021

A Pose-only Solution to Visual Reconstruction and Navigation

Visual navigation and three-dimensional (3D) scene reconstruction are essential for robotics to interact with the surrounding environment. Large-scale scenes and critical camera motions are great challenges facing the research community to achieve this goal. We raised a pose-only imaging geometry framework and algorithms that can help solve these challenges. The representation is a linear function of camera global translations, which allows for efficient and robust camera motion estimation. As a result, the spatial feature coordinates can be analytically reconstructed and do not require nonlinear optimization. Experiments demonstrate that the computational efficiency of recovering the scene and associated camera poses is significantly improved by 2-4 orders of magnitude. This solution might be promising to unlock real-time 3D visual computing in many forefront applications.

cs.CV↗

arXiv2021

Attitude Reconstruction from Inertial Measurement: Mitigating Runge Effect for Dynamic Applications

Time-equispaced inertial measurements are practically used as inputs for motion determination. Polynomial interpolation is a common technique of recovering the gyroscope signal but is subject to a fundamentally numerical stability problem due to the Runge effect on equispaced samples. This paper reviews the theoretical results of Runge phenomenon in related areas and proposes a straightforward borrowing-and-cutting (BAC) strategy to depress it. It employs the neighboring samples for higher-order polynomial interpolation but only uses the middle polynomial segment in the actual time interval. The BAC strategy has been incorporated into attitude computation by functional iteration, leading to accuracy benefit of several orders of magnitude under the classical coning motion. It would potentially bring significant benefits to the inertial navigation computation under sustained dynamic motions.

cs.RO↗

arXiv2021

A Trident Quaternion Framework for Inertial-based Navigation Part II: Error Models and Application to Initial Alignment

This work deals with error models for trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles. By linearizing the trident quaternion kinematic equation, the left and right trident quaternion error models are obtained, which are found to be equivalent to those derived from profound group affine. The two error models are used to design their corresponding extended Kalman filters (EKF), namely, the left-quaternion EKF (LQEKF) and the right-quaternion EKF (RQEKF). Simulations and field tests are conducted to evaluate their actual performances. Owing to the high estimation consistency, the L/RQEKF converge much faster in the static alignment than the traditional error model-based EKF, even under arbitrary large heading initialization. For the in-motion alignment, the L/RQEKF possess much larger convergence region than the traditional EKF does, although they still require the aid of attitude initialization so as to avoid large initial attitude errors.

cs.RO↗

arXiv2021

A Trident Quaternion Framework for Inertial-based Navigation Part I: Rigid Motion Representation and Computation

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This paper proposes a compact and elegant representation of the body's attitude, velocity and position, with the aid of a devised trident quaternion tool in which the position is accounted for by adding a second imaginary part to the dual quaternion. Eventually, the kinematics of strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion equation. In addition, the computation of this trident quaternion-based kinematic equation is implemented with the recently proposed functional iterative integration approach. Numerical results verify the analysis and show that incorporating the new representation into the functional iterative integration scheme achieves high inertial navigation computation accuracy as well.

cs.RO↗

arXiv2020

f2IMU-R: Pedestrian Navigation by Low-cost Foot-Mounted Dual IMUs and Inter-foot Ranging

Foot-mounted inertial sensors become popular in many indoor or GPS-denied applications, including but not limited to medical monitoring, gait analysis, soldier and first responder positioning. However, the foot-mounted inertial navigation relies largely on the aid of Zero Velocity Update (ZUPT) and has encountered inherent problems such as heading drift. This paper implements a pedestrian navigation system based on dual foot-mounted low-cost inertial measurement units (IMU) and inter-foot ultrasonic ranging. The observability analysis of the system is performed to investigate the roles of the ZUPT measurement and the foot-to-foot ranging measurement in improving the state estimability. A Kalman-based estimation algorithm is mechanized in the Earth frame, rather than in the common local-level frame, which is found to be effective in depressing the linearization error in Kalman filtering. An ellipsoid constraint in the Earth frame is also proposed to further restrict the height drift. Simulation and real field experiments show that the proposed method has better robustness and positioning accuracy (about 0.1-0.2% travelled distance) than the traditional pedestrian navigation schemes do.

cs.HC↗

arXiv2020

Segmenting Epipolar Line

Identifying feature correspondence between two images is a fundamental procedure in three-dimensional computer vision. Usually the feature search space is confined by the epipolar line. Using the cheirality constraint, this paper finds that the feature search space can be restrained to one of two or three segments of the epipolar line that are defined by the epipole and a so-called virtual infinity point.

cs.CV↗

arXiv2020

INS/Odometer Land Navigation by Accurate Measurement Modeling and Multiple-Model Adaptive Estimation

Land vehicle navigation based on inertial navigation system (INS) and odometers is a classical autonomous navigation application and has been extensively studied over the past several decades. In this work, we seriously analyze the error characteristics of the odometer (OD) pulses and investigate three types of odometer measurement models in the INS/OD integrated system. Specifically, in the pulse velocity model, a preliminary Kalman filter is designed to obtain accurate vehicle velocity from the accumulated pulses; the pulse increment model is accordingly obtained by integrating the pulse velocity; a new pulse accumulation model is proposed by augmenting the travelled distance into the system state. The three types of measurements, along with the nonhonolomic constraint (NHC), are implemented in the standard extended Kalman filter. In view of the motion-related pulse error characteristics, the multiple model adaptive estimation (MMAE) approach is exploited to further enhance the performance. Simulations and long-distance experiments are conducted to verify the feasibility and effectiveness of the proposed methods. It is shown that the standard pulse velocity measurement achieves the superior performance, whereas the accumulated pulse measurement is most favorable with the MMAE enhancement.

cs.RO↗