Rotation Estimation Research Articles

Spin-orbit alignment in very low mass tight binaries: results for the 2MASS J0746425+200032AB and 2MASS J1314203+132001AB systems using spectroscopic and optically derived rotational estimates

Context. Constraining the coplanarity status of very low mass (VLM) tight binary systems provides valuable information towards understanding the dominant mechanisms in star and planetary formation at the lower end of the initial mass function. Aims. We sought to constrain the v sin i degeneracies of two nearby tight VLM binary systems, 2MASS J0746+20AB and 2MASS J1314+13AB, by independently determining each companion’s rotational period and so characterize each system’s spin-orbit alignment. Methods. Long observational baseline high cadence I band photometry data were obtained for both systems using the Galway Ultra Fast Imager (GUFI) on the Mount Graham International Observatory’s Vatican Advanced Technology Telescope. Previously known rotational periods determined in other passbands were used as a basis for recovering additional periodic modulations in the time-series data. Results. Using the known rotational period of 3.32 hours for 2MASS J0746425+200032A, we recovered an underlying periodic modulation of 2.14 ± 0.11 hours, which we associate with 2MASS J0746425+200032B. Breaking each components’ v sin i corresponds to equatorial inclination angles of 32 ± 4 degrees and 37 ± 4 degrees for components A & B respectively. We recover a weaker 2.06 ± 0.05 hours modulation separate from the known 3.79 hour signature for J1314203+132001B, which we associate with J1314203+132001A. We place a lower limit on J1314203+132001A’s equatorial inclination angle to be in the range of 24.5−3+3.5 degrees, which deviates from the system’s orbital plane previously determined to be 49.34−0.23+0.28 degrees. Conclusions. We confirm long term, consistent periodic modulations from both binary systems and report the first definitive rotational period for J1314203+132001A of 2.06 ± 0.05 hours, in addition to coplanarity to within 10 degrees in the spin-orbit alignment of the 2MASS J0746425+200032AB system. The lack of separate v sin i values for the 2MASS J1314203+132001AB system limits a definitive assessment but best estimates suggest coplanarity to be unlikely.

Performance improvement of Grid-Connected Wind Energy Conversion System through Definite Time Horizon Control and MPPT based on Adaptive Observers

This research work investigates the implementation of Definite Time Horizon Control (DTHC) through an observer in a grid-connected Wind Energy Conversion System (WECS) equipped with a Permanent Magnet Synchronous Generator (PMSG). The main objective is to achieve sensorless Maximum Power Point Tracking (MPPT). To achieve this goal, mechanical rotational speed and torque estimates are exploited from an adaptive nonlinear observer. In addition, this work explores how the DTHC improves on the MPPT technique, enabling faster and more accurate tracking of the maximum power point. The proposed controller, unlike traditional non-linear controllers, rapidly stabilizes the WECS, tracking reference trajectories in a short, pre-determined period of time. Indeed, it demonstrates robustness in the face of unpredictable WECS parameters, adapting to variations thanks to a robust control design. Mathematical demonstrations of the defined time horizon stability and the resilience of the suggested WECS controllers are detailed in this investigation. This DTHC method improves rotor speed control, enabling more efficient sensorless MPPT. It contributes to improved WECS performance for following dynamic references and enhances adaptability against unpredictable parameters. In addition, it provides sophisticated control capabilities for the grid connected converter, improving the smoothness and efficiency of electrical energy injection.

Certifiably optimal rotation and pose estimation based on the Cayley map

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.

Loss-tolerant and supersensitive angular rotation estimation based on quantum-enhanced interferometers

Loss-tolerant and supersensitive angular rotation estimation based on quantum-enhanced interferometers

Detection of diffusion anisotropy from an individual short particle trajectory

In parallel with advances in microscale imaging techniques, the fields of biology and materials science have focused on precisely extracting particle properties based on their diffusion behavior. Although the majority of real-world particles exhibit anisotropy, their behavior has been studied less than that of isotropic particles. In this study, we introduce a method for estimating the diffusion coefficients of individual anisotropic particles using short-trajectory data on the basis of a maximum likelihood framework. Traditional estimation techniques often use mean-squared displacement (MSD) values or other statistical measures that inherently remove angular information. Instead, we treated the angle as a latent variable and used belief propagation to estimate it while maximizing the likelihood using the expectation-maximization algorithm. Compared to conventional methods, this approach facilitates better estimation of shorter trajectories and faster rotations, as confirmed by numerical simulations and experimental data involving bacteria and quantum rods. Additionally, we performed an analytical investigation of the limits of detectability of anisotropy and provided guidelines for the experimental design. In addition to serving as a powerful tool for analyzing complex systems, the proposed method will pave the way for applying maximum likelihood methods to more complex diffusion phenomena. Published by the American Physical Society 2024

A Novel Method and System Implementation for Precise Estimation of Single-Axis Rotational Angles.

Accurately estimating single-axis rotational angle changes is crucial in many high-tech domains. However, traditional angle measurement techniques are often constrained by sensor limitations and environmental interferences, resulting in significant deficiencies in precision and stability. Moreover, current methodologies typically rely on fixed-axis rotation models, leading to substantial discrepancies between measured and actual angles due to axis misalignment. To address these issues, this paper proposes an innovative method for single-axis rotational angle estimation. It introduces a calibration technique for installation errors between inertial measurement units and the overall measurement system, effectively translating dynamic rotational inertial outputs to system enclosure outputs. Subsequently, the method employs triaxial accelerometers combined with zero-velocity detection technology to estimate the rotation axis position. Finally, it delves into analyzing the relationship between quaternion and axis-angle, aimed at reducing noise interference for precise rotational angle estimation. Based on this proposed methodology, a Low-Cost, a High Accuracy Measurement System (HAMS) integrating sensor fusion was designed and implemented. Experimental results demonstrate static measurement errors below ±0.15° and dynamic measurement errors below ±0.5° within a ±180° range.

9D Rotation Representation-SVD Fusion with Deep Learning for Unconstrained Head Pose Estimation

Abstract Accurately estimating human head pose poses a significant challenge across various application domains. To address the inherent limitations of previous approaches, this research proposes an unconstrained head pose estimation strategy. The method combines deep learning with rotation matrices, utilizing nine-dimensional vectors output by the neural network, which are projected back to rotation matrices in SO (3) space through singular value decomposition. This ensures both the smoothness and uniqueness of the rotation representation. The approach demonstrates distinct advantages in handling the rotation estimation task, particularly when the rotated representation is used as the model output. It not only avoids the discontinuity and double-coverage issues associated with prior methods but also enhances the stability of the representation in high-dimensional space, thereby improving the learning process. Additionally, the geodesic loss function is incorporated to train the network. The proposed strategy surpasses previous state-of-the-art methods, as evidenced by experiments conducted on the AFLW2000 and BIWI datasets.

A method for estimating the rotation errors of BDS broadcast ephemeris using global satellite laser ranging data

Abstract The BeiDou-3 Navigation Satellite System (BDS-3) generates navigation messages from a regional ground tracking network and inter-satellite links, relying on predicted station coordinates and Earth rotation parameters (ERPs). These procedures, however, may lead to orientation errors in the broadcast ephemeris, termed constellation rotation errors. Traditionally, these errors are monitored through Helmert transformation analysis comparing broadcast and post-processed orbits, a method that highlights discrepancies between the global navigation satellite system (GNSS) terrestrial reference frame (TRF) and the International TRF (ITRF) but suffers from a two-week evaluation delay. This study proposes a near real-time approach for estimating constellation rotation errors using high-precision satellite laser ranging (SLR) data, representing the difference between GNSS TRF and ITRF through the International laser ranging service TRF. The impact of SLR data quantity and distribution on rotation estimation accuracy is investigated, and the effectiveness of this method on BDS-3 orbits with ERP-induced orientation deficiencies is validated. Results show that the root mean square of broadcast orbit errors and the orbit user ranging error reduce from 0.8/0.7/0.2 m to 0.1/0.1/0.1 m, respectively. This demonstrates the method’s capability for real-time monitoring and correcting orientation errors within BDS-3 navigation messages.

Automated estimation of thoracic rotation in chest X-ray radiographs: a deep learning approach for enhanced technical assessment.

This study aims to develop an automated approach for estimating the vertical rotation of the thorax, which can be used to assess the technical adequacy of chest X-ray radiographs (CXRs). Total 800 chest radiographs were used to train and establish segmentation networks for outlining the lungs and spine regions in chest X-ray images. By measuring the widths of the left and right lungs between the central line of segmented spine and the lateral sides of the segmented lungs, the quantification of thoracic vertical rotation was achieved. Additionally, a life-size, full body anthropomorphic phantom was employed to collect chest radiographic images under various specified rotation angles for assessing the accuracy of the proposed approach. The deep learning networks effectively segmented the anatomical structures of the lungs and spine. The proposed approach demonstrated a mean estimation error of less than 2° for thoracic rotation, surpassing existing techniques and indicating its superiority. The proposed approach offers a robust assessment of thoracic rotation and presents new possibilities for automated image quality control in chest X-ray examinations. This study presents a novel deep-learning-based approach for the automated estimation of vertical thoracic rotation in chest X-ray radiographs. The proposed method enables a quantitative assessment of the technical adequacy of CXR examinations and opens up new possibilities for automated screening and quality control of radiographs.

Unsupervised denoising of the non-invasive fetal electrocardiogram with sparse domain Kalman filtering and vectorcardiographic loop alignment

Objective. Even though the electrocardiogram (ECG) has potential to be used as a monitoring or diagnostic tool for fetuses, the use of non-invasive fetal ECG is complicated by relatively high amounts of noise and fetal movement during the measurement. Moreover, machine learning-based solutions to this problem struggle with the lack of clean reference data, which is difficult to obtain. To solve these problems, this work aims to incorporate fetal rotation correction with ECG denoising into a single unsupervised end-to-end trainable method. Approach. This method uses the vectorcardiogram (VCG), a three-dimensional representation of the ECG, as an input and extends the previously introduced Kalman-LISTA method with a Kalman filter for the estimation of fetal rotation, applying denoising to the rotation-corrected VCG. Main results. The resulting method was shown to outperform denoising auto-encoders by more than 3 dB while achieving a rotation tracking error of less than 33∘. Furthermore, the method was shown to be robust to a difference in signal to noise ratio between electrocardiographic leads and different rotational velocities. Significance. This work presents a novel method for the denoising of non-invasive abdominal fetal ECG, which may be trained unsupervised and simultaneously incorporates fetal rotation correction. This method might prove clinically valuable due the denoised fetal ECG, but also due to the method’s objective measure for fetal rotation, which in turn might have potential for early detection of fetal complications.

Anchor-Based Multi-Scale Deep Grasp Pose Detector With Encoded Angle Regression

An intelligent robot grasping system should be able to automatically grasp a variety of objects that have never been seen, which requires accurate and efficient grasp pose detection. To this end, we propose a deep grasp detector designed for the robot equipped with a parallel gripper. The deep model consumes RGB or depth data and extracts features via a feature pyramid network (FPN), followed by multiple grasp prediction units to output grasp parameters in a single stage without refining process. Attaching grasp prediction units to different FPN stages increases the model capability to predict different-size grasps. Furthermore, in each prediction unit, the grasp parameters are regressed with the horizontal anchor as a reference to overcome the challenges posed by the various shapes of the grasp regions. We improve the accuracy and efficiency of grasp rotation estimation by regressing the angle directly and encoding the angle with a continuous Gaussian-like curve during training. This encoded angle regression strategy provides distance information of different angle predictions without introducing additional computational costs. Evaluations on three datasets prove the superior performance of our method than state of the arts. The experiments in real scenarios further validate the effectiveness of our grasping system. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a robot system that can automatically grasp novel objects with a parallel gripper and RGB-D camera. We focus on generating accurate grasp configurations for various objects using the captured color or depth image, which is the cornerstone of a successful grasp. To obtain effective and efficient grasp pose detection, we present a deep model that generates robust grasp poses represented by rotated bounding boxes for multiple novel objects. The first step of the grasp detector is to capture the image features through a feature pyramid network (FPN). Then, we attach separate grasp prediction units to each layer of the FPN stage and adopt anchors as references to make the model robust to variable grasp rectangle sizes. In each grasp prediction unit, two separate subnetworks are used to directly output the grasp rectangles and their probabilities, without using an extra second stage to refine the predicted grasp areas. For the prediction of rotation angle, we encode the rectangle angles with a continuous Gaussian-like curve during training to improve the prediction accuracy. Our grasp detector is trained and tested on three datasets and validated on real-scene grasp experiments. Comparisons with state-of-the-art methods show that our model is more accurate while maintaining high efficiency. The proposed grasp detection model can be applied to generate stable grasps for novel objects with different shapes, colors, and materials. Our grasping system is capable of working in multiple scenarios, including homes, factories, and warehouses.

A protocol to quantify cross-sectional and longitudinal differences in duction patterns.

Currently, there is no established system for quantifying patterns of ocular ductions. This poses challenges in tracking the onset and evolution of ocular motility disorders, as current clinical methodologies rely on subjective observations of individual movements. We propose a protocol that integrates image processing, a statistical framework of summary indices, and criteria for evaluating both cross-sectional and longitudinal differences in ductions to address this methodological gap. We demonstrate that our protocol reliably transforms objective estimates of ocular rotations into normative patterns of total movement area and movement symmetry. This is a critical step towards clinical application in which our protocol could first diagnose and then track the progression and resolution of ocular motility disorders over time.

Accelerating Globally Optimal Consensus Maximization in Geometric Vision.

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.

A New Order Tracking Method for Fault Diagnosis of Gearbox under Non-Stationary Working Conditions Based on In Situ Gravity Acceleration Decomposition

Rotational speed measuring is important in order tracking under non-stational working conditions. However, sometimes, encoders or coded discs are not easy to mount due to the limited measurement environment. In this paper, a new in situ gravity acceleration decomposition method (GAD) is proposed for rotational speed estimation, and it is applied in the order tracking scene for fault diagnosis of a gearbox under non-stationary working conditions. In the proposed method, a MEMS accelerometer is locally embedded on the rotating shaft or disc in the tangential direction. The time-varying gravity acceleration component is sensed by the in situ accelerometer during the rotation of the shaft or disc. The GAD method is established to exploit the gravity acceleration component based on the linear-phase finite impulse response (FIR) filter and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) methods. Then, the phase signal of time-varying gravity acceleration is derived for rotational speed estimations. A motor–shaft–disc experimental setup is established to verify the correctness and effectiveness of the proposed method in comparison to a mounted encoder. The results show that both the estimated average and instantaneous rotational speed agree well with the mounted encoder. Furthermore, both the proposed GAD method and the traditional vibration-based tacholess speed estimation methods are applied in the context of order tracking for fault diagnosis of a gearbox. The results demonstrate the superiority of the proposed method in the detection of tooth spalling faults under non-stationary working conditions.

Improved motion correction in brain MRI using 3D radial trajectory and projection moment analysis.

To develop a generalized rigid body motion correction method in 3D radial brain MRI to deal with continuous motion pattern through projection moment analysis. An assumption was made that the multichannel coil moves with the head, which was achieved by using a flexible head coil. A two-step motion correction scheme was proposed to directly extract the motion parameters from the acquired k-space data using the analysis of center-of-mass with high noise robustness, which were used for retrospective motion correction. A recursive least-squares model was introduced to recursively estimate the motion parameters for every single spoke, which used the smoothness of motion and resulted in high temporal resolution and low computational cost. Five volunteers were scanned at 3 T using a 3D radial multidimensional golden-means trajectory with instructed motion patterns. The performance was tested through both simulation and in vivo experiments. Quantitative image quality metrics were calculated for comparison. The proposed method showed good accuracy and precision in both translation and rotation estimation. A better result was achieved using the proposed two-step correction compared to traditional one-step correction without significantly increasing computation time. Retrospective correction showed substantial improvements in image quality among all scans, even for stationary scans. The proposed method provides an easy, robust, and time-efficient tool for motion correction in brain MRI, which may benefit clinical diagnosis of uncooperative patients as well as scientific MRI researches.

Estimation of Distance and Rotation With an Optical Correlator

Estimation of Distance and Rotation With an Optical Correlator

A novel three-module real-time adjustable accuracy speed estimator for active magnetic bearing system

This research aims to investigate the rotational speed estimation in active magnetic bearing (AMB) system. Rotational speed sensors are commonly employed for speed acquisition. Nevertheless, with the continuous advancement of AMB system, the inherent weaknesses of the speed sensors are becoming increasingly prominent in practical applications. Therefore, achieving online speed estimation can effectively address the engineering challenges arising from deficiencies in speed sensors. However, in terms of robustness, accuracy, and tracking performance, the existing speed estimation algorithms are insufficient to simultaneously meet the requirements of the AMB system. Moreover, present techniques are challenging to address prevalent issues in the AMB system, such as noise, harmonic interference, amplitude variations, and misalignment of the rotor axis trajectory. To tackle these problems, this work designs a novel three-module real-time adjustable accuracy speed estimator for AMB system. The algorithm employs displacement signals to estimate the rotational speed. And, it can flexibly adjust its noise resistance and accuracy through parameter tuning. Additionally, it can significantly diminish the influence of noise, harmonic interference, amplitude variations, and misalignment of the rotor axis trajectory. Finally, the simulation and experimental results demonstrate the effectiveness of this algorithm and validate its superior performance in robustness, accuracy, and tracking performance.

A Multilayer Perceptron-Based Spherical Visual Compass Using Global Features.

This paper presents a visual compass method utilizing global features, specifically spherical moments. One of the primary challenges faced by photometric methods employing global features is the variation in the image caused by the appearance and disappearance of regions within the camera's field of view as it moves. Additionally, modeling the impact of translational motion on the values of global features poses a significant challenge, as it is dependent on scene depths, particularly for non-planar scenes. To address these issues, this paper combines the utilization of image masks to mitigate abrupt changes in global feature values and the application of neural networks to tackle the modeling challenge posed by translational motion. By employing masks at various locations within the image, multiple estimations of rotation corresponding to the motion of each selected region can be obtained. Our contribution lies in offering a rapid method for implementing numerous masks on the image with real-time inference speed, rendering it suitable for embedded robot applications. Extensive experiments have been conducted on both real-world and synthetic datasets generated using Blender. The results obtained validate the accuracy, robustness, and real-time performance of the proposed method compared to a state-of-the-art method.

Least-Squares Estimation of Tangent Space for a Triangular Mesh

This paper presents a novel method for computing an orthonormal tangent space at every vertex of a triangular mesh provided with texture coordinates, which is essential in normal mapping. Our method employs least-squares estimation of rotation between two sets of corresponding points: one set from the positions of the 1-ring neighbors of a vertex in texture space and the other set from their corresponding positions in world space. This optimal rotation represents a local space transformation that defines the tangent space at the vertex. Consequently, our method ensures that the resulting tangent space is inherently orthonormal, eliminating the need for intricate operations such as averaging and orthonormalization, which are required in the previous methods. In addition, we introduce texture space alignment of triangles to address vertices on seams, which are inevitable in texture mapping to a closed surface mesh. Experimental results demonstrate the effectiveness of the proposed methods in various experiments.

Particle tracking in snow avalanches with in situ calibrated inertial measurement units

Abstract In the course of an artificially triggered avalanche, a particle tracking procedure is combined with supplementary measurements, including Global Navigation Satellite System (GNSS) positioning, terrestrial laser scanning and Doppler radar measurements. Specifically, an intertial measurement unit is mounted inside a rigid sphere, which is placed in the avalanche track. The sphere is entrained by the moving snow, recording translational accelerations, angular velocities and the flux density of Earth's magnetic field. Based on the recorded data, we present a threefold analysis: (i) a qualitative data interpretation, identifying different particle motion phases which are associated with corresponding flow regimes, (ii) a quantitative time integration algorithm, determining the corresponding particle trajectory and associated velocities on the basis of standard sensor calibration, and (iii) an improved quantitative evaluation relying on a novel in situ sensor calibration technique, which is motivated by the limitations of the given dataset. The final results, i.e. the evolution of the angular orientation of the sensor unit, translational and rotational velocities and estimates of the sensor trajectory, are assessed with respect to their reliability and relevance for avalanche dynamics as well as for future design of experiments.