Arbitrary Misalignment Research Articles

A rapid alignment method for high-precision rotational INS within group affine

In this paper, a rapid alignment method for high-precision rotation inertial navigation system (RINS) within group affine is proposed based on the Lie group theory. The proposed method can effectively solve the ultimate contradiction of initial alignment: speed and accuracy. It meets the requirements of fast response and high accuracy of high-precision RINS. We abandon the conventional coarse alignment + fine alignment scheme and realize a linear Kalman filter alignment method with arbitrarily initial misalignment based on the Earth-centered Earth-fixed frame RINS mechanization and the Lie group theory. Subsequently, considering the error characteristics of RINS two-position alignment, new left-invariant error model and observation model satisfying the group affine property are constructed to improve the convergence speed and accuracy of alignment. It is verified that the method can complete the initial alignment of arbitrary large misalignment and reach the ultimate accuracy in a short time, and the land vehicle navigation test shows that the proposed alignment method can complete the initial alignment of arbitrary misalignment in 5 min under the swaying disturbance and achieve better pure inertial navigation accuracy compared with the traditional scheme.

Measuring spin in coalescing binaries of neutron stars that show double precursors

Gamma-ray bursts resulting from binary neutron-star mergers are sometimes preceded by precursor flares. These harbingers can be ignited by quasi-normal modes, excited by orbital resonances, shattering the stellar crust of one of the inspiralling stars up to ≳10 s before coalescence. In the rare case when a system displays two precursors, successive overtones of either interface modes or g modes can be responsible for the overstrainings. Since the free-mode frequencies of these overtones have an almost constant ratio, and the inertial-frame frequencies for rotating stars are shifted relative to static ones, the spin frequency of the flaring component can be constrained as a function of the equation of state, the binary mass ratio, the mode quantum numbers, and the spin-orbit misalignment angle. As a demonstration of the method, we find that the precursors of GRB090510 hint at a spin frequency range of 2 ≲ ν⋆/Hz ≲ 20 for the shattering star if we allow for an arbitrary misalignment angle, assuming ℓ = 2 g modes account for the events.

Methods of calculating areas of overlapping inks of ellipsoidal raster elements

The mechanisms of moire occurrence during dot-to-dot printing for various forms of raster elements (circle, square, rhombus, ellipse) are considered. The algorithms for calculating the areas of common overlay of raster elements of neighboring inks of round, square and rhombic form are presented. An algorithm and methodology for calculating the areas of common overlay of raster elements of ellipsoidal form with arbitrary misalignment along the coordinate axes has been developed. The program code for calculating the areas of common overlay of ellipses using the Pascal 7.0 programming language was writtеn. The Monte Carlo method was used to calculate the area of the common overlap of two ellipses. The optimal geometric parameters for the stochastic process of the Monte Carlo method were found. The dependences of the areas of common overlay of ellipsoidal raster elements on misalignment along the x-axis for different misalignments along the y-axis were obtained

Particle-ray tracing through misaligned lattice elements in accelerators

Particle-ray tracing through misaligned lattice elements can be modelled by sandwiching the transfer-map for the aligned element between two transformations, one applied at the entrance and the other at the exit of the element. We derive the explicit form of these two transformations for an arbitrary misalignment using elementary geometry.

Robust full-pose-parameter estimation for the LED array in Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) can achieve quantitative phase imaging with a large space-bandwidth product by synthesizing a set of low-resolution intensity images captured under angularly varying illuminations. Determining accurate illumination angles is critical because the consistency between actual systematic parameters and those used in the recovery algorithm is essential for high-quality imaging. This paper presents a full-pose-parameter and physics-based method for calibrating illumination angles. Using a physics-based model constructed with general knowledge of the employed microscope and the brightfield-to-darkfield boundaries inside captured images, we can solve for the full-pose parameters of misplaced LED array, which consist of the distance between the sample and the LED array, two orthogonal lateral shifts, one in-plane rotation angle, and two tilt angles, to correct illumination angles precisely. The feasibility and effectiveness of the proposed method for recovering random or remarkable pose parameters have been demonstrated by both qualitative and quantitative experiments. Due to the completeness of the pose parameters, the clarity of the physical model, and the high robustness for arbitrary misalignments, our method can significantly facilitate the design, implementation, and application of concise and robust FPM platforms.

Polarization rotation and near-Earth quantum communications

We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of 10^-10. Under the same conditions the Wigner phase of special relativity is typically of the order 10^-4--10^-5. These phases lead to the physical lower bound on communication errors. However, both types of errors can be simultaneously mitigated. Moreover, they are countered by a fully reference frame independent scheme that also handles arbitrary misalignment between the reference frames of sender and receiver.

Cross-polarization induced crosstalk impact analysis on the BER performance of 100-Gbps CPDM 8-QAM CO-FOC system over unrepeatered 100-km SSMF link

This proposed article presents a comprehensive investigation of a coherent optical (CO) circular-polarization division multiplexed (CPDM) 8-quadrature amplitude modulation (8-QAM) for the fiber optic communication (FOC) system over an unrepeatered 100 km SSMF link to find the impact of cross-polarization (XPol) induced crosstalk by arbitrary misalignment of the states of polarization (SOPs) on the bit error rate (BER) performance. A thorough study with a mathematical analysis is demonstrated, considering the Maxwellian distribution for the mean misalignment angle, to acquire the output expression of the signal to cross-talk plus noise ratio (SCNR) and average BER for a CO homodyne CPDM 8-QAM receiver. Numerical simulations exhibit that BER performance deteriorates due to the XPol effects. Results show that the system experiences a power penalty for the mean misalignment angle to acquire a definite BER of 10−9 for a fixed local oscillator power. Besides, a detailed comparison between the existing PDM-QPSK and our proposed CPDM 8-QAM model is elucidated where our proposed model is significantly better than the existing model in terms of SCNR-BER performances, spectral-efficiency (SE) and capacity of the system as well.

Performance evaluation of low-cost GPS/INS in-motion alignment model under ECEF frame

ABSTRACT Low-cost GPS/INS integration system is the ideal combination of navigation and positioning. However, the sensitivity of low-cost INS is not good enough for the initial alignment in statics base before navigation. Considering this problem, this paper presents an arbitrary misalignment angle error propagation model which does not rely on small misalignment angles assumption and two simplified versions. These models are presented in the ECEF frame approach and are suitable to implement the in-motion alignment with GPS aided. Another three error models based on quaternion, Rodrigues parameters and modified Rodrigues parameters were also proposed. Three experiments were designed to verify the accuracy and computational efficiency of these error models. The experiments’ results showed that the small misalignment angle model was applicable to the small misalignment angle for higher computational efficiency but without improvement of accuracy. And the large misalignment angle is the best error model for the initial alignment of the arbitrary misalignment angle.

A Novel Polar Rapid Transfer Alignment for Shipborne SINS Under Arbitrary Misalignments

The traditional polar rapid transfer alignment (RTA) are generally modeled under small angle misalignment assumption. Those linearized and nonlinear polar RTA error models presented, so far, are not capable of accurately representing the nonlinear properties of the system where the all-orientation large attitude errors happen between the master and slave strap-down inertial navigation systems (SINS). It cannot satisfy the accuracy for the SINS initialization and has a singularity in computation. In this article, the misalignment quaternion in the grid frame was selected as the state and observation. An innovative polar RTA algorithm using the quaternion matching and the augmented unscented Kalman filter (UKF) was then proposed to estimate all-orientation large attitude misalignments in polar regions. Furthermore, the associated error propagation equations were redesigned in the grid frame and with compensations for the lever-arm effect. The augmented UKF model was further adjusted to apply. Simulation and semi-physical experiment results demonstrated that the performance of the innovative polar RTA algorithm proposed here outperformed those via traditional polar RTA techniques, especially with 3-axis large-angle misalignments, and was even robust with the disturbance of lever-arm effect aggravated by the harsh polar environment.

Integrability of black hole orbits in maximal supergravity

We study the dynamics of a pair of extremal (half-BPS) black holes in mathcal{N} = 8 supergravity, as a potentially solvable model of gravitational dynamics. As a diagnosis of hidden symmetries, we ask whether the perihelion of the orbits precesses over time. We consider black hole charge vectors with arbitrary misalignment. First, we use scattering amplitude methods to compute the leading post-Newtonian correction for general mass ratios. This computation is greatly simplified by introducing a suitable on-shell superspace. Second, we study the probe limit to all orders in velocity and Newton’s constant through a ten-dimensional brane setup. In all cases we find no precession. We relate this to the absence of scalar triangle integrals.

Analytical model for mutual inductance between two rectangular coils in driver pickup mode for eddy current testing

The electromagnetic induction method by means of eddy current plays an important role in non-destructive testing. In detecting a defect from the impedance variation, there is the driver pickup coils method, which arranges two coils on the one side of the tested material. In most studies, circular coils have been analysed. In this paper, the electromagnetic field and mutual inductance between two rectangular eddy current coils in driver pickup mode are calculated analytically for different sizes and arbitrary misalignment above a planar conductor. Firstly, the second-order vector potential formulation is used for the calculation of the fields produced by a rectangular transmitter coil of multi-turns and rectangular cross section placed on a conducting half-space. Then, the closed-form expressions are provided for the mutual inductance between two rectangular coils in free-space and its change due to the eddy current in the conducting half-space. Finally, the mutual inductance and its change are calculated for different frequencies, lift-off, distances and misalignments. The validity of the theoretical analysis and calculation is confirmed by the experiments.

A unified model for transfer alignment at random misalignment angles based on second-order EKF

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Direct Voltage Depression Calculation of Arbitrary Electron Beams in Misaligned Coaxial Gyrotron Cavities

Coaxial-cavity gyrotrons for electron cyclotron heating in plasma experiments for nuclear fusion can operate with very high-order modes, having reduced mode competition and decreased voltage depression compared with hollow-cavity tubes. However, since exact alignment of coaxial insert and cavity wall can only be ensured up to a certain precision, the effects of misalignment must be properly understood. In this paper, an efficient method is presented to determine the voltage depression on beam electrons for arbitrary misalignment between cavity wall and insert, and for a beam with arbitrary shape and density distribution. The method has been verified using a 3-D code, and it can be generalized to some other geometries.

Electromechanical modelling and design for phase control of locked modes in the DIII-D tokamak

A basic nonlinear electromechanical model is developed for the interaction between a pre-existing near-saturated tearing-mode, a conducting wall, active coils internal to the wall, and active coils external to the wall. The tearing-mode is represented by a perturbed helical surface current and its island has a small but finite moment of inertia. The model is shown to have several properties that are qualitatively consistent with the experimental observations of mode-wall and mode-coil interactions. The main purpose of the model is to guide the design of a phase control system for locked modes (LMs) in tokamaks. Such a phase controller may become an important component in integrated disruption avoidance systems. A realistic feedback controller for the LM phase is designed and tested for the electromechanical model. The results indicate that a simple fixed-gain controller can perform phase control of LMs with a range of sizes, and at arbitrary misalignment relative to a realistically dimensioned background error field. The basic model is expected to be a useful minimal dynamical system representation also for other aspects of mode-wall-coil interactions.

New rapid transfer alignment method for SINS of airborne weapon systems

Transfer alignment is an effective alignment method for the strapdown inertial navigation system (SINS) of airborne weapon systems. The traditional transfer alignment methods for large misalignment angles alignment use nonlinear transfer alignment models and incorporate nonlinear filtering. A rapid transfer alignment method with linear models and linear filtering for arbitrary misalignment angles is presented. Through the attitude quaternion decomposition, the purpose of transfer alignment is converted to estimate a constant quaternion. Employing special manipulations on measurement equation, velocity and attitude linear measurement equations are derived. Then the linear transfer alignment model for arbitrary misalignment angles is built. An adaptive Kalman filter is developed to handle modeling errors of the measurement noise statistics. Simulation results show feasibility and effectiveness of the proposed method, which provides an alternative rapid transfer alignment method for airborne weapons.

Misalignment Effect Function Measurement for Oblique Rotation Axes

The Misalignment Effect Function (MEF) describes the decrement in manual performance associated with a rotation between operators’ visual display frame of reference and that of their manual control. It now has been empirically determined for rotation axes oblique to canonical body axes and is compared with the MEF previously measured for rotations about canonical axes. A targeting rule, called the Secant Rule, based on these earlier measurements is derived from a hypothetical process and shown to describe some of the data from three previous experiments. It explains the motion trajectories determined for rotations less than 65° in purely kinematic terms without the need to appeal to a mental rotation process. Further analysis of this rule in three dimensions applied to oblique rotation axes leads to a somewhat surprising expectation that the difficulty posed by rotational misalignment should get harder as the required movement is shorter. This prediction is confirmed. Geometry underlying this rule also suggests analytic extensions for predicting more generally the difficulty of making movements in arbitrary directions subject to arbitrary misalignments.

Hybrid-type spatial mask–panel alignment system for manufacturing flat panel displays

A hybrid-type three-dimensional visual alignment system is suggested, which is to align pattern mask and glass panel for manufacturing flat panel displays. In order to compensate for the spatial misalignments between mask and panel, a pair of decoupled positioning mechanisms are adopted, where the lower 4-PPR parallel kinematic machine provides 3-degree-of-freedom motions to the pattern mask like the current in-plane alignment systems, while the upper 4-RPS machine gives an independent 3-degree-of-freedom mobility to the glass panel along the directions excluded in the mask movement. Hence, the combinatorial motion of the two positioning mechanisms completes a spatial mask–panel alignment. In this article, two fundamental issues are solved for the operation of the hybrid alignment system. First, the inverse kinematic solutions for the hybrid parallel mechanisms are derived to determine the displacements of active joints for an arbitrary misalignment in the task space. Second, it is developed how to extract the spatial misalignment between mask and panel in real time in terms of three in-plane cameras and the focus value Gaussian model.

A homogenization theory for elastic–viscoplastic materials with misaligned internal structures

In this study, a homogenization theory for non-linear time-dependent materials is rebuilt for periodic elastic–viscoplastic materials with misaligned internal structures, by employing a unit cell defined for the aligned structure as an analysis domain. For this, it is shown that the perturbed velocity fields in such materials possess periodicity in the directions of misaligned unit cell arrangement. This periodicity is used as a novel boundary condition for unit cell analysis to rebuild the homogenization theory. The resulting theory is able to deal with arbitrary misalignment using the same unit cell, avoiding not only geometry and mesh generation of a unit cell for every misalignment, but also the influence of mesh dependence. To verify the theory, an elastic–viscoplastic analysis of plain-woven glass fiber/epoxy laminates with misaligned internal structures is performed. It is shown that the misalignment of internal structures affects viscoplastic properties of the plain-woven laminates both macroscopically and microscopically.

Reverse-optimization Alignment Algorithm using Zernike Sensitivity

When aligning catoptric or catadioptric telescopes for space cameras, it is difficult to align precisely if the field of view is large or there are several reflective surfaces. The quantitative knowledge of mirror misalignments greatly helps align a misaligned telescope precisely, and also reduce the alignment time. This paper describes a generalized reverse-optimization alignment solution algorithm using Zernike sensitivity, and proposes the minimum number of fields to take interferograms. This method was successfully applied on a Cassegrain telescope design for Earth observation from space with arbitrary misalignments and a model including some primary mirror deformation.

Analysis of an arbitrarily misaligned self-acting gas film journal bearing of finite length

To date, there has been no comprehensive study of the pressure distribution and related features of the operation and design of gas film journal bearings of finite length undergoing arbitrary misalignment. In this paper the afore-named study is presented. Direct application of the finite difference method to the non-linear partial differential equation of Reynolds, governing the phenomenon of lubrication, proved to be very effective in handling the geometry of “double-planed” misalignment. The results of the study reveal a very smooth asymmetric pressure distribution, strongly affected by the misalignment parameters. The load capacity, attitude angle and misaligning moment vs. the operational and design variables are presented in dimensionless form. This investigation reveals that the load capacity increases with the misalignment severity ratio — an unexpected feature of gas-lubricated journal bearings — providing that the rupture of the gas film at the ends is effectively prevented. The effect of the misalignment orientation angle is almost insignificant, except for the minimum film thickness at the ends.