RMS Error Research Articles

GAINN: The Galaxy Assembly and Interaction Neural Networks for High-redshift JWST Observations

We present the Galaxy Assembly and Interaction Neural Networks (Gainn), a series of artificial neural networks for predicting the redshift, stellar mass, halo mass, and mass-weighted age of simulated galaxies based on James Webb Space Telescope (JWST) photometry. Our goal is to determine the best neural network for predicting these variables at 11 < z < 15. The parameters of the optimal neural network can then be used to estimate these variables for real, observed galaxies. The inputs of the neural networks are JWST filter magnitudes of a subset of five broadband filters (F150W, F200W, F277W, F356W, and F444W) and two medium-band filters (F162M and F182M). We compare the performance of the neural networks using different combinations of these filters, as well as different activation functions and numbers of layers. The best neural network predicted redshift with a normalized rms error of 0.010−0.001+0.003 , stellar mass with rms = 0.089−0.022+0.044 , halo mass with a mean-squared error of 0.022−0.008+0.014 , and mass-weighted age with rms = 12.466−2.408+5.065 . We also test the performance of Gainn on real data from MACS0647JD, an object observed by JWST. Predictions from Gainn for the first projection of the object (JD1) have normalized bias 〈Δz〉 < 0.00228, which is significantly smaller than found with template-fitting methods. We find that the optimal filter combination is F277W, F356W, F162M, and F200W when considering both theoretical accuracy and observational resources from JWST.

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM + . For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed.The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. Given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

2D Modeling and Simulation of Pyrolysis of a Thermally Thick Biomass Particle

ABSTRACT A transient 2D kinetic-heat transfer model incorporating primary and secondary reactions is proposed to investigate the effect of reactor temperature and particle length/diameter (L/D) ratio on the pyrolysis behavior and validate it with the experimental results. The RMS error between the experimental and the model predictions are found to be 0.36–1.89% for 2D model and 13.00–13.11% for 1D model at reactor temperatures 723–798 K and L/D of 1.0. This uncderscores the necessity for the use of the 2D model in place of the 1D model, particularly at the lower L/D ratio. Temporal propagation of temperature and mass fractional residue profiles at different locations of the pyrolyzing casuarina (Casuarina equisetifolia) biomass particle is analyzed. At a high L/D (~6), two symmetric hot spots are found to appear at two axial end faces, which gradually merge to form a dumbbell-shaped hot spot near the central core. For a low L/D (~1), a symmetrical, concentric, elliptical, shell-shaped hot spot appears at a short distance from the outer surface, which quickly propagates toward the center, eventually merging into a sphere at the particle center. It is estimated that for a 0.0254 m diameter particle at the reactor temperature of 673 K, the optimal residence time is 10 min for L/D = 1, while it is 17 min for L/D = 2.

Environmental information-assisted intelligent fusion localization for vehicles in urban area

In this paper, we propose a localization methodology aimed at improving accuracy through two primary aspects: environment information assisting fusion algorithm and the elaborate localization errors prediction. First, the environment-assisted particle filter (EA-PF) is proposed by enhancing the particle filter algorithm with perceived environmental feature information, which is reflected by the rasterized map constructed based on LiDAR sensors. Then, an elaborate localization error prediction model is designed to accurately forecast Inertial Navigation System (INS) errors. The model comprises the noise characteristic feature extraction and encoding network and multi-feature error prediction network. The localization errors in the EA-PF output can be further compensated. The proposed localization methodology can be divided into two operational modes based on the availability of Global Navigation Satellite System (GNSS) signal: GNSS-available and GNSS-unavailable modes. In the GNSS-available mode, the EA-PF algorithm yields precise localization results, while in the GNSS-unavailable modes, the elaborate localization error prediction model can effectively predict INS errors and provide the compensation for the EA-PF. To validate the effectiveness of the proposed methodology, relevant test experiments were performed using the KITTI dataset. The experimental validation results demonstrate the feasibility and effectiveness of the proposed methodology. The experimental results demonstrate that the EA-PF outperforms traditional PF methods by improving the root mean square error (RMS.) by 32.70 % on average during 90 s GNSS outages. Moreover, the proposed localization methodology achieves 2.30 m RMS error on average during 90 s GNSS outage.

Kinematic models for Cable-driven Continuum Robots with multiple segments and varying cable offsets

Cable-driven Continuum Robots (CCRs) represent a subset of flexible robotic systems with diverse applications encompassing medical, quality control, and search and rescue. Multi-segmented CCRs can independently actuate different CCR segments and deform into a series of connected circular arcs. While this method generates constant-curvature profiles, CCRs with varying radial cable offsets can generate shapes with varying curvatures. However, there are no kinematic models for such robots in the literature. This paper introduces optimization-based formulations to accurately estimate the deformed profile of CCRs, considering both variable cable offset and multi-segment configurations. The presented kinematic approach can predict the deformed profiles with an RMS error less than 5% of the total length of the robot. The application of the proposed method to determine the inverse kinematics of multi-segmented CCRs is demonstrated—even considering obstacles in the robot’s workspace. Practical implementation of the formulation is illustrated using a 3-segmented CCR with a cable-driven soft gripper that imitates biological grippers such as an elephant’s trunk or creeper vine to grasp objects.

A multimodal multitask deep learning framework for vibrotactile feedback and sound rendering

Data-driven approaches are often utilized to model and generate vibrotactile feedback and sounds for rigid stylus-based interaction. Nevertheless, in prior research, these two modalities were typically addressed separately due to challenges related to synchronization and design complexity. To this end, we introduce a novel multimodal multitask deep learning framework. In this paper, we developed a comprehensive end-to-end data-driven system that encompasses the capture of contact acceleration signals and sound data from various texture surfaces. This framework introduces novel encoder-decoder networks for modeling and rendering vibrotactile feedback through an actuator while routing sound to headphones. The proposed encoder-decoder networks incorporate stacked transformers with convolutional layers to capture both local variability and overall trends within the data. To the best of our knowledge, this is the first attempt to apply transformer-based data-driven approach for modeling and rendering of vibrotactile signals as well as sounds during tool-surface interactions. In numerical evaluations, the proposed framework demonstrates a lower RMS error compared to state-of-the-art models for both vibrotactile signals and sound data. Additionally, subjective similarity evaluation also confirm the superiority of proposed method over state-of-the-art.

Accuracy of artificial intelligence‐based segmentation of the mandibular canal in CBCT

AbstractObjectivesTo investigate the accuracy of artificial intelligence (AI)‐based segmentation of the mandibular canal, compared to the conventional manual tracing, implementing implant planning software.Materials and methodsLocalization of the mandibular canals was performed for 104 randomly selected patients. A localization was performed by three experienced clinicians in order to serve as control. Five tracings were performed: One from a clinician with a moderate experience with a manual tracing (I1), followed by the implementation of an automatic refinement (I2), one manual from a dental student (S1), and one from the experienced clinician, followed by an automatic refinement (E). Subsequently, two fully automatic AI‐driven segmentations were performed (A1,A2). The accuracy between each method was measured using root mean square error calculation.ResultsThe discrepancy among the models of the mandibular canals, between the experienced clinicians and each investigated method ranged from 0.21 to 7.65 mm with a mean of 3.5 mm RMS error. The analysis of each separate mandibular canal's section revealed that mean RMS error was higher in the posterior and anterior loop compared to the middle section. Regarding time efficiency, tracing by experienced users required more time compared to AI‐driven segmentation.ConclusionsThe experience of the clinician had a significant influence on the accuracy of mandibular canal's localization. An AI‐driven segmentation of the mandibular canal constitutes a time‐efficient and reliable procedure for pre‐operative implant planning. Nevertheless, AI‐based segmentation results should always be verified, as a subsequent manual refinement of the initial segmentation may be required to avoid clinical significant errors.

Highly sensitive and easy-to-attach wearable sensor for measuring finger force based on curvature changes in an ellipse-shaped finger ring

Technologies for digitizing worker actions to enhance human labor tasks, mitigate accidents, and prevent disabling injuries have garnered significant attention. This study focuses on monitoring the force exerted by the fingers and developing a wearable fingertip force sensor based on a simple elliptical ring structure in conjunction with a commercially available resistive bend sensor. Resembling a ring accessory, the sensor is easy to attach and detach, and exhibits high sensitivity, with a resistance change of approximately 9% for a fingertip load of 1 N. Furthermore, to mitigate crosstalk during finger flexion, we propose a combined configuration employing this ring-shaped sensor alongside another sensor designed for measuring and rectifying finger flexion angles. Additionally, we introduce an empirically derived fitting function and a straightforward calibration procedure to extract the function’s parameters. The proposed system achieves an average RMS error of 0.53 N for force estimations of approximately 5 N, even during finger flexion and postural changes.

Effect of Panel Misalignment Error Distribution on the Radiation Pattern of Leighton Chajnantor Telescope’s Antenna

The Leighton dish formerly at the Caltech Submillimeter Observatory will be reassembled to become the Leighton Chajnantor Telescope (LCT). It will be required to demonstrate high surface accuracy and controlled radiation patterns at high frequency, which are largely limited by surface error due to panel misalignment on the primary reflector. Not only the surface rms error but also the error distribution has effect on the radiation pattern of the antenna. Therefore, analyzing the effect of error distributions resulting from various panel misalignments on the radiation pattern of the antenna will facilitate better compensation of surface errors during the reassembly process. To acquire the radiation pattern of LCT’s antenna with panel misalignments, we first propose a simulation method based on physical optics and the physical theory of diffraction, which offers precise results but is time-consuming, especially at high frequencies. Then, we propose a rapid computation method that combines the method of calculating the optical path difference (OPD), the OPD fitting method, and the aperture integration method for segmented reflectors. Experimental results demonstrate that the rapid computation method is highly efficient and accurate compared to the simulation method. In order to show the effect of error distributions due to two typical panel misalignments (i.e., piston and tip-tilt) on radiation patterns, experiments are conducted using the two proposed methods for various error distributions. These experiments indicate that for the same surface rms error, smaller panel errors at smaller normalized aperture radii are more conducive to achieving improved characteristics of the radiation patterns, such as reduced peak gain losses and lower sidelobe levels. Additionally, comparison experiments also reveal that variations in piston error have a greater impact on the radiation patterns than variations in tip-tilt error under the same surface rms error.

Machine Learning Techniques for the Classification of Thyroid Disease

Abstract: In the healthcare system, dealing with a large amount of data is challenging. The techniques of machine learning are used in dealing with such data. As per NFHS – 5 statistics, thyroid diseases are increasing in India. Roughly 1 in 10 Indian adults suffer from a thyroid disorder. It has been expected that more than 42 million peoples suffer from thyroid disease. For the proper diagnosis of disease, it is vital to process the medical data accurately. This study classified thyroid disease cases into hyperthyroid, euthyroid, hypothyroid, and sick. This paper aims to inspect Logistic regression for multiclass categorizing the thyroid dataset. This logistic regression model is evaluated based on its precision, recall, F measure, ROC, RMS Error, and accuracy metrics. Based on the thyroid dataset, we find that logistic regression using the One-vs.-Rest heuristic is 85% accurate, while logistic regression using the multinomial is 86% accurate.

Advancing state estimation for lithium-ion batteries with hysteresis through systematic extended Kalman filter tuning

Knowledge of remaining battery charge is fundamental to electric vehicle deployment. Accurate measurements of state-of-charge (SOC) cannot be obtained directly and estimation methods must be used instead. This requires both a good model of a battery and a well-designed state estimator. Here, hysteretic reduced-order battery models and adaptive extended Kalman filter estimators are shown to be highly effective, accurate predictors of SOC. A battery model parameterisation framework is proposed, which enhances standardised methods to capture hysteresis effects. The hysteretic model is parameterised for three independent NMC811 lithium-ion cells and is shown to reduce voltage RMS error by 50% across 18 h automotive drive-cycles. Parameterised models are used alongside an extended Kalman filter, which demonstrates the value of adaptive filter parameterisation schemes. When used alongside an extended Kalman filter, adaptive covariance matrices yield highly accurate SOC estimates, reducing SOC estimation error by 85%, compared to the industry standard battery model.

Oblique radiographic measurement of knot position and orientation in logs

A novel X-ray scanner system to identify the positions of knots in logs is described. The scanner has a simple, low-cost design that is suitable for use in medium and smaller sawmills. It makes X-ray measurements in an oblique direction as the log moves longitudinally past the X-ray source and line-detector. This unconventional oblique measurement direction creates a more side-on view that better reveals the spatial arrangement of the knots within the log. This view, when combined with the knowledge that all knots start from along the pith and radiate outwards gives sufficient information to identify knot orientations in space. Experimental oblique X-ray measurements on a sample log are described, followed by the processing and analysis of the measured radiographs, and a comparison of the results with independent measurements of knot locations. With the knot identification algorithms developed, knot axial position could be identified within 11 mm, and knot circumferential orientation with a root mean square (rms) error of 7.9°–11.6° when using a single view X-ray scanner, or 5.6°–7.7° when using a dual view scanner.

Strategic Analysis of Feature Selection Methods for Enhanced Dental Therapy Recognition in Machine Learning Applications

The popularity of smart clinics has increased significantly as a result of technical developments in fields like computer vision. At the heart of such systems is the ability to recognize objects and activities as well as perceive the environment as a whole. This is crucial for both eco-independent systems and human-machine interaction, especially in settings with constrained workspaces, like dental care. Our study delves into an extensive analysis of multiple machine learning models designed to robustly predict dental treatments. These models encompass Lazy Instance-based Learning, Sequential Minimal Optimization, Hoeffding Tree, and Random Tree. Leveraging object-oriented input sourced from gaze-guided wearable cameras, we scrutinize intricate attributes such as material properties, patients' dental conditions, and the array of instruments in use. Notably, we exploit the insight that identifying visual cues during an activity holds the potential to address the specific therapy identification challenge. Utilizing a dental data set that we gathered in the real world, we conducted our experiments and discovered that combining multiple criteria enhances accuracy in comparison to using each one alone. We did see, nevertheless, that in certain circumstances employing the symptoms alone produced superior outcomes. Additionally, symptoms demonstrated to have lesser error than combination in terms of RMS error convergence. Finally, we observed that the machine learning models' build and test durations increased as a result of the combined method. This demonstrates that adding additional parameters does not necessarily result in better outcomes in machine learning applications generally and in medical/dental applications in particular. Instead, it relies on the machine learning tool used, the settings taken into account and the input data provided. The versatility of our approach extends beyond dental contexts. It has been systematically validated across diverse domains, including the recognition of kitchen activities within smart home environments. This methodology holds relevance for various outdoor scenarios where the focal point of attention guides ongoing activities.

Beyond isotropic repulsion: Classical anisotropic repulsion by inclusion of p orbitals.

Accurate modeling of intermolecular repulsion is an integral component in force field development. Although repulsion can be explicitly calculated by applying the Pauli exclusion principle, this approach is computationally viable only for systems of limited sizes. Instead, it has previously been shown that repulsion can be reformulated in a "classical" picture: the Pauli exclusion principle prohibits electrons from occupying the same state, leading to a depletion of electronic charge between atoms, giving rise to an enhanced nuclear-nuclear electrostatic repulsion. This classical picture is called the isotropic S2/R approximation, where S is the overlap and R is the interatomic distance. This approximation accurately captures the repulsion of isotropic atoms such as noble gas dimers; however, a key deficiency is that it fails to capture the angular dependence of the repulsion of anisotropic molecules. To include directionality, the wave function must at least be a linear combination of s and p orbitals. We derive a new anisotropic S2/R repulsion model through the inclusion of the anisotropic p orbital term in the total wave function. Because repulsion is pairwise and decays rapidly, it can be truncated at a short range, making it amenable for efficient calculation of energy and forces in complex biomolecular systems. We present a parameterization of the S101 dimer database against the abinitio benchmark symmetry-adapted perturbation theory, which yields an rms error of only 0.9 kcal/mol. The importance of the anisotropic term is demonstrated through angular scans of water-water dimers and dimers involving halobenzene. Simulation of liquid water shows that the model can be computed efficiently for realistic system sizes.

Rapid Initial Heading Alignment Using Single-Antenna GNSS and a Low-Grade IMU

For the integrated system incorporating a low-cost inertial measurement unit (IMU) and global navigation satellite system (GNSS), rapid and accurate initial heading alignment is still a significant challenge, especially for marine applications in challenging ocean conditions. To overcome this difficulty, we propose an in-motion coarse heading alignment method using single-antenna GNSS and a low-grade IMU based on the basic principle of trajectory similarity. The heading angle is determined by dead reckoning (DR)-derived trajectory and GNSS-derived trajectory using gyro measurements and GNSS positioning solutions. The proposed alignment method can be implemented in real-time and the alignment period is just 1s, which indicates that the method could continuously output heading when the carrier is in motion. Therefore, the continuous heading output calculated by the proposed algorithm can be applied to the state and fault detection of the carrier. Experimental results show that the heading could be determined with an accuracy of 0.48°, 3.14°, and 2.43° at a 95% confidence level for the land vehicle, unmanned surface vessel (USV), and unmanned underwater vehicle (UUV) tests, respectively. Besides, the RMS of the alignment errors calculated by our method reaches 0.20°, 1.42°, and 1.22° for the land vehicle, USV, and UUV tests, respectively.

Feasibility of Estimating Sea Surface Height Anomalies from Surface Ocean Currents and Winds

Abstract We propose a method to reconstruct sea surface height anomalies (SSHA) from vector surface currents and winds. This analysis is motivated by the proposed satellite ODYSEA, which is a Doppler scatterometer that measures coincident surface vector winds and currents. If it is feasible to estimate SSHA from these measurements, then ODYSEA could provide collocated fields of SSHA, currents, and winds over a projected wide swath of ∼1700 km. The reconstruction also yields estimates of the low-frequency surface geostrophic, Ekman, irrotational, and nondivergent current components and a framework for separation of balanced and unbalanced motions. The reconstruction is based on a steady-state surface momentum budget including the Ekman drift, Coriolis acceleration, and horizontal advection. The horizontal SSHA gradient is obtained as a residual of these terms, and the unknown SSHA is solved for using a Helmholtz–Hodge decomposition given an imposed SSHA boundary condition. We develop the reconstruction using surface currents, winds, and SSHA off the U.S. West Coast from a 43-day coupled ROMS–WRF simulation. We also consider how simulated ODYSEA measurement and sampling errors and boundary condition uncertainties impact reconstruction accuracy. We find that temporal smoothing of the currents for periods of 150 h is necessary to mitigate large reconstruction errors associated with unbalanced near-inertial motions. For the most realistic case of projected ODYSEA measurement noise and temporal sampling, the reconstructed SSHA fields have an RMS error of 2.1 cm and a model skill (squared correlation) of 0.958 with 150-h resolution. We conclude that an accurate SSHA reconstruction is feasible using information measured by ODYSEA and external SSHA boundary conditions.

Sentinel-6 Michael Freilich precise orbit determination using PODRIX and TriG receiver measurements

The Sentinel-6 Michael Freilich altimetry mission flies two GNSS receivers: a primary multi-GNSS (GPS plus Galileo) PODRIX receiver and a GPS-only TriG receiver. Each of these receivers is independently capable of supporting the precise orbit determination (POD) requirement for < 1.5 cm radial rms error. In this study, we characterize the performance of single-receiver solutions and evaluate the benefits of a combined TriG and PODRIX orbit solution. The availability of both sets of receiver observations revealed a 10 mm in-track difference between orbit solutions derived independently from TriG and PODRIX tracking data. Based on satellite laser ranging (SLR) residuals, this bias has been isolated to an apparent inconsistency between the estimated TriG receiver clock and observation time-tags of approximately 1.3 μs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu \\hbox {s}$$\\end{document}, which is equivalent to a common range error of roughly 400 m in the TriG observations. After applying this calibration, the TriG and PODRIX displayed similar performance in terms of orbit overlap precision. PODRIX-Galileo observations showed lower code and phase tracking residual rms values compared to the GPS observations. Overall, processing the calibrated TriG and PODRIX observations separately results in highly accurate orbit solutions with radial orbit accuracies better than 1 cm rms as indicated by one-way SLR residual rms of 7.2 mm or better for each solution. Orbit solution accuracy is slightly improved by processing both TriG and PODRIX observations together, resulting in one-way SLR residual rms of 7.0 mm.

Quantification of pitting corrosion resistance in stainless steel with hyperspectral imaging in the Vis/NIR range

The impact of 316L stainless steel discolouration on chloride induced pitting corrosion was quantified. Several degrees of discolouration were produces by chemical passivation, simulated rouging or anodic polarization. Discolouration was characterized by spectral analysis in the visible and NIR range (400-1000 nm). Pitting corrosion resistance was quantified by pitting potential measurements. The spectra were used to indicate whether pitting or transpassive behaviour would occur using chemometric classification techniques with 88% accuracy. In addition, pitting potentials were predicted combining chemometrics and survival analysis techniques with a 90 mV RMS error in cross-validation. XPS analysis linked pitting resistance with the Cr/Fe balance.

Methodology for Robotic In Vitro Testing of the Knee.

The knee joint plays a pivotal role in mobility and stability during ambulatory and standing activities of daily living. Increased incidence of knee joint pathologies and resulting surgeries has led to a growing need to understand the kinematics and kinetics of the knee. In vivo, in silico, and in vitro testing domains provide researchers different avenues to explore the effects of surgical interactions on the knee. Recent hardware and software advancements have increased the flexibility of in vitro testing, opening further opportunities to answer clinical questions. This paper describes best practices for conducting in vitro knee biomechanical testing by providing guidelines for future research. Prior to beginning an in vitro knee study, the clinical question must be identified by the research and clinical teams to determine if in vitro testing is necessary to answer the question and serve as the gold standard for problem resolution. After determining the clinical question, a series of questions (What surgical or experimental conditions should be varied to answer the clinical question, What measurements are needed for each surgical or experimental condition, What loading conditions will generate the desired measurements, Do the loading conditions require muscle actuation) must be discussed to help dictate the type of hardware and software necessary to adequately answer the clinical question. Hardware (type of robot, load cell, actuators, fixtures, motion capture, ancillary sensors) and software (type of coordinate systems used for kinematics and kinetics, type of control) can then be acquired to create a testing system tailored to the desired testing conditions. Study design and verification steps should be decided upon prior to testing to maintain the accuracy of the collected data. Collected data should be reported with any supplementary metrics (RMS error, dynamic statistics) that help illuminate the reported results. An example study comparing two different ACL reconstruction techniques is provided to demonstrate the application of these guidelines. Adoption of these guidelines may allow for better interlaboratory result comparison to improve clinical outcomes.

Spatially synchronous fringe detection: a method to facilitate the alignment of an echelle grating mosaic by separating the compensative angular errors

Alignment of mosaic gratings is traditionally supported by two interferometric verifications: on the zero order to verify the grating surfaces and on the blaze to verify the groove direction. In the case of low frequency echelle grating an interferometric measurement on the zero order is hardly feasible due to extremely low contrast of the fringes. The complete alignment has then to be carried out on high order (close to the blaze) where the two misalignment errors (the tip and rotation) show the same effect on the interferogram. The acquisition of a low and a high diffraction order image simultaneously, referred to as the spatially synchronous fringe detection method (SSFD), is used to analyze the misalignment. Iterative adjustment with the autocollimation configuration at the low and high order is used to separate the compensative errors of Δθ x and Δθ z . A prototype mosaic with two 110mm×220mm segments has been aligned with the support of this method. A numerical simulation of the alignment procedure as well as the error orientation analysis of this mosaic grating are presented. The mosaic grating with an accuracy of Δθ x &lt;0.64µrad, Δθ y &lt;1.13µrad, Δθ z &lt;0.65µrad and a wavefront RMS error of 0.149λ has been completed. This method can greatly facilitate the alignment of an echelle mosaic for an astronomical spectrograph.