THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

A New Calibration Method and Device for Certified Flow Measurements With Laser Velocimetry

2012 ◽  
Author(s):  
Katsuaki Shirai ◽  
Lars Büttner ◽  
Jürgen Czarske ◽  
Carsten Kykal
Keyword(s):  
Positional Information ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Uncertainty Budget ◽  
New Method ◽  
Direct Access ◽  
Flow Measurements ◽  
Laser Velocimetry ◽  
Traceability Chain ◽  
Calibration Methods

We aim to establish traceability at calibration and hence to enable a certified flow measurement with a calibrated measurement system. A new calibration method is presented for laser velocimetry. We develop a simple, unique method which establishes traceability of its uncertainty. The device is transportable and calibratable by any users for their own instruments on-site. Our new method requires only a rotating disk and a precision linear stage providing positional information. In former calibration methods, the uncertainty of the orbit radius of a scattering object was dominant due to the difficulty of accessing the true center of the rotation. The diffuculty was solved in our new method. The new method provides an accurate estimate of the orbit radius and hence the velocity of the calibration object through a linear regression. The calibration constant is obtained even without the need of direct access to the absolute value of the rotation radius. The uncertainty budget is examined throughout the calibration procedure. The traceability chain is established once the traceabilities are maintained to the translation stage and the motor used for rotating the calibration disk. The new method has been realized with three different calibration setups and their performances were investigated. We demonstrate that the new calibration method can achieve uncertainty down to 0.1%.

scholarly journals Technical Note: Weight approximation of coccoliths using a circular polarizer and interference colour derived retardation estimates – (The CPR Method)

2014 ◽  
Vol 11 (7) ◽  
pp. 1899-1910 ◽  
Author(s):  
J. Bollmann
Keyword(s):  
Theoretical Calculations ◽  
Polarized Light ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Technical Note ◽  
New Method ◽  
Interference Colour ◽  
Circular Polarizer ◽  
Empirical Calibration ◽  
First Time

Abstract. A circular polarizer is used for the first time to image coccoliths without the extinction pattern of crossed polarized light at maximum interference colour. The combination of a circular polarizer with retardation measurements based on grey values derived from theoretical calculations allows for the first time accurate calculations of the weight of single coccoliths thinner than 1.37 μm. The weight estimates of 364 Holocene coccoliths using this new method are in good agreement with published volumetric estimates. A robust calibration method based on the measurement of a calibration target of known retardation enables the comparison of data between different imaging systems. Therefore, the new method overcomes the shortcomings of the error prone empirical calibration procedure of a previously reported method based on birefringence of calcite. Furthermore, it greatly simplifies the identification of coccolithophore species on the light microscope as well as the calculation of the area and thus weight of a coccolith.

Computation of Rigid-Body Angular Acceleration From Point-Acceleration Measurements

1987 ◽  
Vol 109 (2) ◽  
pp. 124-127 ◽  
Author(s):  
Jorge Angeles
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Measurement Errors ◽  
Angular Acceleration ◽  
The Body ◽  
The Other ◽  
Compatibility Conditions ◽  
Other Hand ◽  
The One

The computation of the angular acceleration of a rigid body from measurements of accelerations of three noncollinear points of the body is presented in this paper. This is based on algorithms presented previously for the computation of the orientation and the angular velocity of a rigid body from measurements of position and velocity of three noncollinear points of the body. Moreover, compatibility conditions that the said point measurements should verify are introduced. These are necessary to verify the rigidity assumption on the one hand; on the other hand, they are introduced as a means of filtering roundoff and/or measurement errors, which is particularly useful if redundant measurements are taken, i.e., on more than three points. The procedure is illustrated with a fully solved example.

scholarly journals Geometric Model and Calibration Method for a Solid-State LiDAR

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2898 ◽  
Author(s):  
Pablo García-Gómez ◽  
Santiago Royo ◽  
Noel Rodrigo ◽  
Josep R. Casas
Keyword(s):  
Solid State ◽  
Angular Resolution ◽  
Geometric Model ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Geometrical Model ◽  
Scanning System ◽  
Order Of Magnitude ◽  
The One ◽  
Scanning Systems

This paper presents a novel calibration method for solid-state LiDAR devices based on a geometrical description of their scanning system, which has variable angular resolution. Determining this distortion across the entire Field-of-View of the system yields accurate and precise measurements which enable it to be combined with other sensors. On the one hand, the geometrical model is formulated using the well-known Snell’s law and the intrinsic optical assembly of the system, whereas on the other hand the proposed method describes the scanned scenario with an intuitive camera-like approach relating pixel locations with scanning directions. Simulations and experimental results show that the model fits with real devices and the calibration procedure accurately maps their variant resolution so undistorted representations of the observed scenario can be provided. Thus, the calibration method proposed during this work is applicable and valid for existing scanning systems improving their precision and accuracy in an order of magnitude.

scholarly journals Technical Note: Weight approximation of single coccoliths inferred from retardation estimates using a light microscope equipped with a circular polariser – (the CPR Method)

2013 ◽  
Vol 10 (7) ◽  
pp. 11155-11179 ◽  
Author(s):  
J. Bollmann
Keyword(s):  
Light Microscope ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Technical Note ◽  
New Method ◽  
Imaging Method ◽  
Empirical Calibration ◽  
Polarised Light ◽  
First Time ◽  
Good Agreement

Abstract. A new method for weight estimates of single coccoliths using the birefringence of calcite is described. The weight estimates of 364 Holocene coccoliths using this new method are in good agreement with published volumetric estimates. A robust calibration method based on the measurement of a calibration target of known retardation enables the comparison of data between different imaging systems. Therefore, the new method overcomes the shortcomings of the error prone empirical calibration procedure of a previously reported method based on birefringence of calcite. In addition, the new method includes the application of a circular polariser that eliminates the extinction pattern in crossed polarised light. This imaging method allows for the first time the imaging of complete coccoliths on a light microscope at maximum interference colours without moving any mechanical part of the microscope. Therefore, it greatly simplifies the identification of coccolithophore species on the light microscope as well as the calculation of the area and thus weight of a coccolith.

scholarly journals SOME PROBLEMS ABOUT THE MOTION OF A RIGID BODY IN A RESISTIVE MEDIUM

2021 ◽  
Vol 3 (2) ◽  
pp. 6-17
Author(s):  
D. Leshchenko ◽  
◽  
T. Kozachenko ◽  
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Modern Technology ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
The Body ◽  
Body Motion ◽  
Body Rotation ◽  
Angular Velocity Vector ◽  
Resistive Medium

The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistive medium. The presence of the velocity of proper rotation of the rigid body leads to the apearance of dissipative torques causing the braking of the body rotation. These torques depend on the properties of resistant medium in which the rigid body motions occur, on the body shape, on the properties of the surface of the rigid body and the distribution of mass in the body and on the characters of the rigid body motion. Therefore, the dependence of the resistant torque on the orientation of the rigid body and its angular velocity can de quite complicated and requires consideration of the motion of the medium around the body in the general case. We confine ourselves in this paper to some simple relations that can qualitative describe the resistance to rigid body rotation at small angular velocities and are used in the literature. In setting up the equations of motion of a rigid body moving in viscous medium, we need to consider the nature of the resisting force generated by the motion of the rigid body. The evolution of rotations of a rigid body influenced by dissipative disturbing torques were studied in many papers and books. The problems of motion of a rigid body about fixed point in a resistive medium described by nonlinear dynamic Euler equations. An analytical solution of the problem when the torques of external resistance forces are proportional to the corresponding projections of the angular velocity of the rigid body is obtain in several works. The dependence of the dissipative torque of the resistant forces on the angular velocity vector of rotation of the rigid body is assumed to be linear. We consider dynamics of a rigid body with arbitrary moments of inertia subjected to external torques include small dissipative torques.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals ClusterSLAM: A SLAM backend for simultaneous rigid body clustering and motion estimation

2021 ◽  
Author(s):  
Jiahui Huang ◽  
Sheng Yang ◽  
Zishuo Zhao ◽  
Yu-Kun Lai ◽  
Shi-Min Hu
Keyword(s):  
Motion Estimation ◽  
Rigid Body ◽  
Iterative Scheme ◽  
Dynamic Environments ◽  
Rigid Bodies ◽  
Factor Graph ◽  
Agglomerative Clustering ◽  
Multiple Objects ◽  
Graph Optimization ◽  
Dynamic Objects

AbstractWe present a practical backend for stereo visual SLAM which can simultaneously discover individual rigid bodies and compute their motions in dynamic environments. While recent factor graph based state optimization algorithms have shown their ability to robustly solve SLAM problems by treating dynamic objects as outliers, their dynamic motions are rarely considered. In this paper, we exploit the consensus of 3D motions for landmarks extracted from the same rigid body for clustering, and to identify static and dynamic objects in a unified manner. Specifically, our algorithm builds a noise-aware motion affinity matrix from landmarks, and uses agglomerative clustering to distinguish rigid bodies. Using decoupled factor graph optimization to revise their shapes and trajectories, we obtain an iterative scheme to update both cluster assignments and motion estimation reciprocally. Evaluations on both synthetic scenes and KITTI demonstrate the capability of our approach, and further experiments considering online efficiency also show the effectiveness of our method for simultaneously tracking ego-motion and multiple objects.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

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