scholarly journals Estimating the Position of an Image with Unknown Intensity Shape

2020 ◽  
Vol 23 (1) ◽  
pp. C15-C22
Author(s):  
Yury E. Korchagin ◽  
Viacheslav N. Vereshchagin ◽  
Alexander V. Terekhov ◽  
Kirill A. Melnikov
Keyword(s):  
Maximum Likelihood Method ◽  
A Priori ◽  
Likelihood Method ◽  
Real Image ◽  
Markov Approximation ◽  
Signal Function ◽  
Image Intensity ◽  
Extended Object ◽  
Spatially Extended ◽  
Image Position

The problem considered is to estimate the image position of a spatially extended object. It is assumed that the shape of the image intensity is a priori unknown, but it can be predicted with some error. In order to synthesize the estimate of the image position, the quasi-likelihood version of the maximum likelihood method is used. Behavior of the signal function in the neighborhood of the real image position is studied. Characteristics of the resulting estimate, such as bias and dispersion, are found by means of the local Markov approximation method. Influence of non-uniformity of the received image intensity upon the estimate accuracy is demonstrated by an example of receiving the rectangular image with linearly varying intensity.

scholarly journals Eccentricity Parameters Identification for a Motorized Spindle System Based on Improved Maximum Likelihood Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wengui Mao ◽  
Chaoliang Hu ◽  
Jianhua Li ◽  
Zhonghua Huang ◽  
Guiping Liu
Keyword(s):  
Maximum Likelihood ◽  
Measurement Errors ◽  
Maximum Likelihood Method ◽  
Search Algorithm ◽  
A Priori ◽  
Likelihood Method ◽  
Step Size ◽  
Spindle System ◽  
Grinding Machine ◽  
Search Interval

As a kind of rotor system, the electric spindle system is the core component of the precision grinding machine. The vibration caused by the mass imbalance is the main factor that causes the vibration of the grinding machine. Identifying the eccentricity parameters in an electric spindle system is a key issue in eliminating mass imbalances. It is difficult for engineers to understand the approximate range of eccentricity by experience; that is, it is difficult to obtain a priori information about eccentricity. At the same time, due to the geometric characteristics of the electrospindle system, the material factors and the randomness of the measurement response, these uncertain factors, even in a small case, are likely to cause large deviations in the eccentricity recognition results. The search algorithm used in the maximum likelihood method to identify the eccentricity parameters of the electrospindle system is computationally intensive, and the sensitivity in the iterative process brings some numerical problems. This paper introduces an Advance-Retreat Method (ARM) of the search interval to the maximum likelihood method, the unknown parameter increment obtained by the maximum likelihood method is used as the step size in the iteration, and the Advance-Retreat Method of the search interval is used to adjust the next design point so that the objective function value is gradually decreasing. The recognition results under the three kinds of measurement errors show that the improved maximum likelihood method improves the recognition effect of the maximum likelihood method and can reduce the influence of uncertainty factors on the recognition results, and the robustness is satisfactory.

scholarly journals Measuring Subclusters in Galaxy Clusters

1999 ◽  
Vol 186 ◽  
pp. 417-417
Author(s):  
Z.Y. Shao
Keyword(s):  
Maximum Likelihood ◽  
Radial Velocity ◽  
Galaxy Clusters ◽  
Maximum Likelihood Method ◽  
Velocity Space ◽  
Likelihood Method ◽  
Cluster Region ◽  
Distribution Parameters ◽  
Celestial Sphere ◽  
Image Position

We assume that there are Kc subclusters and Kf fields (foreground or background) in a cluster region. Then, the distribution of all galaxies in this region can be described as follow: where, nc and nf are normalized numbers of subcluster members and field galaxies. φc, φf, are their normalized distributions in radial velocity space. Both of them can be assumed as Gaussian. μc and μf are normalized distributions in the projected surface of the celestial sphere. For field galaxies, it's uniform, and for subcluster members, usually we use the King's approximate formulae. Distribution parameters and their uncertainties can be found by using the standard maximum likelihood method. And membership probabilities of the ith galaxy belonging to the cth subcluster can be calculated as Pc(i) = φc(i)/φp(i).

scholarly journals Multistage Curve Fitting

1977 ◽  
Vol 9 (1-2) ◽  
pp. 191-202 ◽  
Author(s):  
Christoph Haehling von Lanzenauer ◽  
Don Wright
Keyword(s):  
Distribution Function ◽  
Method Of Moments ◽  
Curve Fitting ◽  
Maximum Likelihood Method ◽  
Graphical Method ◽  
Decision Makers ◽  
Third Party ◽  
Likelihood Method ◽  
Bodily Injury ◽  
Image Position

One of the most important properties of a distribution function is that it fits the data well enough for the decision-makers' or analysts' purposes. The statisticians' problem is to select a specific form for the distribution function and to determine its parameters from the available data. Various methods (graphical method, method of moments, maximum likelihood method) are available for that purpose.In many real world situations a single distribution function, however, may not be appropriate over the entire range of the available data. This suggests that the underlying process changes over the range of the respective variable. This fact should be considered in curve fitting. A typical example of such a situation is given in Figure 1 representing third party liability losses for trucks.It is interesting to speculate about the different raisons d'être (Seal [5]) for the observed discontinuity. It may be the result of out-of-court or in-court settlements or could stem from differences between bodily injury and property damages.

Dealing with propositions, not with the characters: the ability of three-taxon statement analysis to recognise groups based solely on ‘reversals’, under the maximum-likelihood criteria

2016 ◽  
Vol 29 (2) ◽  
pp. 119 ◽  
Author(s):  
Evgeny V. Mavrodiev
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
A Priori ◽  
Actual Data ◽  
Likelihood Method ◽  
Maximum Likelihood Analysis ◽  
Likelihood Analysis

Three-taxon statement matrices can be analysed using the maximum-likelihood method. In the present paper, it is demonstrated that groups based solely on putative reversals are always recognisable after maximum-likelihood analysis of three-taxon statement matrices, even without a priori recoding of the putative reversals as new character states or fractional weighting of three-taxon statements. Parametric implementations of three-taxon statement analysis still require more investigation. However, it must be highlighted that a focus on the set of hypotheses, rather than on the ‘actual data’, is required.

The co-responsibility of mass and environment in the formation of lenticular galaxies

2020 ◽  
Vol 15 (S359) ◽  
pp. 173-174
Author(s):  
A. Cortesi ◽  
L. Coccato ◽  
M. L. Buzzo ◽  
K. Menéndez-Delmestre ◽  
T. Goncalves ◽  
...  
Keyword(s):  
Active Galactic Nuclei ◽  
Maximum Likelihood Method ◽  
Spiral Galaxies ◽  
Galactic Nuclei ◽  
Rotation Velocity ◽  
Elliptical Galaxies ◽  
Likelihood Method ◽  
Data Set ◽  
Lenticular Galaxies ◽  
Galaxies Kinematics

AbstractWe present the latest data release of the Planetary Nebulae Spectrograph Survey (PNS) of ten lenticular galaxies and two spiral galaxies. With this data set we are able to recover the galaxies’ kinematics out to several effective radii. We use a maximum likelihood method to decompose the disk and spheroid kinematics and we compare it with the kinematics of spiral and elliptical galaxies. We build the Tully- Fisher (TF) relation for these galaxies and we compare with data from the literature and simulations. We find that the disks of lenticular galaxies are hotter than the disks of spiral galaxies at low redshifts, but still dominated by rotation velocity. The mechanism responsible for the formation of these lenticular galaxies is neither major mergers, nor a gentle quenching driven by stripping or Active Galactic Nuclei (AGN) feedback.

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