Huit campagnes d’observations de Saturne a l’Astrolabe Danjon a San Fernando

1978 ◽  
Vol 48 ◽  
pp. 471-478
Author(s):  
M. Sanchez
Keyword(s):  
Theoretical Development ◽  
Mean Square ◽  
Mean Values ◽  
San Fernando ◽  
The Mean ◽  
Mean Square Errors ◽  
Right Ascension

Abstract:This paper contains an analysis of Saturn observations with Danjon astrolabe at San Fernando. These observations were obtained during eight winter campaigns (1970-1978). Table 1 gives the mean values for each of the quantities Δα and Δδ (astrolabe - American Ephemeris) and the mean square errors. Figure 1 to 8 shows the results (right ascension and declination) and the corresponding smoothing curves. The accuracy of these curves is also given in table 1. The analysis of the values Δα and Δδ seem to show that there are differences, between the theoretical development of ephemeris and the observations, of periodical character.

scholarly journals Realization of the Primary Terrestrial Reference Frame

1991 ◽  
Vol 127 ◽  
pp. 108-115
Author(s):  
W. Kosek ◽  
B. Kołaczek
Keyword(s):  
Reference Frame ◽  
Geographic Distribution ◽  
Terrestrial Reference Frame ◽  
Mean Square ◽  
Minimum Value ◽  
Collocation Points ◽  
Station Coordinates ◽  
The Mean ◽  
Transformation Parameters ◽  
Mean Square Errors

AbstractThe PTRF is based on 43 sites with 64 SSC collocation points with the optimum geographic distribution, which were selected from all stations of the ITRF89 according to the criterion of the minimum value of the errors of 7 parameters of transformation. The ITRF89 was computed by the IERS Terrestrial Frame Section in Institut Geographique National - IGN and contains 192 VLBI and SLR stations (points) with 119 collocation ones. The PTRF has been compared with the ITRF89. The errors of the 7 parameters of transformation between the PTRF and 18 individual SSC as well as the mean square errors of station coordinates are of the same order as those for the ITRF89. The transformation parameters between the ITRF89 and the PTRF are negligible and their errors are of the order of 3 mm.

Mathematical-Statistical Methods for the Analysis of Aerial Triangulation Adjustment Errors Using a Computer Program

1975 ◽  
Vol 29 (2) ◽  
pp. 175-188
Author(s):  
M. Mosaad Allam
Keyword(s):  
Computer Program ◽  
Frequency Interval ◽  
Mean Square ◽  
Fisher Criterion ◽  
Statistical Parameters ◽  
Sample Distribution ◽  
Development Section ◽  
The Mean ◽  
Kolmogorov Criterion ◽  
Mean Square Errors

In practice, photogrammetrists use a single statistic reliability interval criterion, based on the mean square errors, to judge the accuracy of adjustment of photogrammetric blocks. Even in some cases, if the practical and theoretical distributions of frequency interval agree, such a test does not make it possible to establish the closeness of their convergence nor the degree of their difference. In other words, to get a complete picture of the character of the distribution of errors in the adjusted photogrammetric blocks, it is insufficient to investigate any single statistic. In the Research and Development Section of the Topographical Survey Directorate, a computer program (SABA) has been designed to analyze the errors of photogrammetric block adjustments, compute various statistical parameters and check the sample distribution using Kolmogorov criterion. Based on the decision taken, the correspondence between the empirical and theoretical distribution series are checked using the criterion χ2. The program divides the adjusted block to make a comparative evaluation of accuracies in the different sub-blocks. In this case, in addition to Kolmogorov and χ2 tests, the program checks the reliability intervals of the means and mean square errors of the samples and uses Fisher criterion ‘F’ to check the hypothesis of the equality of dispersion. SABA is coded in Fortran IV and Compass for the CDC CYBER 74 and requires a central memory of 28K decimal works. SABA is the acronym for Statistical Analysis of Block Adjustment.

Extrapolation Problem for Continuous Time Periodically Correlated Isotropic Random Fields

2017 ◽  
Vol 19 ◽  
pp. 1-23
Author(s):  
Iryna Golichenko ◽  
Oleksand Masyutka ◽  
Mikhail Moklyachuk
Keyword(s):  
Random Field ◽  
Spectral Characteristics ◽  
Mean Square ◽  
Spectral Densities ◽  
Optimal Linear ◽  
Extrapolation Problem ◽  
Time Argument ◽  
The Mean ◽  
Mean Square Errors ◽  
Isotropic Random

The problem of optimal linear estimation of functionals depending on the unknown values of a random fieldζ(t,x), which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the unit sphere Sn with respect to spatial argumentxєSn. Estimates are based on observations of the fieldζ(t,x) +Θ(t,x) at points (t,x) :t< 0;xєSn, whereΘ(t,x) is an uncorrelated withζ(t,x) random field, which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the sphereSnwith respect to spatial argumentxєSn. Formulas for calculating the mean square errors and the spectral characteristics of the optimal linear estimate of functionals are derived in the case of spectral certainty where the spectral densities of the fields are exactly known. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics are proposed in the case where the spectral densities are not exactly known while a class of admissible spectral densities is given.

Application of on-line Adaptive Weighted Fusion in Mine Gas Measurement System

2012 ◽  
Vol 239-240 ◽  
pp. 1395-1398
Author(s):  
Yan Ju Wang ◽  
Li Kun Yang ◽  
Yu Tian Wang
Keyword(s):  
Measurement System ◽  
Mean Square ◽  
Least Mean Square ◽  
Fusion Algorithm ◽  
Important Indicator ◽  
Weighted Fusion ◽  
Environmental Monitoring System ◽  
The Mean ◽  
Mine Gas ◽  
Mean Square Errors

In mine environmental monitoring system, the concentration of mine gas is an important indicator. Aiming at the redundant information from multi-gas sensors in the measurement system, adaptive weighted fusion algorithm was presented. Using this algorithm, it was unnecessary to be aware of any pre-defined knowledge about these datas measured by the sensors. That the algorithm could adjust the fused sensor’s weight in time according to the variation in sensors’ variances makes the mean square error minimal. It was also proved theoretically that this fusion algorithm is linear and unbiased, in respect of the least mean square errors. Simulation results showed that this fusion algorithm is effective and the result of fused data is superior to the mean estimate algorithm in respect of accuracy and fault tolerance.

Realization of the Precise Point Positioning (PPP) technique and its accuracy

2017 ◽  
Vol 927 (9) ◽  
pp. 42-49
Author(s):  
A.V. Voytenko
Keyword(s):  
Precise Point Positioning ◽  
Russian Language ◽  
Convergence Time ◽  
Practical Implementation ◽  
Mean Square ◽  
Dual Frequency ◽  
Russian Scientist ◽  
The Mean ◽  
Point Positioning ◽  
Mean Square Errors

The article notes that the replacement of the English name «Precise Point Positioning» (PPP) in Russian-language sources is possible using the term «accurate differential positioning» (TDP) technique. The author proposes to use both terms. This article contains information about the practical implementation of the PPP in the on-line service. The author has analyzed the research on the accuracy of PPP foreign and domestic experts and scholars. The author analyzed the data about the convergence time for PPP solutions. These data belong to another Russian scientist. The results of evaluating the accuracy of the PPP of different scientists led to the next. The author of this article gave the mean square errors topocentric coordinates of the geodetic points. The coordinates of the points must be obtained by dual-frequency GPS-measurements for a period of 24 hours with the help of PPP. The author proposed a formula for the calculation of the mean square error of the spatial position of geodetic point, if its position is obtained in the processing of dual-frequency GPS-observations of less than 24 hours. The article written conclusions about the features, defects and PPP development.

scholarly journals Reproducibility of Peripheral Quantitative Computed Tomography Measurements at the Radius and Tibia in Healthy Pre- and Postmenopausal Women

2011 ◽  
Vol 62 (3) ◽  
pp. 183-189 ◽  
Author(s):  
Kristina A. Szabo ◽  
Colin E. Webber ◽  
Christopher Gordon ◽  
Jonathan D. Adachi ◽  
Richard Tozer ◽  
...  
Keyword(s):  
Postmenopausal Women ◽  
Root Mean Square ◽  
Subcutaneous Fat ◽  
Quantitative Computed Tomography ◽  
Distal Tibia ◽  
Mean Square ◽  
Cross Sectional ◽  
Mean Values ◽  
The Mean

Purpose The objectives of this study were to utilise the XCT-2000 pQCT scanner to determine the mean values and the reproducibility of in vivo total, trabecular, and cortical volumetric bone measurements at distal and diaphyseal sites of the radius and the tibia, as well as calf muscle and subcutaneous fat areas, in healthy pre- and postmenopausal women. Methods Twenty-nine women (14 premenopausal and 15 postmenopausal) were recruited to participate in this study. Distal and diaphyseal sites of the radius (at 4% and 20% of the length of the radius) and tibia (at 4%, 38%, and 66% of the length of the tibia) were examined. Results The root mean square coefficient of variation for measurements at the distal tibia gave the most favorable reproducibility values for total (1.5%) and trabecular (1.6%) density, whereas the diaphyseal tibia showed the most favorable reproducibility value for cortical density (0.3%). The root mean square coefficients of variation for measurements of muscle and fat cross-sectional areas at the calf were 0.6% and 0.7%, respectively. At the distal tibia, the mean values for total ( P < .05) and trabecular ( P < .01) density were significantly lower in postmenopausal women than in premenopausal women. Conclusions The data presented here indicate that XCT-2000 pQCT scans at the tibia provide highly reproducible measurements of total, cortical, and trabecular bone as well as muscle and fat cross-sectional areas. Furthermore, significant differences in volumetric bone measurements between healthy pre- and postmenopausal women were evident only at the distal tibia, suggesting that this site warrants further study.

scholarly journals Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Feng Lian ◽  
Chen Li ◽  
Chongzhao Han ◽  
Hui Chen
Keyword(s):  
Monte Carlo ◽  
Convergence Analysis ◽  
Sequential Monte Carlo ◽  
Mean Square ◽  
Convergence Results ◽  
Mean Square Convergence ◽  
The Mean ◽  
Mean Square Errors

The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence.

scholarly journals Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

2020 ◽  
Vol 8 (2) ◽  
pp. 631-654
Author(s):  
Iryna Golichenko ◽  
Mikhail Moklyachuk
Keyword(s):  
Interpolation Problem ◽  
Spectral Characteristics ◽  
Optimal Estimation ◽  
Mean Square ◽  
Missing Observations ◽  
Linear Functionals ◽  
Spectral Densities ◽  
Optimal Estimates ◽  
The Mean ◽  
Mean Square Errors

The problem of mean square optimal estimation of linear functionals which depend on the unknown values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise. Formulas for calculation the mean square errors and the spectral characteristics of the optimal estimates of functionals are derived in the case of spectral certainty, where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, where spectral densities of the sequences are not exactly known while some classes of admissible spectral densities are specified.

scholarly journals Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments

2020 ◽  
Vol 8 (3) ◽  
pp. 684-721
Author(s):  
Maksym Luz ◽  
Mikhail Moklyachuk
Keyword(s):  
Long Memory ◽  
Spectral Characteristics ◽  
Optimal Estimation ◽  
Mean Square ◽  
Linear Functionals ◽  
Spectral Densities ◽  
Optimal Estimates ◽  
Optimal Linear ◽  
The Mean ◽  
Mean Square Errors

We introduce a stochastic sequence $\zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of the stochastic sequence $\zeta(k)$  based on its  observations at points $ k<0$. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

Mathematical Modeling of Thin-Layer Solar Drying of Eland (Taurotragus oryx) Jerky

2015 ◽  
Vol 11 (2) ◽  
pp. 229-242 ◽  
Author(s):  
Iva Kucerova ◽  
Anna Hubackova ◽  
Bo-Anne Rohlik ◽  
Jan Banout
Keyword(s):  
Mathematical Modeling ◽  
Thin Layer ◽  
Suitable Model ◽  
Solar Drying ◽  
Mean Square ◽  
Drying Process ◽  
Beef Jerky ◽  
The Mean ◽  
Mean Square Errors ◽  
Kinetics Of

Abstract Mathematical modeling of thin-layer solar drying of eland jerky was investigated in this study. Eland jerky was compared to traditional beef jerky, inasmuch as both were treated with traditional jerky marinade (TM), traditional marinade with honey (TMH) and compared to an untreated control (C). The influence of the marinades on the drying process was statistically significant. Based on the coefficients of determination, the root mean square errors and the chi-squares, the two-term model was found to be the most suitable model for describing the solar drying kinetics of eland jerky. The mean effective moisture diffusivities of solar dried eland meat for the C, TM and TMH samples were 2.07×10−10, 1.45×10−10 and 1.43×10−10 m2.s−1, respectively. The activation energy values for solar dried eland jerky were 23.75, 26.22 and 26.97 kJ mol−1 for C, TM and TMH, respectively.

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