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 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.

scholarly journals Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qinghui Du ◽  
Chaoli Wang
Keyword(s):  
Convergence Analysis ◽  
Analytical Solutions ◽  
Numerical Approximation ◽  
Approximate Solutions ◽  
Mean Square ◽  
Variable Delays ◽  
Age Dependent ◽  
The Mean ◽  
Euler Methods ◽  
Random Jump

We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.

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.

Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part

1975 ◽  
Vol 7 (03) ◽  
pp. 468-494
Author(s):  
H. Hering
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Transition Function ◽  
Mean Square ◽  
Second Moments ◽  
Mean Square Convergence ◽  
The Mean ◽  
Parameter Dependent ◽  
Dependent Probability

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.

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.

Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps

2016 ◽  
Vol 8 (6) ◽  
pp. 1004-1022 ◽  
Author(s):  
Xu Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Theoretical Result ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Mean Square ◽  
Nonlinear Stochastic Differential Equations ◽  
Mean Square Convergence ◽  
The Mean

AbstractIn this paper, we investigate the mean-square convergence of the split-step θ-scheme for nonlinear stochastic differential equations with jumps. Under some standard assumptions, we rigorously prove that the strong rate of convergence of the split-step θ-scheme in strong sense is one half. Some numerical experiments are carried out to assert our theoretical result.

scholarly journals VARIANCE PREDICTION FOR POPULATION SIZE ESTIMATION

2019 ◽  
Vol 38 (2) ◽  
pp. 131 ◽  
Author(s):  
Ana Isabel Gomez ◽  
Marcos Cruz ◽  
Luis Manuel Cruz-Orive
Keyword(s):  
Monte Carlo ◽  
Population Size ◽  
Error Variance ◽  
Unbiased Estimation ◽  
Mean Square ◽  
Size Estimation ◽  
Automatic Computer ◽  
Variance Estimators ◽  
Efficient Alternative ◽  
Mean Square Errors

Design unbiased estimation of population size by stereological methods is an efficient alternative to automatic computer vision methods, which are generally biased. Moreover, stereological methods offer the possibility of predicting the error variance from a single sample. Here we explore the statistical performance of two alternative variance estimators on a dataset of 26 labelled crowd pictures. The empirical mean square errors of the variance predictors are compared by means of Monte Carlo resampling.

scholarly journals Econometric Estimation of Production Function with Applications

2019 ◽  
pp. 57-61 ◽  
Author(s):  
Awoingo Adonijah Maxwell ◽  
Isaac Didi Essi
Keyword(s):  
Monte Carlo ◽  
Mean Square Error ◽  
Production Function ◽  
Least Square ◽  
Production Model ◽  
Mean Square ◽  
Unknown Parameters ◽  
Data Generating Process ◽  
The Mean ◽  
Input Variables

This study focuses on Monte Carlo Methods in parameter estimation of production function. The ordinary least square (OLS) method is used to estimate the unknown parameters. The Monte Carlo simulation methods are used for the data generating process. The Cobb-Douglas production model with multiplicative error term is fitted to the data generated. From tables 1.1 to 1.3, the mean square error (MSE) of 1 are 0.007678, 0.001972 and 0.001253 respectively for sample sizes 20, 40 and 80. Our finding showed that the mean square error (MSE) value varies with the sum of the powers of the input variables.

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