scholarly journals Accurate Solution of Navigation Equations in GPS Receivers for Very High Velocities Using Pseudorange Measurements

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
N. Rahemi ◽  
M. R. Mosavi ◽  
A. A. Abedi ◽  
S. Mirzakuchaki
Keyword(s):  
Least Squares ◽  
Navigation System ◽  
Variance Estimation ◽  
Least Squares Method ◽  
Accurate Solution ◽  
Estimation Methods ◽  
Gps Receivers ◽  
The Earth ◽  
Exact Position ◽  
Very High

GPS is a satellite-based navigation system that is able to determine the exact position of objects on the Earth, sky, or space. By increasing the velocity of a moving object, the accuracy of positioning decreases; meanwhile, the calculation of the exact position in the movement by high velocities like airplane movement or very high velocities like satellite movement is so important. In this paper, seven methods for solving navigation equations in very high velocities using least squares method and its combination with the variance estimation methods for weighting observations based on their qualities are studied. Simulations on different data with different velocities from 100 m/s to 7000 m/s show that proposed method can improve the accuracy of positioning more than 50%.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

scholarly journals Chaotic Multiquenching Annealing Applied to the Protein Folding Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Juan Frausto-Solis ◽  
Ernesto Liñan-García ◽  
Mishael Sánchez-Pérez ◽  
Juan Paulo Sánchez-Hernández
Keyword(s):  
Protein Folding ◽  
Simulated Annealing ◽  
Least Squares ◽  
Simulated Annealing Algorithm ◽  
Least Squares Method ◽  
Equilibrium Phase ◽  
Dynamical Equilibrium ◽  
Annealing Algorithm ◽  
Cooling Function ◽  
Very High

The Chaotic Multiquenching Annealing algorithm (CMQA) is proposed. CMQA is a new algorithm, which is applied to protein folding problem (PFP). This algorithm is divided into three phases: (i) multiquenching phase (MQP), (ii) annealing phase (AP), and (iii) dynamical equilibrium phase (DEP). MQP enforces several stages of quick quenching processes that include chaotic functions. The chaotic functions can increase the exploration potential of solutions space of PFP. AP phase implements a simulated annealing algorithm (SA) with an exponential cooling function. MQP and AP are delimited by different ranges of temperatures; MQP is applied for a range of temperatures which goes from extremely high values to very high values; AP searches for solutions in a range of temperatures from high values to extremely low values. DEP phase finds the equilibrium in a dynamic way by applying least squares method. CMQA is tested with several instances of PFP.

scholarly journals Application of Square Msplit Estimation in Determination of Vessel Position in Coastal Shipping

2017 ◽  
Vol 24 (2) ◽  
pp. 3-12 ◽  
Author(s):  
Marek Hubert Zienkiewicz ◽  
Krzysztof Czaplewski
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Functional Model ◽  
Parameters Estimation ◽  
Estimation Methods ◽  
Research Subject ◽  
Coastal Shipping ◽  
Maritime Navigation ◽  
M Estimation

AbstractThe main aim of this paper is to assess the possibility of using non-conventional geodetic estimation methods in maritime navigation. The research subject of this paper concerns robust determination of vessel’s position using a method of parameters estimation in the split functional model (Msplitestimation). The studies performed will help in finding out if and in which situations the application of Msplitestimation as the method for determining vessel’s position is beneficial from the perspective of navigation safety. The results obtained were compared with the results of traditional estimation methods, i.e. least squares method and robust M-estimation.

Predicting the Earth Orientation Parameters by the Least Squares Method

2020 ◽  
Vol 40 (12) ◽  
pp. 1124-1127
Author(s):  
D. A. Kozorez ◽  
D. M. Kruzhkov ◽  
K. V. Kuznetsov ◽  
E. A. Martynov
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Earth Orientation Parameters ◽  
Earth Orientation ◽  
The Earth ◽  
Orientation Parameters

scholarly journals A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Yuejin Zhou ◽  
Yebin Cheng ◽  
Tiejun Tong
Keyword(s):  
Least Squares ◽  
Nonparametric Regression ◽  
Variance Estimation ◽  
Least Squares Method ◽  
Asymptotic Properties ◽  
Error Variance ◽  
Simulation Studies ◽  
Least Squares Estimators ◽  
Slope Estimator ◽  
Better Than

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings.

scholarly journals Simulating within host human immunodeficiency virus 1 genome evolution in the persistent reservoir

2020 ◽  
Author(s):  
Bradley R Jones ◽  
Jeffrey B Joy
Keyword(s):  
Human Immunodeficiency Virus ◽  
Least Squares ◽  
Temporal Dynamics ◽  
Least Squares Method ◽  
Viral Evolution ◽  
Host Cells ◽  
Estimation Methods ◽  
Immunodeficiency Virus ◽  
Hiv 1 ◽  
Human Immunodeficiency Virus 1

Abstract The complexities of viral evolution can be difficult to elucidate. Software simulating viral evolution provides powerful tools for exploring hypotheses of viral systems, especially in situations where thorough empirical data are difficult to obtain or parameters of interest are difficult to measure. Human immunodeficiency virus 1 (HIV-1) infection has no durable cure; this is primarily due to the virus’ ability to integrate into the genome of host cells, where it can remain in a transcriptionally latent state. An effective cure strategy must eliminate every copy of HIV-1 in this “persistent reservoir” because proviruses can reactivate, even decades later, to resume an active infection. However, many features of the persistent reservoir remain unclear, including the temporal dynamics of HIV-1 integration frequency and the longevity of the resulting reservoir. Thus, sophisticated analyses are required in order to measure these features and determine their temporal dynamics. Here, we present software that is an extension of SANTA-SIM to include multiple compartments of viral populations. We used the resulting software to create a model of HIV-1 within host evolution that incorporates the persistent HIV-1 reservoir. This model is composed of two compartments, an active compartment and a latent compartment. With this model, we compared five different date estimation methods: (Closest Sequence, Clade, Linear Regression, Least Squares and Maximum Likelihood) to recover the integration dates of genomes in our model’s HIV-1 reservoir. We found that the Least Squares method performed the best with the highest concordance (0.80) between real and estimated dates and the lowest absolute error (all pairwise t tests: p < 0.01). Our software is a useful tool for validating bioinformatics software and understanding the dynamics of the persistent HIV-1 reservoir.

scholarly journals Comparison of Least Squares, Ridge Regression and Principal Component Approaches in the Presence of Multicollinearity in Regression Analysis

2019 ◽  
Vol 7 (8) ◽  
pp. 1166 ◽  
Author(s):  
Soner Çankaya ◽  
Samet Eker ◽  
Samet Hasan Abacı
Keyword(s):  
Least Squares ◽  
Ridge Regression ◽  
Least Squares Method ◽  
Principal Component Regression ◽  
Live Weight ◽  
Principal Component ◽  
Multiple Regression Model ◽  
Estimation Methods ◽  
Body Weights ◽  
Research Findings

The aim of this study was to compare estimation methods: least squares method (LS), ridge regression (RR), Principal component regression (PCR) to estimate the parameters of multiple regression model in situations when the underlying assumptions of least squares estimation are untenable because of multicollinearity. For this aim, the effect of some body measurements on body weights (height at withers and rumps, body length, chest width, chest girth and chest depth, front, middle and hind rump width) obtained from totally 85 Karayaka lambs at weaning period raised at Research Farm of Ondokuz Mayis University was examined. Mean square error, R2 value and significance of parameters were used to evaluate estimator performance. The multicollinearity, between front and middle rump width which were used to estimate live weight, was eliminated by using RR and PCR. Although research findings showed that RR method had the smallest MSE and the highest R2 value, the estimates of PCR were determined to be more consistent when the importance tests of parameters were taken into account. The results showed that principal component regression approach should be used to estimate the live weight of Karayaka lambs at weaning period.

scholarly journals PRIME MISURE GEODETICHE E GRAVIMETRICHE NEL ‘700 E ‘800

2014 ◽  
Author(s):  
Pietro Broglia ◽  
Luigi Mussio
Keyword(s):  
Least Squares ◽  
20Th Century ◽  
19Th Century ◽  
Least Squares Method ◽  
Simple Pendulum ◽  
Data Treatment ◽  
European Institutions ◽  
The Earth ◽  
Political Conditions ◽  
The 19Th Century

At the beginning of the 19th century, the Observatory of Brera in Milan and the Observatories of Vienna and Prague were the three most important astronomic institutions of the Austrian empire. In the same period, in Milan, an experiment, concerning the measurement of the gravimetric perturbations on the simple pendulum movement, was prepared to evaluate the density of the earth. Indeed until that epoch, few researches in this field were performed only in England. Unfortunately after the positive conclusion of this first experiment, difficult political conditions caused the stop of the cooperation among European institutions and blocked also a possible continuation of these experiments at a European scale. In Italy, gravimetric surveying restarted al the end of the 19th century and it continued until the ‘60s of the 20th century. In the previous context (August 1825), a relevant step was the application, for the data treatment, of the least squares method, just four years after its issue in 1821.

scholarly journals Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2692
Author(s):  
Bogdan Căruntu ◽  
Mădălina Sofia Paşca
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Analytical Solutions ◽  
General Class ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Test Problems ◽  
Numerical Examples ◽  
Approximate Analytical Solutions ◽  
Very High

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.

scholarly journals Solar vector solving method based on photovoltaic array and its application in attitude estimation of navigation system

2019 ◽  
Vol 53 (1-2) ◽  
pp. 151-163
Author(s):  
Hongmei Zhang ◽  
Huaqing Zhang ◽  
Guangyan Xu ◽  
Hao Liu
Keyword(s):  
Least Squares ◽  
Unmanned Aerial Vehicles ◽  
Navigation System ◽  
Least Squares Method ◽  
The Body ◽  
Integrated Navigation ◽  
Measuring Device ◽  
Photovoltaic Array ◽  
Aerial Vehicles ◽  
Reflected Light

Solar-powered unmanned aerial vehicles usually fly at high altitudes, and they are mainly powered by the photocells covering the body of unmanned aerial vehicles. Considering that the solar vector cannot be affected by the disturbing magnetic field and harmful acceleration, a unit solar vector solving method based on photovoltaic array is proposed in this paper. The photocells with different installation angles are selected to form the photovoltaic array. The solar vector is solved by the least-squares method on the basis of normalization by using the output currents of the photovoltaic array. For eliminating the influence of faults and reflected light on the solving of the solar vector, an adaptive least-squares unit solar vector solving method is proposed. In addition, a solar vector measuring device is designed in order to verify the effectiveness of the proposed methods. By employing the structural advantages of the device, the current generated by the reflected light of the sky can be solved according to the currents generated by all photocells of this device. Thus, the solved current generated by the reflected light of the sky is more accurate. Moreover, strapdown inertial navigation system/solar vector/global positioning system integrated navigation Kalman filtering algorithm is proposed, in which the adaptive least-squares unit solar vector solving method is applied to the measurement update of the filter. The effectiveness of the methods proposed in this paper is illustrated by some numerical and physical simulations.

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