Final Results of Establishment of the Geodetic Vertical Second Order Network of Lithuania

2017 ◽  
Author(s):  
Rosita Birvydienė ◽  
Algirdas Butkus ◽  
Arūnas Būga ◽  
Ramunas Dedela ◽  
Ricardas Kolosovskis ◽  
...  
Keyword(s):  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Observation Data ◽  
Gps Receivers ◽  
Accuracy Estimation ◽  
First Order ◽  
Height System ◽  
Rms Error ◽  
Digital Levels

The methodology of all kinds of geodetic measurements of the Geodetic Vertical Second Order Network, the information on the observation data received and main results of the accuracy estimation and adjustment of the network are presented. In 2006 the development of the Geodetic Vertical First Order Network of Lithuania was completed. It was the basis to adopt the Height System of Lithuania (LAS07). The densification of the Geodetic Vertical First Order Network started in 2010 by development of the Geodetic Vertical Second Order Network. The Second Order Network consists of 74 levelling lines, and total length of them is 3087 km. In the period of 2010–2013 the 16 levelling lines (814 km) were observed. Rest of levelling lines were observed in 2013–2016. Total number of benchmarks is 2099. The levelling was executed by digital levels Trimble DiNi12 and coded rods Nedo LD13. All ground benchmarks were positioned by GPS receivers Trimble 5700 and Trimble Zephyr Geodetic antennas. LitPOS stations served as fiducial points. The gravity accelerations at all benchmarks were observed by gravimeters Scintrex CG-5. The levellings of the Second Order Network carried out is characterized by high precision: the double run of one kilometre levelling RMS error does not exceeds 0.7 mm. The adjustments of the second order levelling lines applying least square method were executed separately in each region outlined by the First Order network lines and border of a country.

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1993 ◽  
Vol 115 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J. C. Wang ◽  
R. F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

System Identification of a Class of Second-Order Continuous System

2014 ◽  
Vol 651-653 ◽  
pp. 528-533 ◽  
Author(s):  
Zhi Gang Jia ◽  
Xing Xuan Wang
Keyword(s):  
Linear Equations ◽  
Continuous System ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Step Response ◽  
Order System ◽  
Simulation Results ◽  
Order Continuous ◽  
Identification Model

An identification method of a class of second-order continuous system is proposed. This method constructs a discrete-time identification model, forms a set of linear equations. The parameters can be obtained by least square method. Simulation results show that the method is effective for a class of second-order system, and is not only for step response but also for square wave signal.

scholarly journals Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method

2020 ◽  
Vol 33 (4) ◽  
pp. 59
Author(s):  
Israa M. Salman ◽  
Eman A. Abdul-Razzaq
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

scholarly journals Statistical Analysis of Nigeria’s Price Sector: An Econometric Approach

2021 ◽  
pp. 29-40
Author(s):  
D. M. O. Omebo ◽  
T. D. Ailobhio ◽  
G. I. Fanen
Keyword(s):  
Predictive Performance ◽  
Least Square Method ◽  
Least Square ◽  
Explanatory Variables ◽  
Ordinary Least Square ◽  
First Order ◽  
Overall Performance ◽  
Econometric Approach ◽  
Good Predictive Performance ◽  
High Measure

This study analyzed Nigeria’s price sector using a formulated model for the price sector of the Nigeria economy. A set of simultaneous equations were used to reflect the implicit gross domestic product deflators for each of the sectors of the Nigeria economy and was found to be over identified under the order condition for identification. The model was estimated by ordinary least square method and two stage least square methods. All the variables have expected signs and as indicated by the F –statistic, the overall performance of the entire regression is significant.  The high measure of R2 and Ṝ2, in each case indicates that the explanatory variables included in the equation jointly account for the entire variation. The small RMSE also indicates that the equations have good fit. Durbin –Watson statistics shows that there is no positive first order autocorrelation. The small value of the Theil’s inequality indicates that the equation has good predictive performance. The researcher therefore recommends that government should employ the model so as to be able to monitor price of each of the sectors of the economy and put proper mechanism in place to control those sectors that affect the overall price sector of the economy.

scholarly journals The Nonlinear Delay Second Order Eigenvalue Problems Consist Of Delay Ordinary Differential Inequalities

2019 ◽  
Vol 17 (72) ◽  
pp. 19-24
Author(s):  
Eman. A. Abdul-Razzaq
Keyword(s):  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Differential Inequalities ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems consist of delay ordinary differential inequalities, one of the expansion methods that called the least square method will be developed to solve this type of problems.

scholarly journals Determination of Observation Weight to Calibrate Freeway Traffic Fundamental Diagram Using Weighted Least Square Method (WLSM)

2017 ◽  
Vol 29 (2) ◽  
pp. 203-212
Author(s):  
Chunbo Zhang ◽  
Xiucheng Guo ◽  
Zhenping Xi
Keyword(s):  
Least Square Method ◽  
Specific Weight ◽  
Interesting Case ◽  
Least Square ◽  
Observation Data ◽  
Fundamental Diagram ◽  
Freeway Traffic ◽  
Weighted Least Square ◽  
Density Relationship ◽  
The One

Due to unbalanced speed-density observations, the one-regime traffic fundamental diagram and speed-density relationship models using least square method (LSM) cannot reflect actual conditions under congested/jam traffic. In that case, it is inevitable to adopt the weighted least square method (WLSM). This paper used freeway Georgia State Route 400 observation data and proposed 5 weight determination methods except the LSM to analyse 5 wellknown one-regime speed-density models to determine the best calibrating models. The results indicated that different one-regime speed-density models have different best calibrating models, for Greenberg, it was possible to find a specific weight using LSM, which is similar for Underwood and Northwestern Models, but different for that one known as 3PL model. An interesting case is the Newell's Model which fits well with two distinct calibration weights. This paper can make contribution to calibrating a more precise traffic fundamental diagram.

Sign in / Sign up

Export Citation Format

Share Document