A LEAST SQUARE METHOD FOR GRAVITY METER BASE STATIONS

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 394-400
Author(s):  
H. H. Pentz
Keyword(s):  
Least Squares ◽  
Least Square Method ◽  
Degree Of Approximation ◽  
Base Station ◽  
Least Square ◽  
Base Stations ◽  
Method Of Least Squares ◽  
Station Network

Two applications of the Method of Least Squares in determining the most probable values from gravity meter base station applications are considered. One is an approximation, the degree of approximation depending on the number of base stations. The second is a rigorous application of the Method of Least Squares in obtaining the most probable values for an expanding base station network.

scholarly journals Processing by Least Square Method of the Measurements Results for Key, Regional and Supplementary Comparison of the Measurement Standards

2018 ◽  
pp. 3-13 ◽  
Author(s):  
Yu. Kuzmenko ◽  
O. Samoylenko
Keyword(s):  
Data Processing ◽  
Least Squares ◽  
Least Square Method ◽  
Least Square ◽  
Mathematical Apparatus ◽  
Method Of Least Squares ◽  
Unknown Parameters ◽  
Measurement Standards ◽  
Measurement Results

The methods of processing the measurement results of several homogeneous transfer standards existing in the form of single-valued or multi-valued measures/sensors or devices performed at many points on several stationary standards, which participate in key, regional or additional comparisons, are proposed in the article. The number of measurements far exceeds the number of unknown parameters of the standards, which are determined by the results of comparisons, that’s why the method of least squares was chosen as the mathematical apparatus for data processing.

Segmented Auxiliary Power Model Based on Particle Swarm Optimization

2014 ◽  
Vol 1044-1045 ◽  
pp. 1321-1324
Author(s):  
Shao Chen Wu ◽  
Hai Sheng Liu ◽  
Fu Liang Deng
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Power Model ◽  
Segmentation Method ◽  
Method Of Least Squares ◽  
Swarm Optimization ◽  
Auxiliary Power ◽  
The Impact

The traditional modeling approach of auxiliary power is the least squares method, however, accuracy of the traditional least squares method is not high in fitting and forecasting, so we introduced segmentation method of least squares model, and consider the impact of many factors on the model ,proposed the improved least square method based on PSO. Application prove this method has a better fitting precision and predicition accuracy.

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.

Localization of Mobile Robot Based on Least Square Method

2013 ◽  
Vol 347-350 ◽  
pp. 808-811
Author(s):  
Jia Lu Li ◽  
Lin Bing Long ◽  
Bao Feng Zhang
Keyword(s):  
Motion Estimation ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Least Squares ◽  
Least Square Method ◽  
Least Square ◽  
Experimental Results ◽  
Sift Algorithm ◽  
Key Techniques ◽  
Point Detection

Localization is the basis for navigation of mobile robots. This paper focuses on key techniques of localization for mobile robots based on vision. Firstly, the specific measures and steps of the algorithm are analyzed and researched in depth. In the study, SIFT algorithm combined with epipolar geometry constraint is used on the environment feature point detection, matching and tracking. And the method of RANSAC combined with the least squares is used to obtain accurate results of the motion estimation. Then the necessary experiments are carried out to verify the correctness and effectiveness of algorithms. The experimental results verified the accuracy of the improved algorithm.

Reduction of a two‐gravimeter base network by linear regression

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 867-869
Author(s):  
C. Patrick Ervin
Keyword(s):  
Linear Regression ◽  
Regression Line ◽  
Field Work ◽  
Base Station ◽  
The Other ◽  
Base Stations ◽  
Simultaneous Operation ◽  
Station Network ◽  
Exploration Environment ◽  
Base Network

In the exploration environment, a primary application of gravity surveying is regional reconnaissance. The first step in such a survey is to establish a base‐station network. Since an error in the network will propagate to many stations in the subsequent survey, careful field work and accurate reduction of these data are particularly critical. Optimally, successive base stations are tied by minimum‐time loops using at least two meters read simultaneously. Using two meters has the obvious advantage of doubling the number of ties with minimal increase in time and cost. Erroneous readings are also much easier to detect and correct with two meters. Furthermore, the simultaneous operation of the meters allows calibrations of the two to be compared by computing a linear regression of the readings of one meter against the corresponding readings of the other. If the meter calibrations are identical, the regression line should have a slope of 1. A significant deviation from 1 indicates a systematic variation in calibration.

Comparing of Coordinate Transformation Based on Total Least Squares and Least Squares

2014 ◽  
Vol 522-524 ◽  
pp. 1211-1214
Author(s):  
Qing Wu Meng ◽  
Lu Meng
Keyword(s):  
Least Squares ◽  
Coordinate Transformation ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Least Square ◽  
Experimental Results ◽  
Transformation Models ◽  
Total Least Square

The coordinate transformation models based on least square method and total least square are built and discussed. The least square model only includes the errors of observation vectors, the total least square model simultaneously takes into consideration to the errors of observation vectors and the errors of coefficient matrix. The both models are verified and compared in experiment. The experimental results showed that the model of total least square is more in line with actual, and more reasonable than by least square theoretically, and the coordinate transformation solution result of total least square with least square is more near.

scholarly journals 3D Localization Algorithm Based on Linear Regression and Least Squares in NLOS Environments

2018 ◽  
Vol 11 (4) ◽  
pp. 1
Author(s):  
Jiang Li ◽  
Zhang Lei
Keyword(s):  
Linear Regression ◽  
Three Dimensional ◽  
Least Square Method ◽  
Mobile Terminal ◽  
Base Station ◽  
Least Square ◽  
Time Of Arrival ◽  
Localization Algorithm ◽  
Positional Accuracy ◽  
The Relationship

Based on the positive bias property of the time of arrival(TOA) measurement error caused by the non-line-of-sight(NLOS) propagation, a simple and effective three dimensional(3D) geometrical localization algorithm was proposed, the algorithm needs no prior knowledge of time delay distribution of TOA, and only linear regression was used to estimate the parameters of the relationship between the NLOS distance error and the true distance, thus, the approximate real distance between mobile terminal (MT) and base station (BS) was reduced, then, the 3D geometric localization of mobile terminal was carried out by the least square method. The experimental results shows the effectiveness of the algorithm, and the positional accuracy is far higher than the required accuracy by E-911 in NLOS environments.

scholarly journals TOF-Based Fast Self-Positioning Algorithm for UWB Mobile Base Stations

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6359
Author(s):  
Yuxiang Han ◽  
Xiaoming Zhang ◽  
Zhengxi Lai ◽  
Yuchen Geng
Keyword(s):  
Local Coordinate System ◽  
Base Station ◽  
Least Square ◽  
Base Stations ◽  
Ultra Wideband ◽  
Positioning Error ◽  
Position Measurement ◽  
Propagation Law ◽  
Positioning Algorithm ◽  
Mobile Base

To solve the problem of heavy workload and high cost when acquiring the position of Ultra-Wideband (UWB) mobile base stations in sports fields, a fast self-positioning algorithm for UWB mobile base stations algorithm based on Time of Flight (TOF) is proposed. First, according to the layout of the base stations in the sports field, the local coordinate system is determined, and an equation based on the ranging information between the base stations is established; the Least Square method is used to calculate the coordinates of each base station, and the Newton Iteration method is used to converge the positioning results. Then the origin and propagation law of positioning error, as well as the method of reducing the positioning error are analyzed. The simulation data and experimental results show that the average positioning accuracy of the mobile base station is within 0.05 m, which meets the expected accuracy of the base station position measurement. Compared with traditional manual measurement methods, base station self-positioning can effectively save deployment time and reduce workload.

scholarly journals Single base station hybrid TOA/AOD/AOA localization algorithms with the synchronization error in dense multipath environment

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Shixun Wu ◽  
Min Li ◽  
Miao Zhang ◽  
Kai Xu ◽  
Juan Cao
Keyword(s):  
Mobile Station ◽  
Base Station ◽  
Least Square ◽  
Location Based Services ◽  
Synchronization Error ◽  
Base Stations ◽  
Identification Algorithm ◽  
Main Challenge ◽  
Localization Algorithms ◽  
Multipath Environment

AbstractMobile station (MS) localization in a cellular network is appealing to both industrial community and academia, due to the wide applications of location-based services. The main challenge is the unknown one-bound (OB) and multiple-bound (MB) scattering environment in dense multipath environment. Moreover, multiple base stations (BSs) are required to be involved in the localization process, and the precise time synchronization between MS and BSs is assumed. In order to address these problems, hybrid time of arrival (TOA), angle of departure (AOD), and angle of arrival (AOA) measurement model from the serving BS with the synchronization error is investigated in this paper. In OB scattering environment, four linear least square (LLS), one quadratic programming and data fusion-based localization algorithms are proposed to eliminate the effect of the synchronization error. In addition, the Cramer-Rao lower bound (CRLB) of our localization model on the root mean-square error (RMSE) is derived. In hybrid OB and MB scattering environment, a novel double identification algorithm (DIA) is proposed to identify the MB path. Simulation results demonstrate that the proposed algorithms are capable to deal with the synchronization error, and LLS-based localization algorithms show better localization accuracy. Furthermore, the DIA can correctly identify the MB path, and the RMSE comparison of different algorithms further prove the effectiveness of the DIA.

Solitary waves of the RLW equation via least squares method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ozlem Ersoy Hepson ◽  
Idris Dag ◽  
Bülent Saka ◽  
Buket Ay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Spline Functions ◽  
Algebraic Equations ◽  
B Spline ◽  
B Splines ◽  
Rlw Equation ◽  
Set Up

Abstract Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

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