scholarly journals Least Squares Method Used in Reduction of Data From Theodolite Measurements on Fast Moving Glaciers

1986 ◽  
Vol 8 ◽  
pp. 42-46 ◽  
Author(s):  
D. Dahl-Jensen ◽  
J.P. Steffensen ◽  
S.J. Johnsen
Keyword(s):  
Least Squares ◽  
Fixed Points ◽  
Statistical Method ◽  
Fast Moving ◽  
Least Squares Method ◽  
Model Parameters ◽  
East Greenland

A statistical method to determine surface velocities from theodolite measurements is described. The method assumes that the measuring points move according to a model and the model parameters are estimated directly from the directional observations. Observations from two fixed points need not be simultaneous, which is an advantage in the case of fast moving glaciers. The method is practised on data from the Daugaard-Jensen glacier, in East Greenland, where the motion of the measuring points is calculated to the accuracy of the directional observations.

scholarly journals Least Squares Method Used in Reduction of Data From Theodolite Measurements on Fast Moving Glaciers

1986 ◽  
Vol 8 ◽  
pp. 42-46 ◽  
Author(s):  
D. Dahl-Jensen ◽  
J.P. Steffensen ◽  
S.J. Johnsen
Keyword(s):  
Least Squares ◽  
Fixed Points ◽  
Statistical Method ◽  
Fast Moving ◽  
Least Squares Method ◽  
Model Parameters ◽  
East Greenland

A statistical method to determine surface velocities from theodolite measurements is described. The method assumes that the measuring points move according to a model and the model parameters are estimated directly from the directional observations. Observations from two fixed points need not be simultaneous, which is an advantage in the case of fast moving glaciers. The method is practised on data from the Daugaard-Jensen glacier, in East Greenland, where the motion of the measuring points is calculated to the accuracy of the directional observations.

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

MEMS Gyro Random Drift Model Parameter Identification Based on Two-Stage Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 1044-1047 ◽  
Author(s):  
Zhao Hua Liu ◽  
Jia Bin Chen ◽  
Yu Liang Mao ◽  
Chun Lei Song
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Average ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Random Drift ◽  
Two Stage ◽  
Autoregressive Moving Average Model ◽  
Drift Model ◽  
Recursive Least Squares Method

Autoregressive moving average model (ARMA) was usually used for gyro random drift modeling. Because gyro random drift was a non-stationary, weak non-linear and time-variant random signal, model parameters were random and time-variant, too. For improving precision of gyro and reducing effects of random drift, this paper adopted two-stage recursive least squares method for ARMA parameter estimation. This method overcame the shortcomings of the conventional recursive extended least squares (RELS) algorithm. At the same time, the forgetting factor was introduced to adapt the model parameters change. The simulation experimental results showed that this method is effective.

Model Parameter Identification and Simulation of Ship Power System Based on Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 482-486 ◽  
Author(s):  
Jin Hui Hu ◽  
Da Bin Hu ◽  
Jian Bo Xiao
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Parameter Identification ◽  
Least Squares ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Design Parameters ◽  
Model Parameters ◽  
Model Parameter ◽  
Model Parameter Identification

According to the lack of the part of the equipment design parameters of a certain type of ship power systems, the algorithm of recursive least squares for model parameter identification is studied. The mathematical model of the propulsion motor is established. The model parameters are calculated and simulated based on parameter identification method of recursive least squares. The simulation results show that a more precise mathematical model can be simple and easily obtained by using of the method.

scholarly journals Georeferencing of Multi-Sheet Maps Based on Least Squares with Constraints—First Military Mapping Survey Maps in the Area of Czechia

2020 ◽  
Vol 11 (1) ◽  
pp. 299
Author(s):  
Tomáš Janata ◽  
Jiří Cajthaml
Keyword(s):  
Problem Solving ◽  
Least Squares ◽  
Statistical Method ◽  
Least Squares Method ◽  
Topographic Maps ◽  
Unknown Parameters ◽  
Habsburg Monarchy ◽  
Typical Representative ◽  
Robust Statistical Method ◽  
M Estimate

The article deals with the possibility of georeferencing old multi-sheet map works. Various approaches to problem solving and a workable method for using the least squares method with the conditions of the adjacency of map sheets are discussed. To increase reliability, the IRLS robust statistical method is used, which uses iterative weighting of individual measurements based on Huber’s M-estimate. The method is applied to the First Military Mapping of the Habsburg monarchy as a typical representative of old topographic maps, which are not easy to georeference due to unknown parameters of the used cartographic projection. A georeferenced layer of the above mentioned mapping is available on the Mapire.eu portal as well. A basic analysis of the comparison of georeferencing results using our method and the mentioned portal is performed.

Sign in / Sign up

Export Citation Format

Share Document