Application of Fitting Estimation Method in GPS Height Fitting

2013 ◽  
Vol 694-697 ◽  
pp. 2545-2549 ◽  
Author(s):  
Qian Wen Cheng ◽  
Lu Ben Zhang ◽  
Hong Hua Chen
Keyword(s):  
Least Squares ◽  
Estimation Method ◽  
Least Square ◽  
Least Squares Collocation ◽  
Normal Height ◽  
Geodetic Height ◽  
The Given ◽  
Surveying And Mapping

The key point researched by many scholars in the field of surveying and mapping is how to use the given geodetic height H measured by GPS to obtain the normal height. Although many commonly-used fitting methods have solved many problems, they all value the pending parameters as the nonrandom variables. Figuring out the best valuations, according to the traditional least square principle, only considers its trend or randomness, which is theoretically incomprehensive and have limitations in practice. Therefore, a method is needed not only considers its trend but also takes randomness into account. This method is called the least squares collocation.

Research into the Model of GNSS Leveling Polynomial Surface Fitting Based on MATLAB

2011 ◽  
Vol 90-93 ◽  
pp. 2907-2912
Author(s):  
Yu Sheng Gong ◽  
Qian Han ◽  
Li Ping Zhang
Keyword(s):  
Least Squares ◽  
Robust Estimation ◽  
Automatic Processing ◽  
Surface Fitting ◽  
Normal Height ◽  
Distortion Model ◽  
Whole Process ◽  
Gross Error ◽  
Geodetic Height ◽  
Polynomial Surface

To make full use of geodetic height results measured by GNSS and improve the accuracy that GNSS geodetic height convert to normal height, method of polynomial surface fitting has been selected in this article to research into fitting of the elevation. In the first place, for least squares estimation do not have the ability of resisting gross error, robust estimation is introduced to data preprocessing, which has solve the problem of distortion model effectively and then combines with specific engineering to make comparison and to analyze accuracy of polynomial surface fitting data of different orders. MATLAB has been used in programming design in the whole process, which has realized automatic processing of data.

scholarly journals Comparing ols and rank-based estimation techniques for production analysis: An application to Ghanaian maize farms.

2016 ◽  
Vol 10 (4-5) ◽  
pp. 125-130
Author(s):  
Henry De-Graft Acquah
Keyword(s):  
Least Squares ◽  
Production Function ◽  
Least Squares Method ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Least Squares Regression ◽  
Estimation Techniques ◽  
Production Analysis ◽  
Douglas Production Function

This paper introduces the rank-based estimation method to modelling the Cobb-Douglas production function as an alternative to the least squares approach. The intent is to demonstrate how a nonparametric regression based on a rank-based estimator can be used to estimate a Cobb-Douglas production function using data on maize production from Ghana. The nonparametric results are compared to common parametric specification using the ordinary least squares regression. Results of the study indicate that the estimated coefficients of the CobbDouglas Model using the Least squares method and the rank-based regression analysis are similar. Findings indicated that in both estimation techniques, land and Equipment had a significant and positive influence on output whilst agrochemicals had a significantly negative effect on output. Additionally, seeds which also had a negative influence on output was found to be significant in the robust rank-based estimation, but insignificant in the ordinary least square estimation. Both the least squares and rank-based regression suggest that the farmers were operating at an increasing returns to scale. In effect this paper demonstrate the usefulness of the rank-based estimation in production analysis. JEL CODE: Q18, D24, Q12, C1 and C67

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

scholarly journals The least-squares collocation method in the mechanics of deformable solids

2021 ◽  
Vol 1715 ◽  
pp. 012029
Author(s):  
Sergey Golushko ◽  
Vasily Shapeev ◽  
Vasily Belyaev ◽  
Luka Bryndin ◽  
Artem Boltaev ◽  
...  
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Least Squares Collocation ◽  
Deformable Solids ◽  
Mechanics Of Deformable Solids

scholarly journals On the uncertainty of height anomaly differences predicted by least-squares collocation

2020 ◽  
Vol 10 (1) ◽  
pp. 53-61
Author(s):  
E. Mysen
Keyword(s):  
Least Squares ◽  
Spatial Separation ◽  
Height Anomaly ◽  
Surface Model ◽  
Least Squares Collocation ◽  
Normal Heights ◽  
Gravimetric Quasigeoid ◽  
The Difference ◽  
Grid Interpolation ◽  
Gps Observations

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

scholarly journals Calibration Method of Array Errors for Wideband MIMO Imaging Radar Based on Multiple Prominent Targets

2021 ◽  
Vol 13 (15) ◽  
pp. 2997
Author(s):  
Zheng Zhao ◽  
Weiming Tian ◽  
Yunkai Deng ◽  
Cheng Hu ◽  
Tao Zeng
Keyword(s):  
Multiple Input Multiple Output ◽  
Estimation Method ◽  
Target Position ◽  
Position Estimation ◽  
Least Square ◽  
Antenna Structure ◽  
Imaging Radar ◽  
Position Errors ◽  
Calibration Methods ◽  
Array Errors

Wideband multiple-input-multiple-output (MIMO) imaging radar can achieve high-resolution imaging with a specific multi-antenna structure. However, its imaging performance is severely affected by the array errors, including the inter-channel errors and the position errors of all the transmitting and receiving elements (TEs/REs). Conventional calibration methods are suitable for the narrow-band signal model, and cannot separate the element position errors from the array errors. This paper proposes a method for estimating and compensating the array errors of wideband MIMO imaging radar based on multiple prominent targets. Firstly, a high-precision target position estimation method is proposed to acquire the prominent targets’ positions without other equipment. Secondly, the inter-channel amplitude and delay errors are estimated by solving an equation-constrained least square problem. After this, the element position errors are estimated with the genetic algorithm to eliminate the spatial-variant error phase. Finally, the feasibility and correctness of this method are validated with both simulated and experimental datasets.

Research on the Wire Drawing Die Pass Parameter Calculation Based on the Least Square Algorithm

2012 ◽  
Vol 591-593 ◽  
pp. 850-853
Author(s):  
Huai Xing Wen ◽  
Yong Tao Yang
Keyword(s):  
Pore Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Piecewise Linear ◽  
Wire Drawing ◽  
Least Square ◽  
Structure Characteristics ◽  
Drawing Die ◽  
The Wire ◽  
Drawing Dies

Drawing Dies meter A / D acquisition module will be collected from the mold hole contour data to draw a curve in Matlab. According to the mold pore structure characteristics of the curve, the initial cut-off point of each part of contour is determined and iteratived optimization to find the best cut-off point, use the least squares method for fitting piecewise linear and fitting optimization to find the function of the various parts of the curve function, finally calculate the pass parameters of drawing mode. Parameters obtained compare with the standard mold, both of errors are relatively small that prove the correctness of the algorithm. Also a complete algorithm flow of pass parameters is designed, it can fast and accurately measure the wire drawing die hole parameters.

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