Pre and Post Least Squares: The Emergence of Robust Estimation

1997 ◽  
pp. 3-13
Author(s):  
C. Radhakrishna Rao
Keyword(s):  
Least Squares ◽  
Robust Estimation

scholarly journals Application of Robust Estimation Methods for the Analysis of Outlier Measurements / Aplikácia Robustných Odhadovacích Metód Pri Analýze Odľahlých Meraní

2011 ◽  
Vol 57 (3) ◽  
pp. 14-29
Author(s):  
Silvia Gašincová ◽  
Juraj Gašinec ◽  
Gabriel Weiss ◽  
Slavomír Labant
Keyword(s):  
Linear Programming ◽  
Least Squares ◽  
Robust Estimation ◽  
Mathematical Analysis ◽  
Physical Environment ◽  
Regression Line ◽  
Measured Data ◽  
Estimation Methods ◽  
Method Of Least Squares ◽  
The Impact

Abstract The basis of mathematical analysis of geodetic measurements is the method of least squares (LSM), whose bicentenary we celebrated in 2006. In geodetic practice, we quite often encounter the phenomenon when outlier measurements penetrate into the set of measured data as a result of e.g. the impact of physical environment. That fact led to modifications of LSM that have been increasingly published mainly in foreign literature in recent years. The mentioned alternative estimation methods are e.g. robust estimation methods and methods in linear programming. The aim of the present paper is to compare LSM with the robust estimation methods on an example of a regression line.

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 A Modified Residual-Based RAIM Algorithm for Multiple Outliers Based on a Robust MM Estimation

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5407
Author(s):  
Wenbo Wang ◽  
Ying Xu
Keyword(s):  
Least Squares ◽  
Robust Estimation ◽  
Subset Selection ◽  
Selection Method ◽  
Practical Application ◽  
Robust Performance ◽  
M Estimator ◽  
Ls Estimator ◽  
Receiver Autonomous Integrity Monitoring ◽  
Mm Estimation

The residual-based (RB) receiver autonomous integrity monitoring (RAIM) detector is a widely used receiver integrity enhancement technology that has the ability to rapidly respond to outliers. However, the sensitivity and vulnerability of the residuals to the outliers are the weaknesses of the method especially in the case of multi-outlier modes. It is an effective method for enhancing the validity of residuals by robust estimation instead of least squares (LS) estimation. In this paper, a modified RB RAIM detector based on a robust MM estimation with a higher detection performance under multi-outlier modes is presented. A fast subset selection method based on the characteristic slope that could reduce the number of subsets to be calculated is also presented. The experimental results show that the proposed algorithm maintains a more robust performance than the RB RAIM detector based on the LS estimator and M estimator with an IGG III function especially with the increase in the number of outliers. The proposed fast subset selection method can reduce the calculation time by at least 80%, demonstrating the practical application value of the algorithm.

scholarly journals Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters

2014 ◽  
Vol 73 (6) ◽  
pp. 2174-2184 ◽  
Author(s):  
Quinten Collier ◽  
Jelle Veraart ◽  
Ben Jeurissen ◽  
Arnold J. den Dekker ◽  
Jan Sijbers
Keyword(s):  
Magnetic Resonance ◽  
Least Squares ◽  
Robust Estimation ◽  
Linear Least Squares ◽  
Resonance Parameters ◽  
Magnetic Resonance Parameters

The robust estimation of autoregressive processes by functional least squares

1983 ◽  
Vol 20 (4) ◽  
pp. 737-753 ◽  
Author(s):  
C. R. Heathcote ◽  
A. H. Welsh
Keyword(s):  
Weak Convergence ◽  
Least Squares ◽  
Robust Estimation ◽  
Autoregressive Model ◽  
Minimum Variance ◽  
Error Distribution ◽  
Autoregressive Processes ◽  
Uniform Consistency ◽  
The Family ◽  
Error Distributions

The stationary autoregressive model but with a long-tailed error distribution is analysed using the method of functional least squares. A family of estimators indexed by a real parameter is obtained and uniform consistency and weak convergence established. The optimum member of the family is chosen to have minimum variance with respect to the parameter, and the parameter value chosen detects and adjusts for long-tailed error distributions. Results of a simulation are given.

Least Squares and Robust Estimation of Local Image Structure

2005 ◽  
Vol 64 (2-3) ◽  
pp. 143-155 ◽  
Author(s):  
Joost Van De Weijer ◽  
Rein Van Den Boomgaard
Keyword(s):  
Least Squares ◽  
Robust Estimation ◽  
Image Structure ◽  
Local Image

Applied Research on ER Algorithm of Gray Modeling

2011 ◽  
Vol 179-180 ◽  
pp. 1384-1389 ◽  
Author(s):  
Yong Li ◽  
Li Ping Tan ◽  
Bao Ru Xu
Keyword(s):  
Least Squares ◽  
Robust Estimation ◽  
Forest Fire ◽  
Applied Research ◽  
Least Squares Method ◽  
Interpolation Method ◽  
Calculation Methods ◽  
Er Algorithm

To improve the precision of gray modeling in forest fire and solve the problem of small date modeling, ER algorithm is proposed. Based on the senior introduced the robust estimation to gray modeling, this method interpolate the modeling date again. The method can achieve small date (3 dates) modeling. This research compared with three calculation methods: least squares method, least squares interpolation method and ER algorithm. According to the fitting precision, least squares method is 10.21%, least squares interpolation method is 1.08% and ER algorithm is 0.00%. That can be obtained by calculating ER algorithm has a good fitting effect.

Sign in / Sign up

Export Citation Format

Share Document