scholarly journals A weighted least squares solution for space intersection of spaceborne stereo SAR data

2001 ◽  
Vol 39 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Pu-Huai Chen ◽  
I.J. Dowman
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Solution ◽  
Sar Data

Convolutional quelling in seismic tomography

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 570-580 ◽  
Author(s):  
Keith A. Meyerholtz ◽  
Gary L. Pavlis ◽  
Sally A. Szpakowski
Keyword(s):  
Least Squares ◽  
Seismic Tomography ◽  
Nearest Neighbor ◽  
Sparse Matrix ◽  
Weighted Least Squares ◽  
Synthetic Data ◽  
Least Squares Solution ◽  
Smoothing Filter ◽  
Imaging Artifacts ◽  
Tomography Data

This paper introduces convolutional quelling as a technique to improve imaging of seismic tomography data. We show the result amounts to a special type of damped, weighted, least‐squares solution. This insight allows us to implement the technique in a practical manner using a sparse matrix, conjugate gradient equation solver. We applied the algorithm to synthetic data using an eight nearest‐neighbor smoothing filter for the quelling. The results were found to be superior to a simple, least‐squares solution because convolutional quelling suppresses side bands in the resolving function that lead to imaging artifacts.

scholarly journals Robust Estimations of Current Velocities with Four-Beam Broadband ADCPs

2009 ◽  
Vol 26 (12) ◽  
pp. 2642-2654 ◽  
Author(s):  
M. Gilcoto ◽  
Emlyn Jones ◽  
Luis Fariña-Busto
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Robust Solution ◽  
Least Squares Solution ◽  
Weighted Least Squares Method ◽  
Radial Beam ◽  
Least Squares Approach ◽  
Variance Covariance Matrix

Abstract An extended explanation of the hypothesis and equations traditionally used to transform between four-beam ADCP radial beam velocities and current velocity components is presented. This explanation includes a dissertation about the meaning of the RD Instrument error velocity and a description of the standard beam-to-current components transformation as a least squares solution. Afterward, the variance–covariance matrix associated with the least squares solution is found. Then, a robust solution for transforming radial beam velocities into current components is derived under the formality of a weighted least squares approach. The associated variance–covariance matrix is also formulated and theoretically proves that the modulus of its elements will be generally lower than the corresponding modulus of the variance–covariance matrix associated with the standard least squares solution. Finally, a comparison between the results obtained using the standard least squares solution and the results of the weighted least squares method, using a high-resolution ADCP dataset, is presented. The results show that, in this case, the weighted least squares solution provides variance estimations that are 4% lower over the entire record period (8 days) and 7% lower during a shorter, more energetic period (12 h).

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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