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Formulation of L1 Norm Minimization in Gauss-Markov Models
Publisher: American Society of Civil Engineers
Abstract: norm minimization adjustment is a technique to detect outlier observations in geodetic networks. The usual method for implementation of
Least-Squares Formula for Zero Error (Z0) of Electromagnetic Distance Measuring Instruments
Publisher: American Society of Civil Engineers
Abstract: The zero error of electromagnetic distance measuring instruments is a near-constant systematic error, which has the same effect on the measured distances. This paper presents a least-squares formula for this correction ...
Weighted Total Least Squares with Singular Covariance Matrices Subject to Weighted and Hard Constraints
Publisher: American Society of Civil Engineers
Abstract: Weighted total least squares (WTLS) has been widely used as a standard method to optimally adjust an errors-in-variables (EIV) model containing random errors both in the observation vector and in the coefficient matrix. ...
Weighted Total Least Squares with Constraints: Alternative Derivation without Using Lagrange Multipliers
Publisher: American Society of Civil Engineers
Abstract: This technical note presents alternative derivations for the weighted total least-squares (WTLS) problem subject to weighted and hard constraints. The derivations do not take into account the Lagrange multipliers, and the ...
Multivariate Weighted Total Least Squares Based on the Standard Least-Squares Theory
Publisher: ASCE
Abstract: The weighted total least squares (WTLS) has been widely used in many geodetic problems to solve the error-in-variable (EIV) models in which both the observation vector and the design matrix contain random errors. This ...
Approach for Equivalent Accuracy Design of Different Types of Observations
Publisher: American Society of Civil Engineers
Abstract: The equivalency of observations in geodetic networks is one of the most important problems in surveying engineering, which has not been seriously considered before. This means that different types of observations should, ...
Recursive Algorithm for L1 Norm Estimation in Linear Models
Publisher: American Society of Civil Engineers
Abstract: L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the ...
Least-Squares Variance Component Estimation Applied to GPS Geometry-Based Observation Model
Publisher: American Society of Civil Engineers
Abstract: To achieve the best linear unbiased estimation of unknown parameters in geodetic data processing a realistic stochastic model for observables is required. This work is a follow-up to work carried out recently in which the ...
On the Covariance Matrix of Weighted Total Least-Squares Estimates
Publisher: American Society of Civil Engineers
Abstract: Three strategies are employed to estimate the covariance matrix of the unknown parameters in an error-in-variable model. The first strategy simply computes the inverse of the normal matrix of the observation equations, in ...
On the Covariance Matrix of Weighted Total Least-Squares Estimates
Publisher: American Society of Civil Engineers
Abstract: Three strategies are employed to estimate the covariance matrix of the unknown parameters in an error-in-variable model. The first strategy simply computes the inverse of the normal matrix of the observation equations, in ...
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