The weighted total least-squares (WTLS) estimate is sensitive to outliers and will be strongly disturbed if there are outliers in the observations and coefficient matrix of the partialerrors-in-variables (EIV) model....
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The weighted total least-squares (WTLS) estimate is sensitive to outliers and will be strongly disturbed if there are outliers in the observations and coefficient matrix of the partialerrors-in-variables (EIV) model. The L-1 norm minimization method is a robust technique to resist the bad effect of outliers. Therefore, the computational formula of the L-1 norm minimization for the partial EIV model is developed by employing the linear programming theory. However, the closed-form solution cannot be directly obtained since there are some unknown parameters in constrained condition equation of the presented optimization problem. The iterated procedure is recommended and the proper condition for stopping iteration is suggested. At the same time, by treating the partial EIV model as the special case of the non-linear Gauss-Helmert (G-H) model, another iterated method for the L-1 norm minimization problem is also developed. At last, two simulated examples and a real data of 2D affine transformation are conducted. It is illustrated that the results derived by the proposed L-1 norm minimization methods are more accurate than those by the WTLS method while the observations and elements of the coefficient matrix are contaminated with outliers. And the two methods for the L-1 norm minimization problem are identical in the sense of robustness. By comparing with the data-snooping method, the L-1 norm minimization method may be more reliable for detecting multiple outliers due to masking. But it leads to great computation burden.
Recent studies have extensively discussed total least squares (TLS) algorithms for solving the errors-in-variables (EIV) model with equality constraints but rarely investigated the inequality-constrained EIV model. Th...
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Recent studies have extensively discussed total least squares (TLS) algorithms for solving the errors-in-variables (EIV) model with equality constraints but rarely investigated the inequality-constrained EIV model. The most existing inequality-constrained TLS algorithms assume that all the elements in the coefficient matrix are random and independent and that their numerical efficiency is significantly limited due to combinatorial difficulty. To solve the above issues, we formulate a partial EIV model with inequality constraints of both unknown parameters and the random elements of the coefficient matrix. Based on the formulated EIV model, the inequality-constrained TLS problem is transformed into a linear complementarity problem through linearization. In this way, the inequality-constrained TLS method remains applicable even when the elements of the coefficient matrix are subject to inequality constraints. Furthermore, the precision of the constrained estimates is put forward from a frequentist point of view. Three numerical examples are presented to demonstrate the efficiency and superiority of the proposed algorithm. The application is accomplished by preserving the structure of random coefficient matrix and satisfying the constraints simultaneously, without any combinatorial difficulty.
An iterative algorithm for variance component estimation based on partialerrors-in-variables (PEIV) model is proposed. Correction of observation vector and random elements of the coefficient matrix is taken as one ki...
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An iterative algorithm for variance component estimation based on partialerrors-in-variables (PEIV) model is proposed. Correction of observation vector and random elements of the coefficient matrix is taken as one kind of posterior information. Variance components in the observation vector and the random elements of the coefficient matrix are estimated according to Helmert estimation method. During the estimating process, the correction factors are used to modify the initial weight matrix, so as to make it more accurate. At the same time, a method for determining correction factors is given. Through examples of linear fitting and numerical simulation experiment of coordinate transformation, the practical effect of this algorithm is verified.
A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectati...
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A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing.
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