Progress towards a rigorous error propagation for total least-squares estimates
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Burkhard Schaffrin
Abstract
After several attempts at a formal derivation of the dispersion matrix for Total Least-Squares (TLS) estimates within an Errors-In-Variables (EIV) Model, here a refined approach is presented that makes rigorous use of the nonlinear normal equations, though assuming a Kronecker product structure for both observational dispersion matrices at this point. In this way, iterative linearization of a model (that can be established as being equivalent to the original EIV-Model) is avoided, which might be preferred since such techniques are based on the last iteration step only and, therefore, produce dispersion matrices for the estimated parameters that are generally too optimistic. Here, the error propagation is based on the (linearized total differential of the) exact nonlinear normal equations, which should lead to more trustworthy measures of precision.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial to the special edition of the JAG on Deformation Monitoring
- Research Articles
- Determination of the tectonic plates motion parameters based on SLR, DORIS and VLBI stations positions
- Deformation detection through the realization of reference frames
- Performance of Msplit estimates in the context of vertical displacement analysis
- Progress towards a rigorous error propagation for total least-squares estimates
- Reducing multipath effect of low-cost GNSS receivers for monitoring by considering temporal correlations
- F2S3: Robustified determination of 3D displacement vector fields using deep learning
- Improved kinematic Precise Point Positioning performance with the use of map constraints
- The direct geodesic problem and an approximate analytical solution in Cartesian coordinates on a triaxial ellipsoid
- A benchmarking measurement campaign in GNSS-denied/challenged indoor/outdoor and transitional environments
- Partially error-affected point-wise weighted closed-form solution to the similarity transformation and its variants
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial to the special edition of the JAG on Deformation Monitoring
- Research Articles
- Determination of the tectonic plates motion parameters based on SLR, DORIS and VLBI stations positions
- Deformation detection through the realization of reference frames
- Performance of Msplit estimates in the context of vertical displacement analysis
- Progress towards a rigorous error propagation for total least-squares estimates
- Reducing multipath effect of low-cost GNSS receivers for monitoring by considering temporal correlations
- F2S3: Robustified determination of 3D displacement vector fields using deep learning
- Improved kinematic Precise Point Positioning performance with the use of map constraints
- The direct geodesic problem and an approximate analytical solution in Cartesian coordinates on a triaxial ellipsoid
- A benchmarking measurement campaign in GNSS-denied/challenged indoor/outdoor and transitional environments
- Partially error-affected point-wise weighted closed-form solution to the similarity transformation and its variants
