Solution for ill-posed EIV model regularization attending to its decreasing regularization characteristic
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Yeqing Tao
,
Juan Yang
Abstract
The errors-in-variables (EIV) model is used for data processing in the field of geodesy. However, the EIV model may be ill-posed. By analyzing the decreasing regularization (D-regularization) characteristic of solutions for EIV models, algorithms using traditional methods such as singular value decomposition or the Tikhonov function can directly determine the irrationality of a model. When an EIV model is ill-posed, solutions in which the observation errors in the coefficient matrix are simulated by variables make the ill-posed nature of the model more serious. This is because the simulated observation errors are subtracted from the coefficient matrix in subsequent computations, which reduces the singular value of the normal matrix. This point is verified using an example. To account for the D-regularization of solutions in EIV models, a modified algorithm is derived by classifying the models into two categories, and the regularization parameters are iteratively revised based on the mean squared error. Finally, some conclusions are drawn from two separate examples.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 41601501
Funding source: Natural Science Found for Colleges and Universities of Jiangsu Province
Award Identifier / Grant number: 16KJD420001
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was financially supported by the National Natural Science Foundation of China (41601501), Natural Science Found for Colleges and Universities of Jiangsu Province (16KJD420001).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
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- Accuracy and reliability of BeiDou clocks
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Articles in the same Issue
- Frontmatter
- Review
- Investigation of the trade-off between the complexity of the accelerometer bias model and the state estimation accuracy in INS/GNSS integration
- Original Research Articles
- Solution for ill-posed EIV model regularization attending to its decreasing regularization characteristic
- Trajectory evaluation using repeated rail-bound measurements
- Global geopotential models evaluation based on terrestrial gravity data over Ethiopia
- A calculation method for GNSS positioning precision based on the posteriori unit weight variance
- Accuracy and reliability of BeiDou clocks
- Positioning performance with dual-frequency low-cost GNSS receivers
- Estimating 3D displacement vectors from line-of-sight observations with application to MIMO-SAR
- Determination of the height reference surface for the Republic of Albania by using global geopotential models
- An integrated adaptive Kalman filter for improving the reliability of navigation systems
