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Application of variance components estimation to calibrate geoid error models.

Guo DM, Xu HZ - Springerplus (2015)

Bottom Line: Secondly, two different statistical models are presented to illustrate the theory.The first method directly uses the errors-in-variables as a priori covariance matrices and the second method analyzes the biases of variance components and then proposes bias-corrected variance component estimators.Several numerical test results show the capability and effectiveness of the variance components estimation procedure in combined adjustment for calibrating geoid error model.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, The Chinese Academy of Science, 340 Xudong Street, Wuhan, China.

ABSTRACT
The method of using Global Positioning System-leveling data to obtain orthometric heights has been well studied. A simple formulation for the weighted least squares problem has been presented in an earlier work. This formulation allows one directly employing the errors-in-variables models which completely descript the covariance matrices of the observables. However, an important question that what accuracy level can be achieved has not yet to be satisfactorily solved by this traditional formulation. One of the main reasons for this is the incorrectness of the stochastic models in the adjustment, which in turn allows improving the stochastic models of measurement noises. Therefore the issue of determining the stochastic modeling of observables in the combined adjustment with heterogeneous height types will be a main focus point in this paper. Firstly, the well-known method of variance component estimation is employed to calibrate the errors of heterogeneous height data in a combined least square adjustment of ellipsoidal, orthometric and gravimetric geoid. Specifically, the iterative algorithms of minimum norm quadratic unbiased estimation are used to estimate the variance components for each of heterogeneous observations. Secondly, two different statistical models are presented to illustrate the theory. The first method directly uses the errors-in-variables as a priori covariance matrices and the second method analyzes the biases of variance components and then proposes bias-corrected variance component estimators. Several numerical test results show the capability and effectiveness of the variance components estimation procedure in combined adjustment for calibrating geoid error model.

No MeSH data available.


Behavior of variance-component estimated by MINQUE.
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Fig5: Behavior of variance-component estimated by MINQUE.

Mentions: In order to study the correlations among observations, numerical tests are performed with diagonal CV matrices. Figure 5 shows the convergence behaviors of the estimated variance components by MINQUE in each of successive iterations for observable. The results demonstrate the computational efficiency.Fig. 5


Application of variance components estimation to calibrate geoid error models.

Guo DM, Xu HZ - Springerplus (2015)

Behavior of variance-component estimated by MINQUE.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4542880&req=5

Fig5: Behavior of variance-component estimated by MINQUE.
Mentions: In order to study the correlations among observations, numerical tests are performed with diagonal CV matrices. Figure 5 shows the convergence behaviors of the estimated variance components by MINQUE in each of successive iterations for observable. The results demonstrate the computational efficiency.Fig. 5

Bottom Line: Secondly, two different statistical models are presented to illustrate the theory.The first method directly uses the errors-in-variables as a priori covariance matrices and the second method analyzes the biases of variance components and then proposes bias-corrected variance component estimators.Several numerical test results show the capability and effectiveness of the variance components estimation procedure in combined adjustment for calibrating geoid error model.

View Article: PubMed Central - PubMed

Affiliation: State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, The Chinese Academy of Science, 340 Xudong Street, Wuhan, China.

ABSTRACT
The method of using Global Positioning System-leveling data to obtain orthometric heights has been well studied. A simple formulation for the weighted least squares problem has been presented in an earlier work. This formulation allows one directly employing the errors-in-variables models which completely descript the covariance matrices of the observables. However, an important question that what accuracy level can be achieved has not yet to be satisfactorily solved by this traditional formulation. One of the main reasons for this is the incorrectness of the stochastic models in the adjustment, which in turn allows improving the stochastic models of measurement noises. Therefore the issue of determining the stochastic modeling of observables in the combined adjustment with heterogeneous height types will be a main focus point in this paper. Firstly, the well-known method of variance component estimation is employed to calibrate the errors of heterogeneous height data in a combined least square adjustment of ellipsoidal, orthometric and gravimetric geoid. Specifically, the iterative algorithms of minimum norm quadratic unbiased estimation are used to estimate the variance components for each of heterogeneous observations. Secondly, two different statistical models are presented to illustrate the theory. The first method directly uses the errors-in-variables as a priori covariance matrices and the second method analyzes the biases of variance components and then proposes bias-corrected variance component estimators. Several numerical test results show the capability and effectiveness of the variance components estimation procedure in combined adjustment for calibrating geoid error model.

No MeSH data available.