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Scaled weighted total least-squares adjustment for partial errors-in-variables model
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| Zeitschriftentitel: | Journal of Geodetic Science |
|---|---|
| Personen und Körperschaften: | |
| In: | Journal of Geodetic Science, 6, 2016, 1 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Walter de Gruyter GmbH
|
| Schlagwörter: |
| author_facet |
Zhao, J. Zhao, J. |
|---|---|
| author |
Zhao, J. |
| spellingShingle |
Zhao, J. Journal of Geodetic Science Scaled weighted total least-squares adjustment for partial errors-in-variables model Applied Mathematics Earth and Planetary Sciences (miscellaneous) Computers in Earth Sciences Geophysics Astronomy and Astrophysics |
| author_sort |
zhao, j. |
| spelling |
Zhao, J. 2081-9943 Walter de Gruyter GmbH Applied Mathematics Earth and Planetary Sciences (miscellaneous) Computers in Earth Sciences Geophysics Astronomy and Astrophysics http://dx.doi.org/10.1515/jogs-2016-0010 <jats:title>Abstract</jats:title> <jats:p>Scaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.</jats:p> Scaled weighted total least-squares adjustment for partial errors-in-variables model Journal of Geodetic Science |
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10.1515/jogs-2016-0010 |
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Walter de Gruyter GmbH, 2016 |
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Journal of Geodetic Science |
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| title |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_unstemmed |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_full |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_fullStr |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_full_unstemmed |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_short |
Scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| title_sort |
scaled weighted total least-squares adjustment
for partial errors-in-variables model |
| topic |
Applied Mathematics Earth and Planetary Sciences (miscellaneous) Computers in Earth Sciences Geophysics Astronomy and Astrophysics |
| url |
http://dx.doi.org/10.1515/jogs-2016-0010 |
| publishDate |
2016 |
| physical |
|
| description |
<jats:title>Abstract</jats:title>
<jats:p>Scaled total least-squares (STLS) unify LS, Data
LS, and TLS with a different choice of scaled parameter.
The function of the scaled parameter is to balance the
effect of random error of coefficient matrix and observation
vector for the estimate of unknown parameter. Unfortunately,
there are no discussions about how to determine
the scaled parameter. Consequently, the STLS solution
cannot be obtained because the scaled parameter is
unknown. In addition, the STLS method cannot be applied
to the structured EIV casewhere the coefficient matrix contains
the fixed element and the repeated random elements
in different locations or both. To circumvent the shortcomings
above, the study generalize it to a scaledweighted TLS
(SWTLS) problem based on partial errors-in-variable (EIV)
model. And the maximum likelihood method is employed
to derive the variance component of observations and coefficient
matrix. Then the ratio of variance component is
proposed to get the scaled parameter. The existing STLS
method and WTLS method is just a special example of the
SWTLS method. The numerical results show that the proposed
method proves to bemore effective in some aspects.</jats:p> |
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| description | <jats:title>Abstract</jats:title> <jats:p>Scaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.</jats:p> |
| doi_str_mv | 10.1515/jogs-2016-0010 |
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| imprint_str_mv | Walter de Gruyter GmbH, 2016 |
| institution | DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229 |
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| publishDate | 2016 |
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| series | Journal of Geodetic Science |
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| spelling | Zhao, J. 2081-9943 Walter de Gruyter GmbH Applied Mathematics Earth and Planetary Sciences (miscellaneous) Computers in Earth Sciences Geophysics Astronomy and Astrophysics http://dx.doi.org/10.1515/jogs-2016-0010 <jats:title>Abstract</jats:title> <jats:p>Scaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.</jats:p> Scaled weighted total least-squares adjustment for partial errors-in-variables model Journal of Geodetic Science |
| spellingShingle | Zhao, J., Journal of Geodetic Science, Scaled weighted total least-squares adjustment for partial errors-in-variables model, Applied Mathematics, Earth and Planetary Sciences (miscellaneous), Computers in Earth Sciences, Geophysics, Astronomy and Astrophysics |
| title | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_full | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_fullStr | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_full_unstemmed | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_short | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_sort | scaled weighted total least-squares adjustment for partial errors-in-variables model |
| title_unstemmed | Scaled weighted total least-squares adjustment for partial errors-in-variables model |
| topic | Applied Mathematics, Earth and Planetary Sciences (miscellaneous), Computers in Earth Sciences, Geophysics, Astronomy and Astrophysics |
| url | http://dx.doi.org/10.1515/jogs-2016-0010 |