EIV models and algorithms of weighted total least squares problem*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

doi:10.11947/j.AGCS.2019.20190155

Acta Geodaetica et Cartographica Sinica ›› 2019, Vol. 48 ›› Issue (7): 931-937.doi: 10.11947/j.AGCS.2019.20190155

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EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

WANG Leyang^1,2, YU Hang³, ZOU Chuanyi², LU Tieding²

1. Collage of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China;
2. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
3. School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China

Received:2019-04-28 Revised:2019-05-09 Online:2019-07-20 Published:2019-07-26
Supported by:
The National Natural Science Foundation of China (Nos. 41664001; 41874001); The Outstanding Youth Talents in Jiangxi Province (No. 20162BCB23050); The National Key Research and Development Program (No. 2016YFB0501405)

Abstract

Abstract: A weighted total least squares (WTLS) method is a kind of parameter estimation method which takes into account the observation errors in both the observation vector and the coefficient matrix of the EIV (errors-in-variables) model. The EIV model presents different structural characteristics in terms of different application scenarios. A EIO model is proposed by the paper "Weighted total least square adjustment EIO model and its algorithms" to deal with the structural problem of the EIV model^*. In order to compare the EIO model method with the existing EIV model parameter estimation method, four kinds of methods are listed to deal with the structural characteristics of the EIV model, and eight parameter estimation formulas are summed up. Furthermore, the first-order and higher-order approximate precision estimation methods of WTLS solutions are discussed. It is emphasized that the EIV model and its parameter estimation theory can be developed from three aspects:functional model, stochastic model and the WTLS parameter estimation method. Although different methods are proposed, the problem is solved in an equivalent way.

Key words: EIV model, weighted total least squares algorithm, precision estimation, coefficient matrix, parameter estimation

CLC Number:

P207

WANG Leyang, YU Hang, ZOU Chuanyi, LU Tieding. EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(7): 931-937.

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EIV models and algorithms of weighted total least squares problem^*: discuss with “Weighted total least square adjustment EIO model and its algorithms”

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