Solution for rank-defect EIV model based on TLS estimation

• Published in: Survey review - Directorate of Overseas Surveys Vol. 49; no. 354; pp. 171 - 175
• Main Authors: Yang, J., Wang, Y.-J., Wang, Q.-X., Tao, Y.-Q.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 04.05.2017
• Subjects: EIV model; Lagrange function; Rank defect model; Total least squares estimation
• ISSN: 0039-6265; 1752-2706
• DOI: 10.1080/00396265.2016.1144499

Coefficient matrix of mathematical model is rank defect because of lacking essential observation data, traditional method of solving this kind of problem is to supplement constraint condition and compute parameters of model under least squares estimation. However, when elements of coefficient matrix are also made up of observation data as observation vector, error in variables model (EIV model) exists while the model is rank defect. In the contribution, EIV model with rank defect problem is talked about. After proposing this problem, the character of rank defect model is analysed under total least squares estimation. Solution for rank defect model based on TLS is presented, and iterative algorithm is established based on Lagrange function in the contribution. Coordinate transformation model with big rotation angle is taken as an example to prove the feasibility and performance of the presented solution. Based on numerical results of the instance, some conclusions are drawn at last of the contribution.