Partial multivariate errors-in-variables model and its application in settlement monitoring

Q. Wang, F. Hu

College of Civil Engineering, Xiangtan University, Xiangtan, Hunan, 411105, China

Abstract: Aiming at the problem that the coefficient matrix of multivariate errors-in-variables (MEIV) model contains constant columns, the MEIV model is extended to partial multivariate errors-in-variables (P-MEIV), and the new algorithm of P-MEIV model is proposed based on the principle of partial errors-in-variables (PEIV) model and indirect adjustment. The algorithm is simple and easy to implement. An example of coordinate transformation is used for verifying, and the results are compared with the existing MEIV model algorithm, which shows the effectiveness of the proposed algorithm. Finally, the P-MEIV algorithm is applied to the multi-point grey model (MGM(1,N)) of settlement monitoring. The results show that the P-MEIV model proposed in this paper can better consider the influence of monitoring point errors, and the estimated results are in good agreement with the actual situation.

Key words: multivariate errors-in-variables model, total least squares, multipoint grey model, settlement monitoring.

MSC: 15A04

Received: 01.12.2023
Revised: 19.03.2024
Accepted: 19.04.2024

DOI: 10.15372/SJNM20240301

 English version: Numerical Analysis and Applications, 2024, 17:3, 215–224