A novel sequential solution for multi-period observations based on the Gauss-Helmert model. (April 2022)

• Record Type: Journal Article
• Authors: Zhou, Tengfei; Lin, Peng; Zhang, Songlin; Zhang, Jingxia; Fang, Jiawei
• Is Part Of: Measurement. Volume 193(2022)
• Publication Date: 2022-04
• Subjects: Multi-epoch observations -- Sequential solution -- Gauss-Helmert model -- TLS; Weights and measures -- Periodicals; Measurement -- Periodicals; Measurement; Weights and measures; Periodicals; 530.8
• DOI: 10.1016/j.measurement.2022.110916
• Languages: English
• ISSNs: 0263-2241

Abstract

Highlights: Took into account the random errors and the stochastic information present in all measurements and was in consequence more rigorous towards dealing with multi-periods observations. Improved the computational efficiency of the non-linear Gauss-Helmert model considerably, compared with its global solution. Presented in the form of an abstract function, it is operationally applicable to a wide range of other problems with multi-period observations. Not limited to the case of multi-period observations, it is also possible to decompose a large amount of unrelated data into multiple components and then process them out using the proposed strategy. Abstract: In view of the inability of the GM model to account for random errors in the coefficient matrix and the fact that high-dimensional matrices reduce operational efficiency for any model, a novel Sequential Solution with reference to the nonlinear Gauss-Hemmert model, namely SSGH, is proposed, in which the associated efficient procedure is implemented by correlating only previous results and observations of the current period. The results show that the accuracy of parameter estimates as well as time-consumption, compared to the batch method based on the non-linear Gauss–Markov model and its sequential method, are significantly improved. Moreover, the proposed method is at least 60% more computationally efficient while maintaining the same level of accuracy as the Gauss-Helmert batch solution. It is undeniable, however, that the impact such as correlations among periods, gross errors and rank deficient, etc., require further investigation.