A novel sequential solution for multi-period observations based on the Gauss-Helmert model

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.