Sequential bias-corrected weighted least squares solution of mixed additive and multiplicative error models

Abstract

In the era of big data, the number of observations in adjustment calculations may reach tens or even hundreds of thousands. When dealing with these large dataset problems, many matrix operations are often required. At this time, the dimensions of the matrix will be large, which will generate a great computational burden. At present, no research results have been published on the computational efficiency of bias-corrected weighted least squares (bcWLS) for mixed additive and multiplicative error models (MAMEM). Sequential adjustment (SEA) groups the observations for calculation and can provide the same computational precision while greatly improving computational efficiency. This paper applies the idea of SEA to the calculation of bcWLS and proposes an iterative solution for sequential bcWLS (SEbcWLS). Using three simulation experiments to verify the effectiveness of our method, it was found that when the number of observations is 10000, the effect is better when the number of groups does not exceed 100, achieving the same precision as the original method while having high computational efficiency. The calculation results of line fitting and plane fitting are not affected by the number of grouping groups. For DEM (Digital elevation model) experiments with strong nonlinearity, when the number of grouping groups is too large, the effect is not very good, but the calculation efficiency is also higher than the original method, and the difference in calculation results is not significant.