Parameter Estimation Methods for Correlated Observation Multiplicative Random Error Model in Geodetic Measurement

In the field of geodetic data processing, the existing literature on the treatment of the multiplicative random error model assumes that the random multiplicative error elements are independent of one another. However, there is no research exploring the correlation between these elements of the multiplicative random error. In this paper, we have developed three parameter estimation methods for the correlated observation multiplicative random error model based on existing literature research. These methods are derived using formulas for variance and correlation coefficients. The three methods are the correlated observation least squares method, the correlated observation weighted least squares method, and the correlated observation bias-corrected weighted least squares method. Additionally, the corresponding formulas for the unit weight mean square error and standard deviation are provided. The numerical simulation results demonstrate that, for the multiplicative random error model of correlated observations, the correlated observation bias-corrected weighted least squares method yields the optimal parameter estimation with higher accuracy, making it the most effective approach for solving this model.