Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy

Objective Adjustment methods for parameter estionation were basically developed on the basis of addi-tive random error models.With advances in the technology for modern geodetic observation,measure-ment errors can change with functional models such as EDM,GPS and VLBI baselines.Thus,ran-dom errors in measurements are proportional to the true values of the measurements themselves.Ob-servational models of this type are called multiplicative error models.The purpose of this paper is tocomplement or extend the work of Xu and Shimada(2000)to mixed additive and multiplicative errormodels.We briefly discuss three least squares(LS)adjustment methods for parameter estimation inmixed additive and multiplicative error models.In case of the weighted LS adjustment,we explicitlydescribe the biases in the adjusted parameters.Then,we construct a bias-corrected weighted leastsquares estimator.Finally,we demonstrate that the bias-corrected weighted LS method is optimal andunbiased using a simulated example.