Least Squares Parameter Estimation in Additive/MultiplicativeError Models for Use in Geodesy
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摘要: 目的 扩展乘性误差模型的参数估计方法至加乘性混合误差模型,推导了其参数最小二乘、加权最小二乘参数估计,并在偏差分析的基础上推导了偏差改正加权最小二乘估计。模拟计算和分析验证了偏差改正加权最小二乘适用于加乘性混合误差模型的大地测量数据处理,具有二阶近似无偏性,且精度较高。
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关键词:
- 加乘性混合误差模型 /
- 最小二乘 /
- 加权最小二乘 /
- 偏差改正加权最小二乘
Abstract: 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. -
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