极大验后估计及其在扩建网中的应用

THE MAXIMUM POSTERIOR ESTIMATOR AND ITS APPLICATION TO EXTENDED NETWORKS

本文基于未知参数具有先验正态分布的广义Ｇ－Ｍ模型，推导了未知参数和方差因子的极大验后估计公式，证明了未知参数的极大验后估计是无偏、有效估计量，方差因子的极大验后估计有偏，并推导了方差因子的边缘极大验后估计，证明了它的无偏及有效性。作为应用，本文最后证明了扩建网极大验后平差成果等于新旧网整体平差成果。

The maximum POSterior estimation formulas of unknown parameters and the variance of unit weight have been derived in this paper based on the generalized Guass--Markov model with the priori normal distribution of the unknowns. It has been proved that the maximum POSterior estimates of the unknown parameters are unbiased and efficient,but the estimate of the varaince is biased. Furthermore the marginal maximum POSterior estimator of the variance proved to be unbiased and efficient has been derived. Finally a numerical example of data processing by using the maximum posterior estimator for a extended network is presented.