不适定平差模型的迭代解法及其在测量中的应用

Iteration Method for Ill-posed Problems and its Application in Geodesy

当平差模型为不适定模型时,比如模型病态时,一般是在均方误差准则条件下求得参数的有偏估计。有偏估计在参数的求解过程中,偏参数的确定是一个关键和困难问题。本文采用迭代解法求解不适定平差模型,无需确定偏参数,不仅可回避病态平差模型偏参数确定的困难,而且试验表明,对于秩亏不适定平差模型解算,也同样收到良好效果。

As is known to all that the least square estimator（LS） is suitable to solve the normal adjustment models and can gain linear unbiased estimation but not to the ill-posed ones. For example, when the adjustment models are ill-conditioned, the biased estimator can be used to solve the models and acquire a group of biased parameter estimation under the mean-square error criterion. By now what is an important and difficult problem for the biased estimator is how to fix the biased parameters and the rationality of some resolution methods of biased parameters used now remain in doubt. In this paper, the iteration methods was used to solve the ill-posed mod- els, for it can solve the ill-posed models without any biased parameters, besides, the examples show that the iterative methods are also fit for solving the rank-deficient adjustment models in Geodesy.