各种平差方法的统一与特性

本文选取了一个能概括各种平差方法的函数模型,即附有限制条件的条件平差模型,详细推导了该平差法的计算公式和精度评定公式,证明了其平差结果的统计性质。该方法的计算公式和精度评定公式可以应用于所有经典平差法和广义平差法,因此,可以称为平差的通用公式。为了说明由通用公式可以很方便地引出其他各种方法的公式的具体形式,本文又以经典条件平差、经典间接平差和广义平差中的滤波推估为例,从通用公式引出了这些方法的相应公式。

Uniformity and Particularity of Various Adjustment Methods

The present paper designs a functional model summerizing various adjustment me-thods——the model of condition adjustment with constraints.Then it derives in detail its formulas of adjustment computation and accuracy estimation,proving the statistical properties of its adjusted result.The formulas of this method are in fact applicable to all the methods of classical adjustment and generalized adjustment,therefore can be termed as the General Adjustment Formulas.In order to illustrate that from the General Adjustment Formulas it is convenient to derive the particular formulas of all the other methods,this paper takes the classical condition adjustment,classical parameter adjust-ment,and the filtering and prediction in the generalized adjustment as examples,and derives respectively the corresponding formulas of those methods from the General Adjustment Formulas. The adjustment textbooks and reference books,both at home and abroad,conven-tionally introduce various adjustment methods in isolation,thus having to derive the formulas of adjustment computation and accuracy estimation of these methods cumber-somely one by one.For this approach there are two obvious disadvantages: 1) its occupation of a very large space for derivation;and 2) its failure to reveal the inner relationships among various methods,and consequently,its difficulty in displaying the uniformity and particularity of those methods.These disadvantages can be desirably overcome if the new system introduced in this paper is adopted.