引用本文: 卢秀山, 宁津生, 冯尊德, 郭英. 观测有效性的度量方法[J]. 武汉大学学报 ( 信息科学版), 2003, 28(2): 144-148.
LU Xiushan, NING Jinsheng, FENG Zunde, GUO Ying. Measure Method to the Effectiveness of Observations[J]. Geomatics and Information Science of Wuhan University, 2003, 28(2): 144-148.
 Citation: LU Xiushan, NING Jinsheng, FENG Zunde, GUO Ying. Measure Method to the Effectiveness of Observations[J]. Geomatics and Information Science of Wuhan University, 2003, 28(2): 144-148.

## Measure Method to the Effectiveness of Observations

• 摘要: 基于Hilbert空间理论,通过对观测方程的系数阵实施格拉姆-施密特(Gram-Schmidt,G-S)正交化过程,分析观测的两个特性,从一个新的角度论证了参数估计的必要观测问题,以及多余观测与必要观测的关系;用欧氏范数‖·‖2和Frobenius‖·‖F范数作为基本度量工具对观测提供参数估计的信息量进行度量分析,研究观测的有效性和参数估计的可靠性。采用观测空间分析方法研究了测绘学科中必要观测、多余观测等基本概念;提出了观测信息量、观测有效性的概念和相应的度量方法;从观测的空间结构出发分析参数估计系统的可靠性,从一个侧面扩展和丰富了测绘学中的可靠性理论;丰富了研究测绘学中一些基本问题的分析方法,也为信息学中的数据挖掘问题提供了一种分析思路。

Abstract: In surveying practice,parameter estimation is based on indirect observations of parameters,and the number of indispensable independent observations is equal to the number of parameters.Generally,it is effective way to add redundant independent observations to ensure the reliability of parameter estimation and enhance the quality of estimation.There are two ignored problems,they are:Can the number of indispensable independent observations ensure finding the solution of the parameters adequately or not?How is about the effectiveness to add redundant independent observations to enhance the quality of estimation.Based on Hilbert pace theory,in this paper,analyzed two characteristics of observations by means of implementing Gram-Schmidt orthogonalizing process to column vectors of a coefficient matrix of observation equations,demon-strated the problem about indispensable observations of parameter estimation and the relationship of indispensable observations and redundant observations.And the information of observations that is offered to estimate the parameters is measured and analyzed with Euclidean norm ‖·‖2 and‖·‖F Frobenius norm they are used as measure tools,studied the effectiveness of observations and the reliability of parameter estimation.The contributions are these:It studied the basic conceptions and corresponding analysis methods about indispensable observation and redundant observation.Offered the conceptions and corresponding measure methods about the information of observations and the effectiveness of observations.Analyzed the reliability of the system of parameter estimation on the space fabric of observations and expanded and enriched the theory of reliability from one side in surveying subject.And enriched analysis methods to study some basic problems in surveying and offered an analysis way for data digging problem in informatics.

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