Measure Method to the Effectiveness of Observations

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.