Research On The Estimation Of Numerical Characteristics Of Length Measurements

Numerical characteristics analysis in length measurements is an important issue in geographic information systems and mapping operations.The length measurements can also be seen as the distance between the two endpoints,and the study of the digital characteristics of the distance measurements between the two endpoints becomes an important problem in the current geometrics.At present,the estimation methods for the numerical features of the measured values are usually measured several times,averaging the mean,and then estimating the variance by expectation;but these methods are meaningful only if the sample is large enough.In practical applications,the sample points are usually not large enough,which makes the use of traditional methods to obtain the observed value of the digital characteristics of a great deal of uncertainty.And then,it is very important to study the estimation methods of numerical characteristics of length measurement from the theoretical points of view.In order to overcome the shortcomings of the existing estimation methods and the existing problems in the literature,in accordance with the mathematical theory and statistical methods,through the rigorous mathematical derivation,this paper presents the Taylor series expansion based on the length of the measurements and the improved method of the numerical features of the measured values based on the Newton interpolation polynomials.The application of Taylor series expansion in the estimation of length measurement is studied.The expression of the length measurement deviation and the nonlinear error propagation formula of the distance equation based on the high order Taylor series expansion are deduced.At the same time,Monte Carlo is used to generate random.The results show that the proposed method has high accuracy and reference value in the estimation of the deviation.The accuracy of the deviation estimation is related to the accuracy of the measured distance.The expansion order of Taylor series expansion also affects the accuracy of the deviation estimation.For the ultra-short segments measurement,the Taylor series expansion estimation method can not achieve the expected calculation results,showing the uncertainty.In order to make further study the ultra-short distance measurements,this paper proposes a digital feature estimation method based on Newton interpolation polynomial approximation and least squares optimization(LS),constructs interpolation polynomials,that is,constructs digitalfeatures by known observations.The accuracy of the proposed method is closely related to the variance matrix of the construction,and the construction matrix affects whether the digital feature estimation is solvable.And then the validity of the method is verified by selecting a shorter distance measurement estimate.