Determination of truncation parameter based on the differences of TSVD parameter estimates for ill-posed problems in geodesy

doi:10.11947/j.AGCS.2022.20210377

Abstract

Abstract: TSVD is an effective method commonly used in solving ill-posed geodetic problems.In this method,truncation parameter is a critical factor.However,the existing methods can only work out effective truncation parameters rather than identify the optimal truncation parameter.Determining truncation parameters based on the minimum mean square error is a relatively complete theoretical way to determine truncation parameters.But the true values of the model parameters required for the calculation of the mean square error cannot be obtained in practical applications,which makes it difficult to calculate the optimal truncation parameter theoretically.To solve these,this paper develops a method to identify the TSVD truncation parameter on the basis of the variation characteristics of the parameter estimation in the influence of the mean square error (including variance and bias).To achieve this,this paper truncates small singular values in turn based on TSVD to acquire the changes of the variance and parameter estimation and analyzes the changes to determine the effects of the biases,which can avoid the calculation biases in the use of the true value of the parameters.Thereby,based on the theory of the minimum mean square error,the truncation parameter can be determined.The results in numerical experiments and practical applications show that the truncation parameters in the new method can effectively improve the quality of TSVD solution.Therefore,the proposed method is an effective method to determine the truncation parameters.

Key words: ill-posed problem, TSVD, truncation parameter, mean square error, bias

CLC Number:

P207

LIN Dongfang, YAO Yibin, ZHENG Dunyong, LI Chaokui. Determination of truncation parameter based on the differences of TSVD parameter estimates for ill-posed problems in geodesy[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(8): 1787-1796.

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