利用TSVD参数估值变化特性确定算法截断参数

TSVD是大地测量病态问题解算的常用有效方法。影响TSVD解算效果的关键因素是截断参数,现有截断参数确定方法可提供有效的截断参数,但仍难以给出最优截断参数。以均方误差最小为准则确定截断参数是一种理论依据较充分的截断参数确定方法,但均方误差计算所需的模型参数真值在实际应用中无法获得,导致该方法难以给出理论最优截断参数。鉴于此,本文研究了基于均方误差影响下(方差与偏差联合影响)参数估值变化特性的TSVD截断参数确定方法。通过TSVD依次截掉小奇异值,获得奇异值截掉前后的方差与参数估值变化,利用两者变化分析确定偏差影响,避免依赖参数真值计算偏差,从而确定出均方误差最小理论下的截断参数。数值与应用试验结果表明,本文方法确定的截断参数可有效改善TSVD解算效果,是一种行之有效的截断参数确定方法。

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

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.