Unbiased Estimation of Unit Weight Variance by TSVD Regularization

The truncated singular value method (TSVD) improves the morbidity of model by truncating small singular values of the ill-posed observational equation matrix and increases the stability and accuracy of the parameter estimation. However, the structure of observation equation has been changed after truncating small singular value, which makes parameter valuation and residual biased, the unit weight variance cannot be calculated by using traditional estimation formula. This paper derives the unbiased formula of unit weight variance for TSVD regularization, and uses the first Fredholm integral equation and ill-posed trilateration network as examples to verify the correctness of the formula.