Abstract:The accuracy of solution for ill-posed model can be significantly improved by introducing the reasonable equality constraint between the adjustment parameters. However, the essence is to improve the ill-posedness of model by introducing regularizated parameters, which results in the change of structure of the observation equation. Therefore, the solution of ill-posed model with equality constraints is biased and its residual is amplified accordingly, which results that the unit weight medium error estimated by traditional formula is biased. In this paper, the unbiased estimation of unit weight medium error of constrained regularizated solution is derived according to mathematic expectancy formula of residual matrix in quadratic form, which is based on the unbiased estimation of unit weight variance for regularizated solution. The correctness of the formula is verified by numerical example and ill-posed trilateration network example and results show that the accuracy of unit weight medium error estimated by formula derived by this paper is better than traditional formula.
JI Kunpu,WANG Jinfang. Unbiased Estimation of Unit Weight Medium Error for Regularized Solution of Ill-Posed Problem with Equality Constraints[J]. jgg, 2019, 39(9): 960-965.