Bias Reduction Method for Parameter Inversion of Ill-Posed Surveying Model

Abstract

Because of ill-posed problems, inverted parameters of ill-posed models always have large variances. The regularization method is widely used to solve this problem. Based on the mean square error (MSE) criterion, the regularization method reduces the parameter estimation variances through introducing biases. However, excessive biases will increase the MSE and the unreliability of the estimates. To improve this situation, this paper first analyzes the calculation of the MSE through the singular value decomposition (SVD) method and then proposes a bias reduction method. Based on this method, a bias-reduced regularization method is proposed to improve the MSE of regularized model parameter estimations. Simulation and practical examples are respectively displayed to demonstrate the effectiveness of the new method. In the simulation example, the root-mean-square error (RMSE) of the regularized model parameter estimates is reduced by 78%. In the polarimetric interferometric synthetic aperture radar (PolInSAR) surveying example, the RMSE of the inverted vegetation height is improved by 23%. Both examples clearly show the effectiveness of the new method.