Regularization parameter determination method based on MSE relative variation rule and its application in PolInSAR surveying inversion

doi:10.11947/j.AGCS.2023.20220453

Abstract

Abstract: The regularization method is currently the most widely used method for solving ill-posed problems in geodesy, and the regularization parameter is the key parameter that affects the solution result of the regularization method. With sufficient theoretical basis, the regularization parameter determination method based on the minimum mean square error (MSE) criterion can increase the estimation accuracy of model parameters efficiently. However, the calculation of the mean square error requires the true value of model parameters which is replaced by the estimated value in practice. As a result, the accurate mean square error is difficult to obtain, which greatly limits the effectiveness of the regularization parameters. In view of this, this paper analyzes the variation law of variance and bias caused by the changes of regularization parameter, and proposes a determination method for relative variation of mean square error. According to the principle that the true value of model parameters does not change under different regularization parameters, the calculation of the relative changes of variance and bias under different regularization parameters can effectively remove the influence of unknown true values of model parameters on mean square error estimation. This paper firstly uses different regularization parameters to calculate the relative changes of variance and standard deviation between the two regularization parameters; then calculates the model parameter estimate change between the two regularization parameters. The relative variation of bias under the two regularization parameters is obtained by difference operation analysis of variance change and model parameter estimate change. Finally, the regularization parameter with the maximum reduction of the mean square error is obtained by integrating the changes of standard deviation and bias. The feasibility of the new method is verified by the polarimetric interferometric synthetic aperture radar (PolInSAR) vegetation height inversion experiment. All Experiments show that the new method can effectively enhance the parameter estimation accuracy of the regularization method. Both of the parameter inversion accuracy of the two PolInSAR surveying experiments are improved. Those reasonably verify the feasibility and effectiveness of the new method.

Key words: mean square error, regularization method, regularization parameter, relative change, PolInSAR surveying

CLC Number:

P227

LIN Dongfang, YAO Yibin, ZHENG Dunyong, LIAO Mengguang, XIE Jian. Regularization parameter determination method based on MSE relative variation rule and its application in PolInSAR surveying inversion[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(9): 1480-1491.

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