摘要
截断奇异值法(TSVD)通过截断参数截掉病态矩阵中较小的奇异值来改善模型病态性的影响,提高模型参数的估计精度.由均方误差的角度分析可知,TSVD通过引入少量偏差,降低方差,来实现均方误差的下降,截断参数则是改善模型参数估值均方误差的关键因素.通过分析截掉奇异值后,TSVD模型参数估计方差与偏差的变化情况,提出了依据引入偏差量小于降低方差量确定截断参数的方法,理论依据更为充分,可靠性与准确性更高.将采用新方法确定截断参数的TSVD应用到测量坐标解算及PolInSAR植被高反演中,验证了新方法的可行性和有效性,相比于GCV法和L曲线法,新方法确定的截断参数有效提高了TSVD的解算质量,提高了坐标解算和植被高参数反演的精度和可靠性.
TSVD（truncated singular value decomposition）truncates small singular values by truncation parameter to improve the parameter estimation of ill-posed model.From the perspective of MSE（mean squared error）,TSVD introduces biases to reduce variances,therefore the MSE of the solution can be improved.Truncation parameter is the key factor of TSVD.The condition discrimination,L-curve and GCV（generalized cross-validation）which are commonly used to determine the truncation parameter are often unstable and unreliable due to that the methods ignore the changes of the MSE.This paper analyzed the changes of variances and biases after truncating the singular values and determined the truncation parameter by the criterily that the reduced variances should be more than the introduced biases.Therefore,the truncation parameter is more reliable.In order to prove the feasibility and effectiveness of the new method,the TSVD in which truncation parameter is determined by the new method was applied in coordinate estimation and PolInSAR（Polarimetric SAR Interferometry）vegetation height inversion.The new method improves the TSVD solution effectively with respect to L-curve and GCV method.The accuracy and reliability of the coordinate estimation and vegetation height inversion are obviously improved.
出处
《中国矿业大学学报》
EI
CAS
CSCD
北大核心
2017年第6期1386-1393,共8页
Journal of China University of Mining & Technology
基金
国家自然科学基金项目(41531068
41474008
41574006
41674012)
