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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.
Truncated singular value method (TSVD) truncated the smaller singular values in the morbid matrix to improve the model’s ill-posedness and improve the estimation accuracy of the model parameters.According to the analysis of mean square error, we can see that by introducing a small amount of bias, Reduce the variance to reduce the mean square error.The truncation parameter is the key factor to improve the mean square error of the model parameter estimation.Based on the analysis of variance and deviation of the TSVD model after the cutoff of the singular value, The deviation is less than the method of reducing the amount of variance to determine the truncation parameters, the theoretical basis is more sufficient, and the reliability and accuracy are higher.With a new method to determine the TSVD truncation parameters applied to the measurement coordinate solution and PolInSAR vegetation inversion, verification Compared with GCV method and L curve method, the truncation parameters determined by the new method effectively improve the solution quality of TSVD and improve the accuracy and reliability of coordinate solution and vegetation high parameter inversion Sex.