引用本文: 李豪, 顾勇为, 韩松辉. 基于信噪比检验的双截断奇异值估计[J]. 武汉大学学报 ( 信息科学版), 2019, 44(2): 228-232, 239.
LI Hao, GU Yongwei, HAN Songhui. Double Truncated Singular Value Estimation Based on Signal-to-Noise Ratio Test[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 228-232, 239.
 Citation: LI Hao, GU Yongwei, HAN Songhui. Double Truncated Singular Value Estimation Based on Signal-to-Noise Ratio Test[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 228-232, 239.

## Double Truncated Singular Value Estimation Based on Signal-to-Noise Ratio Test

• 摘要: 将复共线性对参数估计危害的度量结果与截断奇异值估计相结合，提出了基于信噪比检验的双截断奇异值估计。利用信噪比检验，根据每个参数最小二乘估计信噪比估值的大小将待估参数分为受复共线性危害较大和较小的两部分，并对这两部分参数的截断奇异值估计进行不同强度的截断。对受复共线性危害较大的部分参数，使其截断参数相对较小，对受复共线性危害较小的部分参数，使其截断参数较大。这种精细化的处理在有效降低参数估计方差的同时减少了偏差的引入。将基于信噪比检验的双截断奇异值估计应用于GEO卫星定轨仿真算例中，实验结果表明，新方法的解算精度较高。

Abstract: A double truncated singular value estimation based on signal-to-noise ratio test is proposed by combining the measurement results of the harm degree that complex common linear exerts on parameter estimation and the truncated singular value decomposition(TSVD) estimation. Based on the signal to noise ratio(SNR) test, all the parameters are divided into two parts, according to the estimated SNR value of each parameter's least square estimation. The TSVD estimation of these two parts is truncated at different intensities. We choose a smaller truncated parameter for parameters which suffer more from complex common linear, and a bigger truncated parameter for parameters which suffer less from complex common linear, thus minimize the deviation and reduce the variance of parameter estimation effectively. This new method is applied to the simulation example of the GEO satellite orbit determination. The experimental results show that the new method is more accurate.

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