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含系统性噪声的回归AI 解读

This paper identifies a type of highly correlated noise—systematic noise—that often arises in applications of linear regression to observations of spacecraft. An explicit formula is given for the inverse of the covariance matrix. The inverse matrix has a simple series expansion in ε2, where 1/ε is the amplitude of the systematic noise. When the leading term, the so-called filter matrix, is used in place of the exact inverse to estimate the regression parameters, the…

含系统性噪声的回归AI 解读

This paper identifies a type of highly correlated noise—systematic noise—that often arises in applications of linear regression to observations of spacecraft. An explicit formula is given for the inverse of the covariance matrix. The inverse matrix has a simple series expansion in ε2, where 1/ε is the amplitude of the systematic noise. When the leading term, the so-called filter matrix, is used in place of the exact inverse to estimate the regression parameters, the…