tailieunhanh - Short-Wave Solar Radiation in the Earth’s Atmosphere Part 6

Dữ liệu quan sát Y có chứa các lỗi ngẫu nhiên đặc trưng với SD của các thành phần yi, i = 1,. . , N. Nói chung, các lỗi có thể tương quan, i. e. họ được kết nối với nhau (mặc dù tất cả mọi người nhằm mục đích để tránh điều này tương quan với tất cả các phương tiện có thể trong thực tế). | Accounting for Measurement Uncertainties and Regularization of the Solution 149 Observational data Y contain the random errors characterized with the SD of components yi i 1 . N. In general the errors could correlate i. e. they are interconnected although everybody aims to avoid this correlation with all possible means in practice . Thus the observational errors are described with symmetric covariance matrix Sy of dimension N X N which can be obtained conveniently by writing schematically according to Anderson 1971 as Sy y Y - Y Y - Y where Y is the exact unknown value of the measured vector Y is the observed value of the vector distinguishing from the exact value owing to the observational errors the summation is understood as an averaging over all statistical realizations of the observations of the random vector over the general set . The relation for covariance matrix of the errors Sx of parameters X of dimension K X K written in the same way as . Then substituting relation to it the following is obtained Sx y AY - AY AY - AY A y Y - Y Y - Y A Sx ASy A . A set of important consequences directly follows from Consequence 1. Equation expresses the relationship between the covariance matrices of observational errors Y and parameters X linearly linked with them through i. e. allows the finding of errors of the calculated parameters from the known observational errors. Namely values V Sx kk are the SD of parameters Xk values Sx kjly Sx kk Sx jj are the coefficients of the correlation between the uncertainties of parameters Xk and Xj. In the particular case of non-correlated observational errors that is often met in practice converts to the explicit formula convenient for calculations N Sx kj 2 akiajis2 k 1 . K j 1 . K i 1 where aki are the elements of matrix A si is the SD of parameter yi. In the case of the equally accurate measurements . s s1 . sN the direct proportionality of the SD of the observations and parameters