CovarianceSst

Provides arc wise covariance matrices for satellite-to-satellite observations SST). The inputfileCovarianceFunction provides a temporal covariance function. From it the Toeplitz covariance matrix is constructed \[ \M C = \begin{pmatrix} cov(t_0) & cov(t_1) & \cdots & & & \\ cov(t_1) & cov(t_0) & cov(t_1) & \cdots & & \\ \cdots & cov(t_1) & cov(t_0) & cov(t_1) & \cdots & \\ & \cdots & \ddots & \ddots & \ddots & \cdots \\ \end{pmatrix} \\ \] The complete covariance matrix of an arc is given by \[ \M C_{arc} = \sigma_0^2 \sigma_{arc}^2 \M C + \sigma_{S,arc}^2 \M S_{arc}+ \text{diag}(\sigma_1^2, \sigma_2^2, \ldots, \sigma_n^2) \]where sigma $\sigma_0$ is an overall factor and the arc specific factors $\sigma_{arc}$ can be provided with inputfileSigmasPerArc. The second term describes general covariance matrices for each arc inputfileCovarianceMatrixArc together with the factors $\sigma_{S,arc}$ from sigmasCovarianceMatrixArc. The last matrix can be used to downweight outliers in single epochs and will be added if inputfileSigmasPerEpoch is provided.