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Covariance matrix for a 2D state vector

I'm performing Optimal Interpolation (which in fact is a simplified Kalman filter with constant $\mathbf{K}$). My state variable is a 2D concentration field with a size of 370 x 400 on which I try to ...
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Variance-weighted interpolation

I am trying to fit a function $f$ to the data pictured below: For $\hat{f}(0)$ I can take the sample mean of the 6 observations at $0$, for $\hat{f}(2)$, I average the 2 at 2. For $\hat{f}(1)$, I ...