Fig. 3
From: Data Assimilation Methods for Neuronal State and Parameter Estimation
Example cost function for 4D-Var. (A) Surface generated by taking the logarithm of \(C(\alpha,\beta)\), where \(C(\alpha,\beta) = C (\mathbf{x}_{0}(1-\alpha)(1-\beta) + \alpha x_{\textrm{min,d}} +\beta x_{\textrm{min,s}} )\) so that at \(\alpha =\beta=0\), \(\mathbf{x}=\mathbf{x}_{0}\) (magenta circle), and at \(\alpha=1\) and \(\beta=0\), \(\mathbf{x}=x_{\textrm{min,d}}\) for the deeper minima (gray square), and similarly for the shallower minima (gray diamond). (B) Contour plot of the surface shown in (A)