Generalized Inverse

The variational inverse problems discussed in Chap. 5 can be derived from the Bayesian formulation presented in the previous Chapter by assuming Gaussian statistics for the priors. This was previously demonstrated by van Leeuwen and Evensen (1996) using the results from Jazwinski (1970). We will now derive the generalized inverse formulation for the combined parameter and state estimation problem starting from Bayes’ theorem. Further, the resulting Euler–Lagrange equations are derived and we discuss some solution methods which also allow for the estimation of poorly known model parameters.