How does PEST regularize?
There are two broad types of mathematical regularisation, Both are available through PEST. They can be used either individually or together. Tikhonov regularisation “fixes up” an ill-posed inverse problem by adding information to it, this information pertaining directly to system parameters. For example preferred values can be suggested for all parameters. Alternatively, or as well, preferred relationships between them (such as smoothness relationships) can be suggested. The user then sets a “target measurement objective function” defining a desired level of model-to-measurement misfit – hopefully set in accordance with the expected level of measurement/structural noise associated with the data so that overfitting does not occur. PEST then re-formulates the calibration process as a constrained optimisation process; it minimizes the so-called “regularisation objective function” (thereby maximizing the extent to which preferred parameter values and/or parameter relationships are respecte
