Regularization of Dynamic Data Reconciliation Problems by Projection 1

Dynamic data reconciliation problems are discussed from the perspective of the mathematical theory of ill{posed inverse problems. Regularization is of crucial importance to obtain satisfactory estimation quality of the reconciled variables. Usually, some penalty is added to the least{squares objective to achieve well{posedness of the problem. However, appropriate discretization schemes of the time{continuous problem act as regularization themselves reducing the need of problem modiication. Based on this property, we suggest to successively reene the discretization of the continuous problem starting from a coarse grid to nd a suitable regularization which renders a good compromise between (measurement) data and regularization error of the estimate. We conjecture further, that non{equidistant discretization grids are more advantageous than uniform grids.