A lithographic system includes a lithographic apparatus comprising a projection system which projects a patterned radiation beam onto a target portion of a substrate and an alignment system which measures the position of a feature of the pattern on the substrate at a number of locations over the substrate. A controller compares the measured positions with points on a grid of values and extrapolates values for intermediate positions on the substrate based on values of corresponding intermediate points on the grid, so as to provide an indication of the intermediate positions on the substrate and their displacements relative to the grid. The grid is based on at least one orthogonal basis function, the measurement on the substrate being performed at positions corresponding to the root values of the at least one orthogonal basis function.