Systems, methods and computer program products detect a position of a new alignment mark on a substrate by producing an alignment signal model from sample alignment signals and fitting the new alignment signal to the alignment signal model. The alignment signal model may be produced from the multiple sample alignment signals using singular value decomposition, based on subspace decomposition of the alignment signals. By producing an alignment signal model from multiple sample alignment signals, asymmetries in the sample alignment marks and/or in the coatings that are fabricated on the sample alignment marks, may be taken into account when detecting the position of a new alignment mark.