A lithographic apparatus includes a sensor, such as an alignment sensor including a self-referencing interferometer, configured to determine the position of an alignment target including a periodic structure. An illumination optical system focuses radiation of different colors and polarizations into a spot which scans the structure. Multiple position-dependent signals are detected and processed to obtain multiple candidate position measurements. Asymmetry of the structure is calculated by comparing the multiple position-dependent signals. The asymmetry measurement is used to improve accuracy of the position read by the sensor. Additional information on asymmetry may be obtained by an asymmetry sensor receiving a share of positive and negative orders of radiation diffracted by the periodic structure to produce a measurement of asymmetry in the periodic structure.