An FMCW radar sensor and a method for localizing a radar target, in which FMCW radar measurements are performed with transmitting antennas having different fields of view which differ in terms of an aperture angle and/or a range, the measurements each encompassing temporally interleaved sequences of ramps, and measurements with different fields of view being temporally interwoven with one another; ambiguous values for the relative velocity of the radar target being determined from a position of a peak in a two-dimensional spectrum; phase relationships between spectral values of spectra being checked for agreement with phase relationships expected for several of the determined values of the relative velocity; and on the basis thereof an estimated value for the relative velocity of the radar target being selected from the determined periodic values of the relative velocity.