The estimation and mitigation of swept-tone interferers includes receiving a composite signal comprising a signal of interest and a swept-tone interferer over an observation bandwidth. The estimation of the interfering signal may be based on modeling the interferer over the observation bandwidth as a magnitude periodic signal comprising non-overlapping, contiguous epochs, where each epoch may comprise a common pulse shape and a distinct phase rotation. The period of the magnitude-periodic signal may be initially determined, and the common pulse shape and each of the distinct phase rotations may then be estimated. These estimates may be used to reconstruct an estimate of the swept-tone interferer, which may be subtracted from the composite signal to generate an interference-mitigated signal of interest.