The problem of frequency estimation for noisy sinusoidal signals from multiple segments or channels, which are referred to as gapped data, is addressed. Based on linear prediction and weighted least squares techniques, an iterative relaxation-based frequency estimator is devised and analyzed. The proposed algorithm is also extended to harmonically related frequencies. Computer simulations are conducted to compare the estimation performance of the developed approach with an existing multichannel frequency estimator and Crame¿r-Rao lower bound.