A frequency adaptive technique relying on a linear Kalman filter (KF) is presented here for robust estimation of voltage harmonics under variable frequency conditions in a single-phase system. A relatively simple frequency-locked loop (FLL) is combined with the linear KF (LKF-FLL) to achieve frequency adaptive ability and avoid the use of a non-linear KF. In contrast to the non-linear extended KF (EKF), the LKF-FLL technique has several advantages such as robustness, linearity, simple tuning, having fewer states, requiring no derivative actions, while offering low complexity, excellent convergence, and computational efficiency. When compared to the non-linear extended real KF, it can generate a faster dynamic response and more accurate steady-state estimation of the harmonics under frequency variations. It can also provide an improved estimation for off-nominal frequency conditions when compared to the discrete Fourier transform (DFT) method. The effectiveness of the technique is verified by various simulated and real-time experimental case studies.