A study on the application of estimation theory to predict harmonic bus voltages and line currents which cannot or are not measured directly is proposed. The methodology is based on measurements, state estimators, and harmonic system modeling. A hybrid of quadratic and non-quadratic criterion-based techniques utilizing singular value decomposition is used with a feasible application to large-scale problems. Contrary to the fundamental case, the Jacobian matrix of the power system equations at harmonic frequencies is shown to be ill-conditioned. A robust numerical technique, using linear transformations to scale the Jacobian matrix, is suggested to render the estimation problem solvable in a practical environment.