Fast algorithms are proposed for precise estimation of the Fundamental frequency on a short time interval. The approach is a generalization of the unbiased frequency estimator. Its computational complexity is proportional to that of FFT on the same time interval. A trade-off between approximation error and numerical speed is established. The result is generalized to the linear trend model. The lower bound is obtained for the time interval length with a nonsingular information matrix in the estimation problem. Frequency estimation under big noises is studied in detail.