The robust iterative algorithm for estimating the frequencies of 1-D harmonics in color noise

The three step iterative algorithm (TSI) is utilized to estimate the frequencies of one-dimensional harmonics in color multiplicative and additive noise by constructing observed signals based statistics, the asymptotic distribution is obtained and the consistency of the final estimator is also proved. The TSI algorithm considers the introduced periodogram estimator as the initial estimator, then constructs the statistics basing on the inner property of the harmonic model and raises the precision of the estimator by iterations. It can be proved that the algorithm is guaranteed to convergence in three iterative steps and attain the same sample based convergence rate with the least squares estimator (LSE). Since only three steps are needed for convergence, the computation load is little. Comparing with the traditional iterative algorithm, the TSI algorithm can improve the precision of the estimators for each iteration so as to avoid the deficiency in stability for the traditional iterative algorithm. The consistency for the estimators and the theoretic asymptotic distribution are verified through the simulation experiments, and the feasibility for the algorithm in strong noise is also verified. Finally, since TSI algorithm is computationally efficient and has high precision, it is suitable to be served as online algorithm.