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中文摘要：
本文通过构造基于观测信号的统计量,采用三步迭代（TSI）算法来估计乘性和加性有色噪声中一维谐波信号频率参数,得到了最终估计量的渐近分布,证明了估计的一致性。TSI算法通过引入周期图估计作为初估计,从谐波模型内在特性出发构造统计量,采用迭代方式逐步提高初估计精度,仅需三次迭代就能达到加性噪声情形下最小二乘估计（LSE）的关于样本的收敛速度。由于只需要三次迭代就可以达到收敛,所以算法的计算量比较少。另外相比较传统的迭代算法而言,TSI算法能保证每次迭代后都能够提高估计的精度,从而克服了传统的迭代算法收敛不够稳定不足。仿真实验证实了估计的一致性以及估计的渐近分布,而且在较大噪声情形下该迭代算法依然可行。最后,由于TSI算法具备小的计算量以及高的估计精度,因而十分适合作为一维谐波参数估计的在线算法。
英文摘要：
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 litde.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.
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