二维谐波频率估计的高精度稳健迭代算法

A high-accuracy robust iterative algorithm for estimating the frequencies of two dimensional harmonics

本文运用基于两阶段的稳健迭代算法考虑了加性噪声中二维多分量谐波频率参数的估计问题。可以证明该算法仅需要三次迭代就能达到收敛,且最终估计量达到和最小二乘估计(LSE)相同的收敛速度以及估计方差达到Cramer-Rao下界。由于基于统计量的迭代估计充分利用了谐波模型的内在特性以及噪声分布特性,所以仅需要三步迭代就达到收敛,因而使得算法计算量很小且稳定,另外还可以证明三步迭代之后的估计量为二维谐波频率的无偏以及一致估计。本文证明了[9]中的单分量模型下的迭代算法可用于多分量情形下的估计,并且本文所采用的频率参数的平行估计方式避免了[9]中逐个估计方式下前一个已估计频率对分量对后一个要估计频率对分量的影响。最后模拟实验证实了估计的无偏性和一致性以及估计量在中样本情形下具备很高的估计精度。

The frequencies estimation of two-dimensional multiple harmonics in additive noise is considered in this paper, by a robust iterative algorithm on the basis of a two-stage estimation. It can be proved that the algorithm needs only three it- erative steps to converge and the final estimator attains the same convergence rate as Least Squares Estimator （ LSE）, while the variance of the estimator attains the Cramer-Rao low bound. Since the statistics based estimation makes full use of the inner character of the harmonic model and the noise distribution, thus only three iterations are needed for the algorithm to work, while the robustness and efficiency in computation is also retained. Moreover, the estimator after three iterations is proved to be unbiased and consistent. We prove that the algorithm in [ 9 ] for the mono harmonic model can be generalized to the condition of multiple harmonics. Moreover, the parallel strategy for the frequency pair estimation can avoid the influ- ence of the former frequency pair estimated on the later frequency pair to be estimated. Finally, the unbiasedness and con- sistency are verified via some simulation results, as well as for the high-accuracy under the condition of middle sample size.