Robust Frequency Estimation Using Elemental Sets
Robust Frequency Estimation Using Elemental Sets
复制标题
使用元素集进行鲁棒频率估计
DOI：
10.1080/10618600.2000.10474874
复制
发表时间：
2000
影响因子：
2.4
通讯作者：
D. Hawkins
中科院分区：
文献类型：
--
作者：
G. Smyth;D. Hawkins
从时间序列数据中提取正弦信号是统计和信号处理文献中一直关注的经典问题。获得最小二乘估计是困难的，因为平方和在频率上有局部最小值O（1/n）。在实践中，频率通常使用临时和低效的方法来估计。数据质量问题很少受到关注。元素集是包含最小个数的数据子集，这样模型中的未知参数就可以被识别。本文证明了利用经典proony方法的一种变体，可以从元素集上代数地求得正弦波和的参数估计。元素集方法用于构造有限算法估计器，该估计器近似地最小化最小二乘、最小裁剪平方和或最小平方中位数准则。在仿真中，元素集估计器能够将频率分解为目标函数的正确的局部极小值。当用作MM估计器的第一阶段时，基于裁剪平方和和最小平方中值准则构建的估计器产生具有高分解特性的最终估计器，并且在没有异常值存在时同时有效。该方法也可以应用于指数和，和阻尼正弦。文中包括单正弦和双正弦的仿真以及两个数据实例。
Abstract The extraction of sinusoidal signals from time-series data is a classic problem of ongoing interest in the statistics and signal processing literatures. Obtaining least squares estimates is difficult because the sum of squares has local minima O(1/n) apart in the frequencies. In practice the frequencies are often estimated using ad hoc and inefficient methods. Problems of data quality have received little attention. An elemental set is a subset of the data containing the minimum number of points such that the unknown parameters in the model can be identified. This article shows that, using a variant of the classical method of Prony, parameter estimates for a sum of sinusoids can be obtained algebraically from an elemental set. Elemental set methods are used to construct finite algorithm estimators that approximately minimize the least squares, least trimmed sum of squares, or least median of squares criteria. The elemental set estimators prove able in simulations to resolve the frequencies to the correct local minima of the objective functions. When used as the first stage of an MM estimator, the constructed estimators based on the trimmed sum of squares and least median of squares criteria produce final estimators which have high breakdown properties and which are simultaneously efficient when no outliers are present. The approach can also be applied to sums of exponentials, and sums of damped sinusoids. The article includes simulations with one and two sinusoids and two data examples.