Efficient Iterative Estimation of the Parameters of a Damped Complex Exponential in Noise
Efficient Iterative Estimation of the Parameters of a Damped Complex Exponential in Noise
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DOI：
10.1109/lsp.2014.2320927
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发表时间：
2014-08-01
影响因子：
3.9
通讯作者：
Ye, Shanglin
中科院分区：
文献类型：
--
作者：
Aboutanios, Elias;Ye, Shanglin
噪声中单个衰减指数的频率和衰减因子的估计是一个非常重要的问题。一种流行的估计方案使用离散傅立叶变换（FFT）的计算高效实现来获得粗略估计，然后通过精细估计阶段来改进粗略估计。然而，这样的估计，表现出的性能，退化和偏离克拉美-罗下限（CRLB）的样本数量的增加。为了克服这个问题，我们提出了一个迭代，指数窗口算法。我们推导了新估计量的理论性能，并研究了它在不同窗口衰减率下的行为。我们表明，估计具有良好的性能，跟踪CRLB与增加的样本数量，如果窗口衰减率是适当的设置。
The estimation of the frequency and decay factor of a single decaying exponential in noise is a problem of prime importance. A popular estimation scheme uses the computationally efficient implementation of the Discrete Fourier transform, the FFT, to obtain a coarse estimate which is then improved by a fine estimation stage. Such estimators, however, show a performance that degrades and departs from the Cramer-Rao Lower Bound (CRLB) as the number of samples increases. To overcome this problem, we propose an iterative, exponentially windowed algorithm. We derive the new estimator's theoretical performance and study its behavior under different decay rates of the window. We show that the estimator has excellent performance that tracks the CRLB with increasing number of samples if the window decay rate is appropriately set.