Signal processing of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Besides randomly and independently occurring outliers also correlated data gaps are investigated. Non-parametric estimators for the mean value, the signal variance, the autocovariance and cross-covariance functions and the corresponding power spectral densities are given, which are bias-free, independent of the spectral composition of the data gaps. Bias-free estimation is obtained by averaging over valid samples only from the data set. The procedures abstain from interpolation of missing samples. An appropriate bias correction is used for cases where the estimated mean value is subtracted out from the data. Spectral estimates are obtained from covariance functions using Wiener-Khinchin's theorem.

翻译：针对含缺失样本的均匀采样平稳随机过程信号处理问题展开研究。除随机独立异常值外，还探讨了相关数据间隙的影响。本文提出了均值、信号方差、自协方差与互协方差函数及其对应功率谱密度的非参数估计量，这些估计量具有无偏性且与数据间隙的频谱构成无关。无偏估计通过仅对数据集中有效样本取均值实现，且避免对缺失样本进行插值。针对数据中减去估计均值的情况，采用适当的偏差校正方法。利用维纳-辛钦定理从协方差函数获得频谱估计。