Arithmetic average, geometric average, and ranking: Application to incoherent scatter radar data processing


  • Q. H. Zhou,

  • Q. N. Zhou,

  • J. D. Mathews


We examine the statistical characteristics of three commonly used estimators, arithmetic average, geometric average, and ranking as applied to incoherent scatter radar observations in the presence of interference. While the arithmetic average is effective in reducing the statistical error, it is very sensitive to “outlier” contamination, such as meteor returns. The ranking method is robust in removing outliers but is not effective in reducing the statistical variance. On the other hand, triple ranking and the geometric average are almost as effective as the arithmetic average in reducing the statistical error. If the data contain only outlier contamination, the geometric average is a better choice than either simple arithmetic average or the single ranking method. In dealing with complex interference from radars and various communications systems, one can use the triple ranking method or a combination of the arithmetic average and the single ranking method. In addition, the processes of ranking and geometric average, like those of the arithmetic average, also converge to a Gaussian function when the number of samples is large. We also show that the central limit theorem can be used to obtain interesting approximations.