Allan Variance and Fractal Brownian Motion

Noise filtering is the subject of a voluminous literature on radio engineering. The methods of filtering require knowledge of the frequency response, which is usually unknown. D.W. Allan proposed a simple method of determining the interval between the equally accurate observations which does without this information. In this method, the variances of the increments of noise and signal are equal, so that on observations with greater step the variations caused by noise are smaller than those caused by the signal. This method is the standard accepted by the USA metrology. The present paper is devoted to the statistical analysis of the Allan method and acquisition of additional information.