The largest Cramer-Rao lower bound for variance estimation of acoustic signals

Abstract

The Cramer-Rao Lower Bounds (CRLBs) for variance estimation of acoustic signals is discussed. The CRLB expresses the lower limit of the variance of estimation errors of an unbiased estimator. It is empirically known that the accuracy of variance estimation is improved as the signal length is long because the CRLB for variance estimation is inverse proportion to the length of a signal. Therefore, when the variance of estimation errors is desired to be lower than a certain value, the signal length must be longer than the length that is determined by the CRLB. If the distribution of a signal is known, the CRLB can be easily formulated. In practice, however, acoustic signals follow various distributions and they are unknown in advance. In our research, we focus on the distribution that gives the largest CRLB for variance estimation. In order to find such a distribution, we compare the CRLBs for variance estimation using various signal models. Our results conclude that the Gaussian distribution gives the largest CRLB for variance estimation.