The profound impact of negative power law noise on statistical estimation
Victor S. Reinhardt · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · 2010
This paper investigates the profound impact of negative power law (neg-p) noise - that is, noise with a power spectral density L(p)(f) proportional variant | f |(p) for p > tau(c) is not met, where T is the data collection interval for estimation. Thus, it is shown that neg-p noise, with its infinite Tau(c), can generate anomalous estimation results for all values of T, except in certain circumstances. A covariant theory is developed explaining much of this anomalous estimation behavior. However, simulations of the estimation behavior of neg-p noise demonstrate that the subject cannot be fully understood in terms of covariant theory or mean ergodicity. It is finally conjectured that one must investigate the variance ergodicity properties of neg-p noise through the use of 4th order correlation theory to fully explain such simulated behavior.