Band-Limited Flicker Noise Modeling Using a Series of Correlated Noises

Flicker noise, whose power spectral density (PSD) is inversely proportional to the signal frequency and is described by the half-integral of white noise, cannot be readily described by ordinary differential equations and is sometimes approximated. One of the cases in which this noise is observed is in the measurements of inertial sensors, which is known as bias instability. For the implementation and performance analysis of an inertial navigation system, an accurate stochastic model of each error contributor is needed. However, the models used for flicker noise either do not describe the random characteristics of the noise well or are of high order. Therefore, we propose a novel model based on a series of correlated noises to model the flicker noise. The proposed method models the desired shape of the PSD and Allan variance in an arbitrary frequency band with low order. The error of the proposed model, in terms of the root mean square relative error of the Allan variance, is 2.3%.