A wavelet-based bootstrap method applied to inertial sensor stochastic error modelling using the Allan variance

Abstract

A wavelet-based bootstrap method is proposed to generate surrogate data from inertial sensor noise time series and to construct bootstrap-based confidence intervals of selected parameters which are used to characterize their noise performance. The Allan variance, its links with wavelets and the whitening action of wavelet decompositions applied to long-memory stochastic processes are considered in developing the theory behind the proposed method. The conditions for the wavelet-based bootstrap method to work are discussed in the face of idiosyncrasies of inertial sensors, especially microelectromechanical systems-based (MEMS) inertial sensors. Computer simulation experiments demonstrate the validity of the method and its power in doing the statistical inference from a moderately small-size dataset; additionally, the wavelet-based bootstrap method is applied to the task of stochastic error characterization, in the case of a MEMS orientation sensor, which integrates a tri-axis gyro and a tri-axis accelerometer.