Generalized method of wavelet moments for inertial navigation filter design

Yannick Stebler, Stéphane Guerrier, Jan Skaloud, Maria Pia Victoria-Feser

Research output: Contribution to journalArticlepeer-review


The integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter calibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.

Original languageEnglish (US)
Article number6965773
Pages (from-to)2269-2283
Number of pages15
JournalIEEE Transactions on Aerospace and Electronic Systems
Issue number3
StatePublished - Jul 1 2014


  • Computational modeling
  • Discrete wavelet transforms
  • Estimation
  • Global positioning system
  • Inertial navigation
  • Stochastic processes

ASJC Scopus subject areas

  • Aerospace Engineering
  • Electrical and Electronic Engineering


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