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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 1, Issue 4


An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

Mohammed El-Diasty / Ahmed El-Rabbany / Spiros Pagiatakis
  • 1 Dept. of Earth & Space Science & Engineering, York University, Canada. E-mail:
  • 2 Dept. of Civil Engineering, Ryerson University, Canada. E-mail:
  • 3 Dept. of Earth & Space Science & Engineering, York University, Canada. E-mail:
  • Other articles by this author:
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Published Online: 2008-02-13 | DOI: https://doi.org/10.1515/jag.2007.022


The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Keywords: MEMS; INS/GPS; stochastic process; autoregressive (AR); Gauss-Markov (GM); wavelet network

About the article

Received: 2007-03-01

Accepted: 2007-07-18

Published Online: 2008-02-13

Published in Print: 2007-12-01

Citation Information: Journal of Applied Geodesy jag, Volume 1, Issue 4, Pages 201–212, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag.2007.022.

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