Accessibility to inertial navigation systems (INS) has been severely limited by cost in the past. The introduction of low-cost microelectromechanical system-based INS to be integrated with GPS in order to provide a reliable positioning solution has provided more wide spread use in mobile devices. The random errors of the MEMS inertial sensors may deteriorate the overall system accuracy in mobile devices. These errors are modeled stochastically and are included in the error model of the estimated techniques used such as Kalman filter or Particle filter. First-order Gauss-Markov model is usually used to describe the stochastic nature of these errors. However, if the autocorrelation sequences of these random components are examined, it can be determined that first-order Gauss-Markov model is not adequate to describe such stochastic behavior. A robust modeling technique based on fast orthogonal search is introduced to remove MEMS-based inertial sensor errors inside mobile devices that are used for several location-based services. The proposed method is applied to MEMS-based gyroscopes and accelerometers. Results show that the proposed method models low-cost MEMS sensors errors with no need for denoising techniques and using smaller model order and less computation, outperforming traditional methods by two orders of magnitude. 1. Introduction Presently, GPS-enabled mobile devices offer various positioning capabilities to pedestrians, drivers, and cyclists. GPS provides absolute positioning information, but when signal reception is attenuated and becomes unreliable due to multipath, interference, and signal blockage, augmentation of GPS with inertial navigation systems (INS) or the like is needed. INS is inherently immune to the signal jamming, spoofing, and blockage vulnerabilities of GPS, but the accuracy of INS is significantly affected by the error characteristics of the inertial sensors it employs [1]. GPS/INS integrated navigation systems are extensively used [2], for example, in mobile devices that require low-cost microelectromechanical System (MEMS) inertial sensors (gyroscopes and accelerometers) due to their low cost, low power consumption, small size, and portability. The inadequate long-term performance of most commercially available MEMS-based INS limits their usefulness in providing reliable navigation solutions. MEMSs are challenging in any consumer navigation system because of their large errors, extreme stochastic variance, and quickly changing error characteristics. According to [3], the inertial sensor errors of a low-cost INS consist of
References
[1]
A. Noureldin, T. Karamat, and J. Georgy, Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer, New York, NY, USA, 2012.
[2]
M. Grewal, L. Weil, and A. Andrews, Global Positioning Systems, Inertial Navigation and Integration, John Wiley & Sons, New York, NY, USA, 2nd edition, 2007.
[3]
S. Nassar, K. Schwarz, N. El-Sheimy, and A. Noureldin, “Modeling inertial sensor errors using autoregressive (AR) models,” Navigation, Journal of the Institute of Navigation, vol. 51, no. 4, pp. 259–268, 2004.
[4]
J. Georgy and A. Noureldin, “Vehicle navigator using a mixture particle filter for inertial sensors/odometer/map data/GPS integration,” IEEE Transactions on Consumer Electronics, vol. 58, no. 2, pp. 544–522, 2012.
[5]
M. J. Korenberg, “A robust orthogonal algorithm for system identification and time-series analysis,” Biological Cybernetics, vol. 60, no. 4, pp. 267–276, 1989.
[6]
M. J. Korenberg, “Fast orthogonal identification of nonlinear difference equation models,” in Proceedings of the 30th Midwest Symposium on Circuits and Systems, vol. 1, August 1987.
[7]
J. Armstrong, A. Noureldin, and D. McGaughey, “Application of fast orthogonal search techniques to accuracy enhancement of inertial sensors for land vehicle navigation,” in Proceedings of the Institute of Navigation, National Technical Meeting (NTM '06), pp. 604–614, Monterey, Calif, USA, January 2006.
[8]
A. Noureldin, A. Osman, and N. El-Sheimy, “A neuro-wavelet method for multi-sensor system integration for vehicular navigation,” Measurement Science and Technology, vol. 15, no. 2, pp. 404–412, 2004.
[9]
S. Nassar, A. Noureldin, and N. El-Sheimy, “Improving positioning accuracy during kinematic DGPS outage periods using SINS/DGPS integration and SINS data de-noising,” Survey Review, vol. 37, no. 292, pp. 426–438, 2004.
[10]
K. M. Adeney and M. J. Korenberg, “Fast orthogonal search for array processing and spectrum estimation,” IEE Proceedings: Vision, Image and Signal Processing, vol. 141, no. 1, pp. 13–18, 1994.
[11]
M. J. Korenberg, “Fast orthogonal algorithms for nonlinear system identification and time-series analysis,” in Advanced Methods of Physiological System Modeling, V. Z. Marmarelis, Ed., vol. 2, pp. 165–177, Plenum Press, New York, NY, USA, 1989.
[12]
D. R. McGaughey, M. J. Korenberg, K. M. Adeney, S. D. Collins, and G. J. M. Aitken, “Using the fast orthogonal search with first term reselection to find subharmonic terms in spectral analysis,” Annals of Biomedical Engineering, vol. 31, no. 6, pp. 741–751, 2003.
[13]
Z. Shen, J. Georgy, M. J. Korenberg, and A. Noureldin, “FOS-based modelling of reduced inertial sensor system errors for 2D vehicular navigation,” Electronics Letters, vol. 46, no. 4, pp. 298–299, 2010.
[14]
S. Haykin, Adaptive Filter Theory, Prentice Hall, Upper Saddle River, NJ, USA, 2002.
[15]
L. Jackson, Digital Filters and Signal Processing, Kluwer Academic, Norwell, Mass, USA, 1996.
[16]
R. Kless and P. Broersen, How to Handle Colored Noise in Large Least-Squares Problems, Delft University of Technology, Delft, The Netherlands, 2002.
[17]
M. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, New York, NY, USA, 1996.
[18]
M. J. L. de Hoon, T. H. J. J. van der Hagen, H. Schoonewelle, and H. van Dam, “Why Yule-Walker should not be used for autoregressive modelling,” Annals of Nuclear Energy, vol. 23, no. 15, pp. 1219–1228, 1996.
[19]
J. Burg, Maximum entropy spectral analysis [Ph.D. thesis], Department of Geophysics, Stanford University, Stanford Calif, USA, 1975.
[20]
S. Orfanidis, Optimum Signal Processing: An Introduction, Macmillan, New York, NY, USA, 1988.
[21]
J. M. Pimbley, “Recursive autoregressive spectral estimation by minimization of the free energy,” IEEE Transactions on Signal Processing, vol. 40, no. 6, pp. 1518–1527, 1992.
[22]
S. Marple, Digital Spectral Analysis with Applications, Prentice-Hall, Englewood Cliffs, NJ, USA, 1987.
[23]
I. A. Rezek and S. J. Roberts, “Parametric model order estimation: a brief review,” in Proceedings of the IEE Colloquium on the Use of Model Based Digital Signal Processing Techniques in the Analysis of Biomedical Signals, London, UK, April 1997.
[24]
E. Ifeachor and B. Jervis, Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, USA, 4th edition, 2001.
[25]
K. H. Chon, “Accurate identification of periodic oscillations buried in white or colored noise using fast orthogonal search,” IEEE Transactions on Biomedical Engineering, vol. 48, no. 6, pp. 622–629, 2001.
