Aerospace and Electronic Systems - August 2018 - 36

Online Calibration Platform with Applications to Inertial Sensors
noise calibration. The reference ("true") trajectory is given by a
proper fusion between the GPS, which is extremely precise, and
the IMU. In this experiment, the GPS is turned off at a specific moment, whereas the IMU consequently works on its own to provide
the position solution. In a first test, the noise model of the IMU only
includes the WN. In a second test, the noise model consists of a WN
+ GM, but with wrong parameter values. In the last test the sensor
model WN + GM is correctly parametrized (the GMWM provided
these parameters). The increasing positioning error for the first case
is 60 [m] in the planimetric plane and 15 [m] for the vertical axis.
By improving the noise model in the second case, the error-values
decrease by almost a factor of two. When the proper parameters
are used, an additional improvement is possible, as this situation
closely reflects the reality where the stochastic signal is composed
of a sum of multiple models and not only one single WN.

[3]

Nikolic, J., Furgale, P., Melzer, A., and Siegwart, R. Maximum likelihood identification of inertial sensor noise model parameters. IEEE
Sensors Journal, Vol. 16, 1 (2016), 163-176.
Woodman, O. J. An introduction to inertial navigation. University of
Cambridge, Computer Laboratory, Tech Rep. UCAMCL-TR-696,
Vol. 14, 15, 2007.
El-Sheimy, N., Hou, H., and Niu, X. Analysis and modeling of inertial
sensors using Allan variance. IEEE Transactions on Instrumentation
and Measurement, Vol. 57, 1 (Jan. 2008), 140-149.
Guerrier, S., Molinari, R., and Stebler, Y. Theoretical limitations
of Allan variance-based regression for time series model estimation. IEEE Signal Processing Letters, Vol. 23, 5 (May 2016),
597-601.
Vaccaro, R. J., and Zaki, A. S. Statistical modeling of rate gyros. IEEE
Transactions on Instrumentation and Measurement, Vol. 61, 3 (2012),
673-684.
Guerrier, S., Skaloud, J., Stebler, Y., and Victoria-Feser, M. P. Wavelet
variance-based estimation for composite stochastic processes. Journal of the American Statistical Association, Vol. 108, 503 (2013),
1021-1030.
Percival, D. B. On estimation of the wavelet variance. Biometrika,
Vol. 82, 3 (1995), 619-631.
Zhang, N. F. Allan variance of time series models for measurement
data. Metrologia, Vol. 45, (2008), 549-561.
Guerrier, S., Molinari, R., and Skaloud, J. Automatic identification
and calibration of stochastic parameters in inertial sensors. Navigation, Vol. 62, 4 (2015), 265-272.
Guerrier, S., and Molinari, R. Wavelet variance for random fields: An
M-estimation framework. ArXiv e-prints, Jul. 2016, provided by the
SAO/NASA Astrophysics Data System. [Online] Available: http://
adsabs.harvard.edu/abs/2016arXiv160705858G.
Stebler, Y. Modeling and processing approaches for integrated inertial navigation. Ph.D. dissertation, Ecole Polytechnique Fédérale de
Lausanne, 2013.
Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M. P. Generalized method of wavelet moments for inertial navigation filter design.
IEEE Transactions on Aerospace and Electronic Systems, Vol. 50, 3
(2014), 2269-2283.

[4]

[5]

[6]

[7]

[8]

CONCLUSIONS
This article has given a brief overview of the main features of the
software gui4gmwm implemented in R and based on the package
GMWM, which provides practitioners with readily-available tools
to perform sensor calibration for the stochastic component of their
error signals. Given the flexibility of the GMWM method, this
software envisages updates with new developments of this methodology. Indeed, the main updates and additional tools will include
the implementation and visualization of additional and more complex stochastic signals for the calibration, where, for example, the
model parameters vary over time or are influenced by external factors. Therefore, not only does this platform allow engineers to easily perform complex calibration tasks, but also opens avenues to a
more straightforward tackling of problems that can refine the calibration of inertial sensors even further. Moreover, it must be stated
that the GMWM that underlies the entire GUI for IMU calibration
can be used for all kinds of analyses dealing with other types of
time-dependent data.

[9]
[10]
[11]

[12]

[13]

[14]

ACKNOWLEDGMENTS
The authors would like to thank Prof. Maria-Pia Victoria-Feser for
her institutional and academic support in the development of this
software platform.

REFERENCES
[1]

[2]

APPENDIX
The GUI presented in the article can be found online under:
C

Stebler, Y., Guerrier, S., Skaloud, J., and Victoria-Feser, M. P. Constrained expectation-maximization algorithm for stochastic inertial
error modeling: Study of feasibility. Measurement Science and Technology, Vol. 22, 8 (2011), 1-12.
Zaho, Y., Horemuz, M., and Sjöberg, L. E. Stochastic modelling and
analysis of IMU sensor errors. Archives of Photogrammetry, Cartography and Remote Sensing, Vol. 22, (2011), 437-449.

ggmwm.smac-group.com.

Additional information (including bug-reports) on this application can be found under:
C

gui4gmwm.smac-group.com.

Information on the implementation directly in R can be found
under:
C

github.com/SMAC-Group/gmwm.

IEEE A&E SYSTEMS MAGAZINE

AUGUST 2018

http://adsabs.harvard.edu/abs/2016arXiv160705858G http://adsabs.harvard.edu/abs/2016arXiv160705858G http://ggmwm.smac-group.com http://gui4gmwm.smac-group.com http://www.github.com/SMAC-Group/gmwm

Aerospace and Electronic Systems - August 2018

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