Statistical Models of Inertial Sensors and Integral Error Bounds

  • Richard J. Vaccaro
  • Ahmed S. ZakiEmail author
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


Inertial sensors such as gyroscopes and accelerometers are important components of inertial measurement units (IMUs). Sensor output signals are corrupted by additive noise plus a random drift component. This drift component, also called bias, is modeled using different types of random processes. This chapter considers the random components that are useful for modeling modern tactical-graded MEMS sensors. These components contribute to errors in the first and second integrals of the sensor output. The main contribution of this chapter is the derivation of a statistical bound on the magnitude of the error in the integral of a sensor signal due to noise and drift. This bound is a simple function of the Allan variance of a sensor.


Drift Component Allan Variance Plot Calibration Signal Weighted Least Squares Estimator Altruistic Variant 
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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.Department of Electrical, Computer, and Biomedical EngineeringUniversity of Rhode IslandKingstonUSA
  2. 2.Naval Undersea Warfare CenterDivision NewportNewportUSA

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