Automatic Identification and Calibration of Stochastic Parameters in Inertial Sensors

Abstract

We present an algorithm for determining the nature of stochastic processes and their parameters based on the analysis of time series of inertial errors. The algorithm is suitable mainly (but not only) for situations where several stochastic processes are superposed. The proposed approach is based on a recently developed method called the Generalized Method of Wavelet Moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This method delivers a global selection criterion based on the wavelet variance that can be used to determine the suitability of a candidate model (compared to other models) and apply it to lowcost inertial sensors. By allowing candidate model ranking, this approach enables us to construct an algorithm for automatic model identification and determination. The benefits of this methodology are highlighted by providing practical examples of model selection for two types of MEMS IMUs.

A Computationally Efficient Framework for Automatic Inertial Sensor Calibration

“…In this section, we provide a brief description of the GMWM estimator along with an overview of the main tools that have been derived and are implemented within the package (for a more thorough description the methods and their properties refer to [9], [10], [11]). As mentioned in the previous section, the GMWM relies on the WV, which is the variance of the wavelet coefficients (W j,t ), issued from a wavelet decomposition of a signal (see, for example, [12] for an overview).…”

“…The latter term is sometimes referred to as "optimism" and acts as a complexitybased penalty. There are different manners to compute this term such as parametric bootstrap (see [10], [16]) or using its asymptotic approximation given in [17]. Considering these terms, the goal would be to select the model with the smallest WIC value, meaning that we are selecting the model with the smallest estimated prediction error.…”

Simultaneous End User Calibration of Multiple Magnetic Inertial Measurement Units With Associated Uncertainty

“…While [8] employed Autoregressive (AR) models for stochastic errors of inertial sensors. The work by [9,11,12] adopts a wavelet variance base approach called Generalized Method of Wavelet Moments (GMWM). This method is more suitable than AV since several stochastic processes are superposed in inertial sensors.…”

“…And lastly, stochastic errors require modeling of uncertainty. Though stochastic models have been proposed [7][8][9][10][11][12][13][14][15], but these models require explicit modeling of the noise process. On the other hand, a data-driven model of the uncertainty of sensor output can be learned without an explicit model [16].…”

Performance Criteria for the Identification of Inertial Sensor Error Models

“…The wavelet analysis is becoming increasingly popular nowadays [21]. The approach proposed in [21,22,23] delivers a global selection criterion based on the wavelet variance that can be used to design an algorithm for automatic identification of a model structure.…”